Bất đẳng thức hình học ràng buộc mômen góc và điện tích trong Thuyết Tương đối Tổng quát

Aceña AE, Dain S (2013) Stable isoperimetric surfaces in super-extreme Reissner–Nordström. Class Quantum Grav 30:045013. https://doi.org/10.1088/0264-9381/30/4/045013. arXiv:1210.3509 Aceña A, Dain S, Gabach Clément ME (2011) Horizon area–angular momentum inequality for a class of axially symmetric black holes. Class Quantum Grav 28:105014 arXiv:1012.2413 Alaee A, Kunduri HK (2014) Mass functional for initial data in 4 + 1-dimensional spacetime. Phys Rev D 90:124078. https://doi.org/10.1103/PhysRevD.90.124078. arXiv:1411.0609 Alaee A, Kunduri HK (2016) Remarks on mass and angular momenta for \(U(1)^2\)-invariant initial data. J Math Phys 57:032502. https://doi.org/10.1063/1.4944426. arXiv:1508.02337 Alaee A, Khuri M, Kunduri H (2016) Proof of the mass–angular momentum inequality for bi-axisymmetric black holes with spherical topology. Adv Theor Math Phys 20:1397–1441. https://doi.org/10.4310/ATMP.2016.v20.n6.a4. arXiv:1510.06974 Alaee A, Khuri M, Kunduri H (2017a) Mass–angular-momentum inequality for black ring spacetimes. Phys Rev Lett 119:071101. https://doi.org/10.1103/PhysRevLett.119.071101. arXiv:1705.08799 Alaee A, Khuri M, Kunduri H (2017b) Relating mass to angular momentum and charge in five-dimensional minimal supergravity. Ann Henri Poincaré 18:1703–1753. https://doi.org/10.1007/s00023-016-0542-1. arXiv:1608.06589 Andersson L, Metzger J (2009) The area of horizons and the trapped region. Commun Math Phys 290:941–972. https://doi.org/10.1007/s00220-008-0723-y. arXiv:0708.4252 Andersson L, Mars M, Simon W (2005) Local existence of dynamical and trapping horizons. Phys Rev Lett 95:111102. https://doi.org/10.1103/PhysRevLett.95.111102. arXiv:gr-qc/0506013 Andersson L, Mars M, Simon W (2008a) Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes. Adv Theor Math Phys 12:853–888. https://doi.org/10.4310/ATMP.2008.v12.n4.a5. arXiv:0704.2889 Andersson L, Mars M, Simon W (2008b) Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes. Adv Theor Math Phys 12:853–888. https://doi.org/10.4310/ATMP.2008.v12.n4.a5. http://projecteuclid.org/getRecord?id=euclid.atmp/1216046746 Andersson L, Eichmair M, Metzger J (2011) Jang’s equation and its applications to marginally trapped surfaces. In: Agranovsky M et al (eds) Complex analysis and dynamical systems IV, part 2. General relativity, geometry, and PDE. Contemporary mathematics, vol 554. American Mathematical Society, Providence, pp 13–46 arXiv:1006.4601 Anglada P (2017) Penrose-like inequality with angular momentum for minimal surfaces. ArXiv e-prints arXiv:1708.04646 Anglada P, Dain S, Ortiz OE (2016) Inequality between size and charge in spherical symmetry. Phys Rev D 93:044055. https://doi.org/10.1103/PhysRevD.93.044055. arXiv:1511.04489 Anglada P, Gabach Clément ME, Ortiz OE (2017) Size, angular momentum and mass for objects. Class Quantum Grav 34:125011. https://doi.org/10.1088/1361-6382/aa6f3f. arXiv:1612.08658 Ansorg M, Hennig J (2008) The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter. Class Quantum Grav 25:222001. https://doi.org/10.1088/0264-9381/25/22/222001. arXiv:0810.3998 Ansorg M, Hennig J (2009) The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein–Maxwell theory. Phys Rev Lett 102:221102. https://doi.org/10.1103/PhysRevLett.102.221102. arXiv:0903.5405 Ansorg M, Pfister H (2008) A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter. Class Quantum Grav 25:035009. https://doi.org/10.1088/0264-9381/25/3/035009. arXiv:0708.4196 Ansorg M, Hennig J, Cederbaum C (2011) Universal properties of distorted Kerr–Newman black holes. Gen Relativ Gravit 43:1205–1210. https://doi.org/10.1007/s10714-010-1136-8. arXiv:1005.3128 Arnowitt R, Deser S, Misner CW (1962) The dynamics of general relativity. In: Witten L (ed) Gravitation: an introduction to current research. Wiley, New York, pp 227–265 arXiv:gr-qc/0405109 Ashtekar A, Krishnan B (2002) Dynamical horizons: energy, angular momentum, fluxes and balance laws. Phys Rev Lett 89:261101. https://doi.org/10.1103/PhysRevLett.89.261101. arXiv:gr-qc/0207080 Ashtekar A, Krishnan B (2003) Dynamical horizons and their properties. Phys Rev D 68:104030. https://doi.org/10.1103/PhysRevD.68.104030. arXiv:gr-qc/0308033 Ashtekar A, Krishnan B (2004) Isolated and dynamical horizons and their applications. Living Rev Relativ 7:10. https://doi.org/10.12942/lrr-2004-10. arXiv:gr-qc/0407042 Ashtekar A, Beetle C, Fairhurst S (2000a) Mechanics of isolated horizons. Class Quantum Grav 17:253 arXiv:gr-qc/9907068 Ashtekar A, Fairhurst S, Krishnan B (2000b) Isolated horizons: Hamiltonian evolution and the first law. Phys Rev D 62:104025 arXiv:gr-qc/0005083 Bardeen JM, Carter B, Hawking SW (1973) The four laws of black hole mechanics. Commun Math Phys 31:161–170. https://doi.org/10.1007/BF01645742 Bartnik R (1986) The mass of an asymptotically flat manifold. Commun Pure App Math 39:661–693 Bartnik RA, Chruściel PT (2005) Boundary value problems for Dirac-type equations. J Reine Angew Math 579:13–73. https://doi.org/10.1515/crll.2005.2005.579.13. arXiv:math.DG/0307278 Beetle C, Wilder S (2015) A note on axial symmetries. Class Quantum Grav 32:047001. https://doi.org/10.1088/0264-9381/32/4/047001. arXiv:1401.0075 Beig R, Chruściel PT (1996) Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem. J Math Phys 37:1939–1961. https://doi.org/10.1063/1.531497. arXiv:gr-qc/9510015 Beig R, O’Murchadha N (1996) Vacuum spacetimes with future trapped surfaces. Class Quantum Grav 13:739–752. https://doi.org/10.1088/0264-9381/13/4/014. arXiv:gr-qc/9511070 Beig R, Schoen RM (2009) On static \(n\)-body configurations in relativity. Class Quantum Grav 26:075014. https://doi.org/10.1088/0264-9381/26/7/075014. arXiv:0811.1727 Bode T, Laguna P, Matzner R (2011) Super-extremal spinning black holes via accretion. Phys Rev D 84:064044. https://doi.org/10.1103/PhysRevD.84.064044. arXiv:1106.1864 Bonnor WB (1980) Equilibrium of charged dust in general relativity. Gen Relativ Gravit 12:453–465. https://doi.org/10.1007/BF00756176 Bonnor WB (1998) A model of a spheroidal body. Class Quantum Grav 15:351. https://doi.org/10.1088/0264-9381/15/2/009 Booth I (2005) Black hole boundaries. Can J Phys 83:1073–1099. https://doi.org/10.1139/p05-063. arXiv:gr-qc/0508107 Booth I, Fairhurst S (2008) Extremality conditions for isolated and dynamical horizons. Phys Rev D 77:084005. https://doi.org/10.1103/PhysRevD.77.084005. arXiv:0708.2209 Bray HL, Jauregui JL (2015) Time flat surfaces and the monotonicity of the spacetime Hawking mass. Commun Math Phys 335:285–307. https://doi.org/10.1007/s00220-014-2162-2. arXiv:1310.8638 Bray HL, Jauregui JL, Mars M (2016) Time flat surfaces and the monotonicity of the spacetime Hawking mass II. Ann Henri Poincaré 17:1457–1475. https://doi.org/10.1007/s00023-015-0420-2. arXiv:1402.3287 Bryden ET, Khuri MA (2017) The area–angular momentum–charge inequality for black holes with positive cosmological constant. Class Quantum Grav 34:125017. https://doi.org/10.1088/1361-6382/aa70fd. arXiv:1611.10287 Cabrera-Munguia I (2015) Binary system of unequal counterrotating Kerr–Newman sources. Phys Rev D 91:044005. https://doi.org/10.1103/PhysRevD.91.044005. arXiv:1505.07080 Cabrera-Munguia I, Manko V, Ruiz E (2010) Remarks on the mass–angular momentum relations for two extreme Kerr sources in equilibrium. Phys Rev D 82:124042. https://doi.org/10.1103/PhysRevD.82.124042. arXiv:1010.0697 Cabrera-Munguia I, Lämmerzahl C, Macías A (2013) Exact solution for a binary system of unequal counter-rotating black holes. Class Quantum Grav 30:175020. https://doi.org/10.1088/0264-9381/30/17/175020. arXiv:1302.4843 Callen HB (1985) Thermodynamics and an introduction to thermostatistics, 2nd edn. Wiley, New York Carroll SM, Johnson MC, Randall L (2009) Extremal limits and black hole entropy. JHEP 11:109. https://doi.org/10.1088/1126-6708/2009/11/109. arXiv:0901.0931 Carter B (1973) Black hole equilibrium states. In: Black holes/Les astres occlus (École d’Été Phys. Théor., Les Houches, 1972). Gordon and Breach, New York, pp 57–214 Cha YS, Khuri MA (2014) Deformations of axially symmetric initial data and the mass–angular momentum inequality. Ann Henri Poincaré 1–56. https://doi.org/10.1007/s00023-014-0332-6. arXiv:1401.3384 Cha YS, Khuri MA (2015) Deformations of charged axially symmetric initial data and the mass–angular momentum–charge inequality. Ann Henri Poincaré 16:2881–2918. https://doi.org/10.1007/s00023-014-0378-5. arXiv:1407.3621 Cha YS, Khuri MA (2017) Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities. ArXiv e-prints arXiv:1707.09398 Cha YS, Khuri M, Sakovich A (2016) Reduction arguments for geometric inequalities associated with asymptotically hyperboloidal slices. Class Quantum Grav 33:035009. https://doi.org/10.1088/0264-9381/33/3/035009. arXiv:1509.06255 Chen PN, Wang MT, Yau ST (2016) Quasilocal angular momentum and center of mass in general relativity. Adv Theor Math Phys 20:671–682. https://doi.org/10.4310/ATMP.2016.v20.n4.a1. arXiv:1312.0990 Christodoulou D (1970) Reversible and irreversible transforations in black-hole physics. Phys Rev Lett 25:1596–1597. https://doi.org/10.1103/PhysRevLett.25.1596 Christodoulou D (1999) The instability of naked singularities in the gravitational collapse of a scalar field. Ann Math 149:183–217 Christodoulou D (2008) The formation of black holes in general relativity. In: On recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories. Proceedings, 12th Marcel Grossmann meeting on general relativity, Paris, France, July 12–18, 2009, vol 1–3, pp 24–34. https://doi.org/10.1142/9789814374552_0002. arXiv:0805.3880 Chruściel P (1986) Boundary conditions at spatial infinity from a Hamiltonian point of view. In: Topological properties and global structure of space-time (Erice, 1985). NATO advanced science institutes series B physics, vol 138. Plenum, New York, pp 49–59. http://www.phys.univ-tours.fr/~piotr/scans Chruściel PT (2008) Mass and angular–momentum inequalities for axi-symmetric initial data sets I. Positivity of mass. Ann Phys 323:2566–2590. https://doi.org/10.1016/j.aop.2007.12.010. arXiv:0710.3680 Chruściel PT, Lopes Costa J (2009) Mass, angular–momentum, and charge inequalities for axisymmetric initial data. Class Quantum Grav 26:235013. https://doi.org/10.1088/0264-9381/26/23/235013. arXiv:0909.5625 Chruściel PT, Mazzeo R (2015) Initial data sets with ends of cylindrical type: I. The Lichnerowicz equation. Ann Henri Poincaré 16:1231–1266. https://doi.org/10.1007/s00023-014-0339-z. arXiv:1201.4937 Chruściel PT, Nguyen L (2011) A lower bound for the mass of axisymmetric connected black hole data sets. Class Quantum Grav 28:125001. https://doi.org/10.1088/0264-9381/28/12/125001. arXiv:1102.1175 Chruściel PT, Delay E, Galloway GJ, Howard R (2001) The area theorem. Ann Henri Poincaré 2:109–178. https://doi.org/10.1007/PL00001029. arXiv:gr-qc/0001003 Chruściel PT, Maerten D, Tod P (2006a) Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times. JHEP 11:084. https://doi.org/10.1088/1126-6708/2006/11/084. arXiv:gr-qc/0606064 Chruściel PT, Reall HS, Tod P (2006b) On Israel–Wilson–Perjes black holes. Class Quantum Grav 23:2519–2540. https://doi.org/10.1088/0264-9381/23/7/018. arXiv:gr-qc/0512116 Chruściel PT, Li Y, Weinstein G (2008) Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum. Ann Phys 323:2591–2613. https://doi.org/10.1016/j.aop.2007.12.011. arXiv:0712.4064 Chruściel PT, Eckstein M, Nguyen L, Szybka SJ (2011) Existence of singularities in two-Kerr black holes. Class Quantum Grav 28:245017. https://doi.org/10.1088/0264-9381/28/24/245017. arXiv:1111.1448 Chruściel PT, Costa JL, Heusler M (2012) Stationary black holes: uniqueness and beyond. Living Rev Relativ 15:7. https://doi.org/10.12942/lrr-2012-7. arXiv:1205.6112 Chruściel PT, Mazzeo R, Pocchiola S (2013) Initial data sets with ends of cylindrical type: II. The vector constraint equation. Adv Theor Math Phys 17:829–865. https://doi.org/10.4310/ATMP.2013.v17.n4.a4. arXiv:1203.5138 Chruściel PT, Szybka SJ, Tod P (2017) Towards a classification of near-horizons geometries. ArXiv e-prints arXiv:1707.01118 Compere G (2017) The Kerr/CFT correspondence and its extensions. Living Rev Relativ 20:1. https://doi.org/10.1007/s41114-017-0003-2. arXiv:1203.3561 Corvino J, Gerek A, Greenberg M, Krummel B (2007) On isoperimetric surfaces in general relativity. Pacific J Math 231:63–84. https://doi.org/10.2140/pjm.2007.231.63 Costa JL (2010) Proof of a Dain inequality with charge. J Phys A 43:285202 arXiv:0912.0838 Cvetic M, Gibbons G, Pope C (2011a) Universal area product formulae for rotating and charged black holes in four and higher dimensions. Phys Rev Lett 106:121301. https://doi.org/10.1103/PhysRevLett.106.121301. arXiv:1011.0008 Cvetic M, Gibbons GW, Pope CN (2011b) More about Birkhoff’s invariant and Thorne’s hoop conjecture for horizons. Class Quantum Grav 28:195001. https://doi.org/10.1088/0264-9381/28/19/195001. arXiv:1104.4504 Dafermos M (2005) Spherically symmetric space-times with a trapped surface. Class Quantum Grav 22:2221–2232. https://doi.org/10.1088/0264-9381/22/11/019. arXiv:gr-qc/0403032 Dain S (2004) Trapped surfaces as boundaries for the constraint equations. Class Quantum Grav 21:555–573 arXiv:gr-qc/0308009 Dain S (2006a) Angular momemtum–mass inequality for axisymmetric black holes. Phys Rev Lett 96:101101 arXiv:gr-qc/0511101 Dain S (2006b) Proof of the (local) angular momemtum–mass inequality for axisymmetric black holes. Class Quantum Grav 23:6845–6855 arXiv:gr-qc/0511087 Dain S (2006c) A variational principle for stationary, axisymmetric solutions of Einstein’s equations. Class Quantum Grav 23:6857–6871 arXiv:gr-qc/0508061 Dain S (2008) Proof of the angular momentum–mass inequality for axisymmetric black holes. J Differ Geom 79:33–67 arXiv:gr-qc/0606105 Dain S (2010) Extreme throat initial data set and horizon area–angular momentum inequality for axisymmetric black holes. Phys Rev D 82:104010. https://doi.org/10.1103/PhysRevD.82.104010. arXiv:1008.0019 Dain S (2011) Geometric inequalities for axially symmetric black holes. ArXiv e-prints arXiv:1111.3615 Dain S (2012) Geometric inequalities for axially symmetric black holes. Class Quantum Grav 29:073001. https://doi.org/10.1088/0264-9381/29/7/073001. arXiv:1111.3615 Dain S (2014a) Geometric inequalities for black holes. Gen Relativ Gravit 46:1715. https://doi.org/10.1007/s10714-014-1715-1. arXiv:1401.8166 Dain S (2014b) Inequality between size and angular momentum for bodies. Phys Rev Lett 112:041101. https://doi.org/10.1103/PhysRevLett.112.041101. arXiv:1305.6645 Dain S, Ortiz OE (2009) Numerical evidences for the angular momentum–mass inequality for multiple axially symmetric black holes. Phys Rev D 80:024045. https://doi.org/10.1103/PhysRevD.80.024045. arXiv:0905.0708 Dain S, Reiris M (2011) Area–angular-momentum inequality for axisymmetric black holes. Phys Rev Lett 107:051101. https://doi.org/10.1103/PhysRevLett.107.051101. arXiv:1102.5215 Dain S, Jaramillo JL, Reiris M (2012) Area–charge inequality for black holes. Class Quantum Grav 29:035013 arXiv:1109.5602 Eichmair M (2007) The plateau problem for apparent horizons. J Differ Geom. https://doi.org/10.4310/jdg/1264601035. arXiv:0711.4139 Eichmair M, Metzger J (2013a) Large isoperimetric surfaces in initial data sets. J Differ Geom 94:159–186. https://doi.org/10.4310/jdg/1361889064. arXiv:1102.2999 Eichmair M, Metzger J (2013b) Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions. Invent Math 194:591. https://doi.org/10.1007/s00222-013-0452-5. arXiv:1204.6065 Eichmair M, Galloway GJ, Pollack D (2013) Topological censorship from the initial data point of view. J Differ Geom 95:389–405. https://doi.org/10.4310/jdg/1381931733. arXiv:1204.0278 Epp RJ, McGrath PL, Mann RB (2013) Momentum in general relativity: local versus quasilocal conservation laws. Class Quantum Grav 30:195019. https://doi.org/10.1088/0264-9381/30/19/195019. arXiv:1306.5500 Ernst FJ (1968) New formulation of the axially symmetric gravitational field problem. Phys Rev 167:1175–1179. https://doi.org/10.1103/PhysRev.168.1415 Fajman D, Simon W (2014) Area inequalities for stable marginally outer trapped surfaces in Einstein–Maxwell-dilaton theory. Adv Theor Math Phys 18:687–707. https://doi.org/10.4310/ATMP.2014.v18.n3.a4. arXiv:1308.3659 Gabach Clément ME (2011) Comment on “Horizon area–angular momentum inequality for a class of axially symmetric black holes”. ArXiv e-prints arXiv:1102.3834 Gabach Clément ME (2012) Bounds on the force between black holes. Class Quantum Grav 29:165008. https://doi.org/10.1088/0264-9381/29/16/165008. arXiv:1201.4099 Gabach Clément ME, Jaramillo JL (2012) Black hole area–angular momentum–charge inequality in dynamical non-vacuum spacetimes. Phys Rev D 86:064021. https://doi.org/10.1103/PhysRevD.86.064021. arXiv:1111.6248 Gabach Clément ME, Reiris M (2013) On the shape of rotating black-holes. Phys Rev D 88:044031. https://doi.org/10.1103/PhysRevD.88.044031. arXiv:1306.1019 Gabach Clément ME, Jaramillo JL, Reiris M (2013) Proof of the area–angular momentum–charge inequality for axisymmetric black holes. Class Quantum Grav 30:065017. https://doi.org/10.1088/0264-9381/30/6/065017. arXiv:1207.6761 Gabach Clément ME, Reiris M, Simon W (2015) The area–angular momentum inequality for black holes in cosmological spacetimes. Class Quantum Grav 32:145006. https://doi.org/10.1088/0264-9381/32/14/145006. arXiv:1501.07243 Galloway GJ, O’Murchadha N (2008) Some remarks on the size of bodies and black holes. Class Quantum Grav 25:105009. https://doi.org/10.1088/0264-9381/25/10/105009. arXiv:0802.3247 Gannon D (1975) Singularities in nonsimply connected space-times. J Math Phys 16:2364–2367. https://doi.org/10.1063/1.522498 Gannon D (1976) On the topology of spacelike hypersurfaces, singularities, and black holes. Gen Relativ Gravit 7:219–232. https://doi.org/10.1007/BF00763437 Gibbons GW (1984) The isoperimetric and Bogomolny inequalities for black holes. In: Willmore TJ, Hitchin N (eds) Global Riemannian geometry. Wiley, New York, pp 194–202 Gibbons GW (1997) Collapsing shells and the isoperimetric inequality for black holes. Class Quantum Grav 14:2905–2915. https://doi.org/10.1088/0264-9381/14/10/016 Gibbons GW (1999) Some comments on gravitational entropy and the inverse mean curvature flow. Class Quantum Grav 16:1677–1687. https://doi.org/10.1088/0264-9381/16/6/302. arXiv:hep-th/9809167 Gibbons GW (2009) Birkhoff’s invariant and Thorne’s hoop conjecture. ArXiv e-prints arXiv:0903.1580 Gibbons GW, Holzegel G (2006) The positive mass and isoperimetric inequalities for axisymmetric black holes in four and five dimensions. Class Quantum Grav 23:6459–6478. https://doi.org/10.1088/0264-9381/23/22/022. arXiv:gr-qc/0606116 Gibbons GW, Hull CM (1982) A Bogomolny bound for general relativity and solitons in \(N=2\) supergravity. Phys Lett B 109:190–194. https://doi.org/10.1016/0370-2693(82)90751-1 Gibbons GW, Hawking SW, Horowitz GT, Perry MJ (1983) Positive mass theorems for black holes. Commun Math Phys 88:295–308. https://doi.org/10.1007/BF01213209 Gibbons GW, Kallosh R, Kol B (1996) Moduli, scalar charges, and the first law of black hole thermodynamics. Phys Rev Lett 77:4992–4995. https://doi.org/10.1103/PhysRevLett.77.4992. arXiv:hep-th/9607108 Hájiček P (1974) Three remarks on axisymmetric stationary horizons. Commun Math Phys 36:305–320. https://doi.org/10.1007/BF01646202 Hartle JB, Hawking SW (1972) Solutions of the Einstein–Maxwell equations with many black holes. Commun Math Phys 26:87–101. https://doi.org/10.1007/BF01645696 Hawking SW (1971) Gravitational radiation from collidings black holes. Phys Rev Lett 26:1344–1346. https://doi.org/10.1103/PhysRevLett.26.1344 Hayward SA (2011) Involute, minimal, outer and increasingly trapped surfaces. Int J Mod Phys D 20:401–411. https://doi.org/10.1142/S0218271811018718. arXiv:0906.2528 Hayward SA, Shiromizu T, Nakao K (1994) A cosmological constant limits the size of black holes. Phys Rev D 49:5080–5085. https://doi.org/10.1103/PhysRevD.49.5080. arXiv:gr-qc/9309004 Hennig J (2014) Geometric relations for rotating and charged AdS black holes. Class Quantum Grav 31:135005. https://doi.org/10.1088/0264-9381/31/13/135005. arXiv:1402.5198 Hennig J, Ansorg M (2009) The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein–Maxwell theory: study in terms of soliton methods. Ann Henri Poincaré 10:1075–1095. https://doi.org/10.1007/s00023-009-0012-0. arXiv:0904.2071 Hennig J, Neugebauer G (2011) Non-existence of stationary two-black-hole configurations: the degenerate case. Gen Relativ Gravit 43:3139–3162. https://doi.org/10.1007/s10714-011-1228-0. arXiv:1103.5248 Hennig J, Ansorg M, Cederbaum C (2008) A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter. Class Quantum Grav 25:162002. https://doi.org/10.1088/0264-9381/25/16/162002 Hennig J, Cederbaum C, Ansorg M (2010) A universal inequality for axisymmetric and stationary black holes with surrounding matter in the Einstein–Maxwell theory. Commun Math Phys 293:449–467. https://doi.org/10.1007/s00220-009-0889-y. arXiv:0812.2811 Herzlich M (1998) The positive mass theorem for black holes revisited. J Geom Phys 26:97–111. https://doi.org/10.1016/S0393-0440(97)00040-5 Hildebrandt S, Kaul H, Widman KO (1977) An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math 138:1–16. https://doi.org/10.1007/BF02392311 Hod S (2015) Bekenstein’s generalized second law of thermodynamics: the role of the hoop conjecture. Phys Lett B 751:241–245. https://doi.org/10.1016/j.physletb.2015.10.052. arXiv:1511.03665 Hollands S (2012) Horizon area–angular momentum inequality in higher dimensional spacetimes. Class Quantum Grav 29:065006. https://doi.org/10.1088/0264-9381/29/6/065006. arXiv:1110.5814 Horowitz GT (1984) The positive energy theorem and its extensions. In: Flaherty FJ (ed) Asymptotic behavior of mass and spacetime geometry. Lecture notes in physics, vol 202. Springer, Berlin, pp 1–21. https://doi.org/10.1007/BFb0048063 Huang LH, Schoen R, Wang MT (2011) Specifying angular momentum and center of mass for vacuum initial data sets. Commun Math Phys 306:785–803. https://doi.org/10.1007/s00220-011-1295-9. arXiv:1008.4996 Huisken G (1998) Evolution of hypersurfaces by their curvature in Riemannian manifolds. In: Rehmann U (ed) Proceedings of the international congress of mathematicians (ICM), vol II, Bielefeld. Documenta mathematica, extra volume, pp 349–360. http://eudml.org/doc/227789 Huisken G, Ilmanen T (2001) The inverse mean curvature flow and the Riemannian Penrose inequality. J Differ Geom 59:352–437. https://doi.org/10.4310/jdg/1090349447 Immerman JD, Baumgarte TW (2009) Trumpet-puncture initial data for black holes. Phys Rev D 80:061501. https://doi.org/10.1103/PhysRevD.80.061501. arXiv:0908.0337 Jackson JD (1999) Classical electrodynamics, 3rd edn. Wiley, Hoboken Jaramillo JL (2013) Area inequalities for stable marginally trapped surfaces. In: Sánchez M, Ortega M, Romero A (eds) Recent trends in Lorentzian geometry. Springer proceedings in mathematics and statistics, vol 26. Springer, New York, pp 139–161. https://doi.org/10.1007/978-1-4614-4897-6_5. arXiv:1201.2054 Jaramillo JL, Gourgoulhon E, Cordero-Carrion I, Ibanez JM (2008) Trapping horizons as inner boundary conditions for black hole spacetimes. Phys Rev D 77:047501. https://doi.org/10.1103/PhysRevD.77.047501. arXiv:0709.2842 Jaramillo JL, Reiris M, Dain S (2011) Black hole area–angular momentum inequality in non-vacuum spacetimes. Phys Rev D 84:121503. https://doi.org/10.1103/PhysRevD.84.121503. arXiv:1106.3743 Khuri M, Weinstein G (2016) The positive mass theorem for multiple rotating charged black holes. Calc Var 55:33. https://doi.org/10.1007/s00526-016-0969-8. arXiv:1502.06290 Khuri M, Weinstein G, Yamada S (2017) Proof of the Riemannian Penrose inequality with charge for multiple black holes. J Differ Geom 106:451–498. https://doi.org/10.4310/jdg/1500084023. arXiv:1409.3271 Khuri MA (2009) The hoop conjecture in spherically symmetric spacetimes. Phys Rev D 80:124025. https://doi.org/10.1103/PhysRevD.80.124025. arXiv:0912.3533 Khuri MA (2015a) Existence of black holes due to concentration of angular momentum. JHEP 2015(06):188. https://doi.org/10.1007/JHEP06(2015)188. arXiv:1503.06166 Khuri MA (2015b) Inequalities between size and charge for bodies and the existence of black holes due to concentration of charge. J Math Phys 56:112503. https://doi.org/10.1063/1.4936149. arXiv:1505.04516 Khuri MA, Weinstein G (2013) Rigidity in the positive mass theorem with charge. J Math Phys 54:092501. https://doi.org/10.1063/1.4820469. arXiv:1307.5499 Komar A (1959) Covariant conservation laws in general relativity. Phys Rev 113:934–936. https://doi.org/10.1103/PhysRev.113.934 Kunduri HK, Lucietti J (2009) A classification of near-horizon geometries of extremal vacuum black holes. J Math Phys 50:082502. https://doi.org/10.1063/1.3190480. arXiv:0806.2051 Kunduri HK, Lucietti J (2013) Classification of near-horizon geometries of extremal black holes. Living Rev Relativ 16:8. https://doi.org/10.12942/lrr-2013-8. arXiv:1306.2517 Lee C (1976) A restriction on the topology of Cauchy surfaces in general relativity. Commun Math Phys 51:157. https://doi.org/10.1007/BF01609346 Lewandowski J, Pawlowski T (2003) Extremal isolated horizons: a local uniqueness theorem. Class Quantum Grav 20:587–606. https://doi.org/10.1088/0264-9381/20/4/303. arXiv:gr-qc/0208032 Maeda K, Koike T, Narita M, Ishibashi A (1998) Upper bound for entropy in asymptotically de Sitter space-time. Phys Rev D 57:3503–3508. https://doi.org/10.1103/PhysRevD.57.3503. arXiv:gr-qc/9712029 Maerten D (2006) Positive energy-momentum theorem for AdS-asymptotically hyperbolic manifolds. Ann Henri Poincaré 7:975–1011. https://doi.org/10.1007/s00023-006-0273-9 Majumdar SD (1947) A class of exact solutions of Einstein’s field equations. Phys Rev 72:390. https://doi.org/10.1103/PhysRev.72.390 Malec E (1992) Isoperimetric inequalities in the physics of black holes. Acta Phys Pol B 22:829 Malec E, Xie N (2015) Brown-York mass and the hoop conjecture in nonspherical massive systems. Phys Rev D 91:081501. https://doi.org/10.1103/PhysRevD.91.081501. arXiv:1503.01354 Malec E, Mars M, Simon W (2002) On the Penrose inequality for general horizons. Phys Rev Lett 88:121102. https://doi.org/10.1103/PhysRevLett.88.121102. arXiv:gr-qc/0201024 Manko VS, Ruiz E (2001) Exact solution of the double-Kerr equilibrium problem. Class Quantum Grav 18:L11–L15. https://doi.org/10.1088/0264-9381/18/2/102 Manko VS, Ruiz E, Sadovnikova MB (2011) Stationary configurations of two extreme black holes obtainable from the Kinnersley–Chitre solution. Phys Rev D 84:064005. https://doi.org/10.1103/PhysRevD.84.064005. arXiv:1105.2646 Manko VS, Rabadan RI, Ruiz E (2013) The Breton–Manko equatorially antisymmetric binary configuration revisited. Class Quantum Grav 30:145005. https://doi.org/10.1088/0264-9381/30/14/145005. arXiv:1302.7110 Manko VS, Rabadán RI, Sanabria-Gómez JD (2014) Stationary black diholes. Phys Rev D 89(6):064049. https://doi.org/10.1103/PhysRevD.89.064049. arXiv:1311.2326 Mars M (2009) Present status of the Penrose inequality. Class Quantum Grav 26:193001. https://doi.org/10.1088/0264-9381/26/19/193001. arXiv:0906.5566 Mars M (2014) Stability of marginally outer trapped surfaces and geometric inequalities. In: Bičák J, Ledvinka T (eds) General relativity, cosmology and astrophysics: perspectives 100 years after Einstein’s stay in Prague. Fundamental theories of physics, vol 177. Springer, Cham, pp 191–208. https://doi.org/10.1007/978-3-319-06349-2_8 Mars M, Senovilla JMM (1993) Axial symmetry and conformal Killing vectors. Class Quantum Grav 10:1633–1647. https://doi.org/10.1088/0264-9381/10/8/020. arXiv:gr-qc/0201045 Meeks W III, Simon L, Yau ST (1982) Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Ann Math 2(116):621–659. https://doi.org/10.2307/2007026 Moreschi OM, Sparling GAJ (1984) On the positive energy theorem involving mass and electromagnetic charges. Commun Math Phys 95:113–120. https://doi.org/10.1007/BF01215757 Murchadha NO (1986) How large can a star be? Phys Rev Lett 57:2466–2469. https://doi.org/10.1103/PhysRevLett.57.2466 Murchadha NO, Tung RS, Xie N, Malec E (2010) The Brown-York mass and the Thorne hoop conjecture. Phys Rev Lett 104:041101. https://doi.org/10.1103/PhysRevLett.104.041101. arXiv:0912.4001 Nester JM, Meng FF, Chen CM (2004) Quasilocal center-of-mass. J Korean Phys Soc 45:S22–S25. https://doi.org/10.3938/jkps.45.22. arXiv:gr-qc/0403103 Neugebauer G, Hennig J (2009) Non-existence of stationary two-black-hole configurations. Gen Relativ Gravit 41:2113–2130. https://doi.org/10.1007/s10714-009-0840-8. arXiv:0905.4179 Neugebauer G, Hennig J (2012) Stationary two-black-hole configurations: a non-existence proof. J Geom Phys 62:613–630. https://doi.org/10.1016/j.geomphys.2011.05.008. arXiv:1105.5830 Neugebauer G, Hennig J (2014) Stationary black-hole binaries: a non-existence proof. In: Bičák J, Ledvinka T (eds) General relativity, cosmology and astrophysics: perspectives 100 years after Einstein’s stay in Prague. Fundamental theories of physics, vol 177. Springer, Cham, pp 209–228. https://doi.org/10.1007/978-3-319-06349-2_9. arXiv:1302.0573 Nordström G (1918) On the energy of the gravitational field in Einstein’s theory. Verhandl Koninkl Ned Akad Wetenschap, Afdel Natuurk, Amsterdam 26:1201–1208 Papapetrou A (1945) A static solution of the equations of the gravitational field for an arbitrary charge-distribution. Proc R Irish Acad A 51:191–204 Penrose R (1965) Gravitational collapse and space-time singularities. Phys Rev Lett 14:57–59. https://doi.org/10.1103/PhysRevLett.14.57 Penrose R (1973) Naked singularities. Ann NY Acad Sci 224:125–134. https://doi.org/10.1111/j.1749-6632.1973.tb41447.x Penrose R, Floyd RM (1971) Extraction of rotational energy from a black hole. Nature 229:177–179. https://doi.org/10.1038/physci229177a0 Reiris M (2014a) On extreme Kerr-throats and zero temperature black holes. Class Quantum Grav 31:025001. https://doi.org/10.1088/0264-9381/31/2/025001. arXiv:1209.4530 Reiris M (2014b) On the shape of bodies in general relativistic regimes. Gen Relativ Gravit 46:1777. https://doi.org/10.1007/s10714-014-1777-0. arXiv:1406.6938 Reissner H (1916) Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie. Ann Phys 50:106–120. https://doi.org/10.1002/andp.19163550905 Rogatko M (2014) Mass angular momentum and charge inequalities for black holes in Einstein–Maxwell-axion–dilaton gravity. Phys Rev D 89:044020. https://doi.org/10.1103/PhysRevD.89.044020. arXiv:1402.3376 Rogatko M (2017) Angular momentum, mass and charge inequalities for black holes in Einstein–Maxwell gravity with dark matter sector. ArXiv e-prints arXiv:1701.07643 Schoen R, Yau ST (1979) On the proof of the positive mass conjecture in general relativity. Commun Math Phys 65:45–76. https://doi.org/10.1007/BF01940959 Schoen R, Yau ST (1981) Proof of the positive mass theorem. II. Commun Math Phys 79:231–260. https://doi.org/10.1007/BF01942062 Schoen R, Yau ST (1983) The existence of a black hole due to condensation of matter. Commun Math Phys 90:575–579. https://doi.org/10.1007/BF01216187. https://projecteuclid.org/euclid.cmp/1103940419 Schoen R, Yau S (2017) Positive scalar curvature and minimal hypersurface singularities. ArXiv e-prints arXiv:1704.05490 Schoen R, Zhou X (2013) Convexity of reduced energy and mass angular momentum inequalities. Ann Henri Poincaré 14:1747–1773. https://doi.org/10.1007/s00023-013-0240-1 Senovilla JMM (2008) A reformulation of the hoop conjecture. Europhys Lett 81:20004. https://doi.org/10.1209/0295-5075/81/20004. arXiv:0709.0695 Senovilla JMM (2011) Trapped surfaces. Int J Mod Phys D 20:2139. https://doi.org/10.1142/S0218271811020354. arXiv:1107.1344 Senovilla JMM, Garfinkle D (2015) The 1965 Penrose singularity theorem. Class Quantum Grav 32:124008. https://doi.org/10.1088/0264-9381/32/12/124008. arXiv:1410.5226 Shiromizu T, Nakao K, Kodama H, Maeda KI (1993) Can large black holes collide in de Sitter space-time? An inflationary scenario of an inhomogeneous universe. Phys Rev D 47:R3099–R3102. https://doi.org/10.1103/PhysRevD.47.R3099 Simon W (2012) Bounds on area and charge for marginally trapped surfaces with a cosmological constant. Class Quantum Grav 29:062001. https://doi.org/10.1088/0264-9381/29/6/062001. arXiv:1109.6140 Sorce J, Wald RM (2017) Gedanken experiments to destroy a black hole. II. Kerr–Newman black holes cannot be overcharged or overspun. Phys Rev D 96(10):104014. https://doi.org/10.1103/PhysRevD.96.104014. arXiv:1707.05862 Szabados LB (2004) Quasi-local energy-momentum and angular momentum in GR: a review article. Living Rev Relativ 7:4. https://doi.org/10.12942/lrr-2004-4 Thorne KS (1972) Nonspherical gravitational collapse: a short review. In: Klauder J (ed) Magic without magic: John Archibald Wheeler. A collection of essays in honor of his sixtieth birthday. W.H. Freeman, San Francisco, pp 231–258 Tod KP (1983) All metrics admitting supercovariantly constant spinors. Phys Lett B 121:241–244. https://doi.org/10.1016/0370-2693(83)90797-9 Tung RS (2009) Energy and angular momentum in strong gravitating systems. Int J Mod Phys A A24:3538–3544. https://doi.org/10.1142/S0217751X09047168. arXiv:0903.1036 Visser M (2013) Area products for black hole horizons. Phys Rev D 88:044014. https://doi.org/10.1103/PhysRevD.88.044014. arXiv:1205.6814 Wald R (1999) Gravitational collapse and cosmic censorship. In: Iyer BR, Bhawal B (eds) Black holes, gravitational radiation and the universe. Fundamental theories of physics, vol 100. Kluwer Academic, Dordrecht, pp 69–85. https://doi.org/10.1007/978-94-017-0934-7_5. arXiv:gr-qc/9710068 Wald RM (1984) General relativity. The University of Chicago Press, Chicago Wald RM (2001) The thermodynamics of black holes. Living Rev Relativ 4:6. https://doi.org/10.12942/lrr-2001-6. arXiv:gr-qc/9912119 Wali KC (1982) Chandrasekhar vs. Eddington—an unanticipated confrontation. Phys Today 35:33. https://doi.org/10.1063/1.2914790 Weinstein G (1996) \(N\) black hole stationary and axially symmetric solutions of the Einstein–Maxwell equations. Commun Part Diff Eq 21:1389–1430. https://doi.org/10.1080/03605309608821232. arXiv:gr-qc/9412036 Wieland W (2017) Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations. Gen Relativ Gravit 49:38. https://doi.org/10.1007/s10714-017-2200-4. arXiv:1604.07428 Witten E (1981) A new proof of the positive energy theorem. Commun Math Phys 80:381–402. https://doi.org/10.1007/BF01208277 Woolgar E (1999) Bounded area theorems for higher genus black holes. Class Quantum Grav 16:3005–3012. https://doi.org/10.1088/0264-9381/16/9/316. arXiv:gr-qc/9906096 Yazadjiev S (2013a) Horizon area–angular momentum–charge–magnetic fluxes inequalities in 5D Einstein–Maxwell-dilaton gravity. Class Quantum Grav 30:115010. https://doi.org/10.1088/0264-9381/30/11/115010. arXiv:1301.1548 Yazadjiev SS (2013b) Area–angular momentum–charge inequality for stable marginally outer trapped surfaces in 4D Einstein–Maxwell-dilaton theory. Phys Rev D 87:024016. https://doi.org/10.1103/PhysRevD.87.024016. arXiv:1210.4684 Yodzis P, Seifert HJ, Müller zum Hagen H (1973) On the occurrence of naked singularities in general relativity. Commun Math Phys 34:135–148. https://doi.org/10.1007/BF01646443 Yoon JH (2004) New Hamiltonian formalism and quasilocal conservation equations of general relativity. Phys Rev D 70:084037. https://doi.org/10.1103/PhysRevD.70.084037. arXiv:gr-qc/0406047 Yoshino H (2008) Highly distorted apparent horizons and the hoop conjecture. Phys Rev D 77:041501. https://doi.org/10.1103/PhysRevD.77.041501. arXiv:0712.3907 Zangwill A (2013) Modern electrodynamics. Cambridge University Press, Cambridge Zhang X (1999) Angular momentum and positive mass theorem. Commun Math Phys 206:137–155. https://doi.org/10.1007/s002200050700 Zhou X (2012) Mass angular momentum inequality for axisymmetric vacuum data with small trace. ArXiv e-prints arXiv:1209.1605