General Relativity and Gravitation

We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the black hole mass variation. Although the resulting equation may seem obvious due to a form of it appearing as a step in the derivation of the Schwarzschild metric, this geometrical argument is necessary to fix the added degree of freedom one gets for allowing the mass to vary with time. This result has applications on cosmological accretion models and provides a derivation from first principles to serve as a basis to the accretion equations already in use in the literature.

We show that combinations of (in general,non-linear) two- and threeform fields, analogous to theMaxwell (one-form) field, completely describe perfectfluids, including the rotating ones. In the non-rotating case, the two-form field is sufficient, and afree three-form field proves to be equivalent toappearance of the cosmological term in Einstein'sequations (the square-root non-linearity correspondingto Λ = 0). The gauge degrees of freedombreak down when a rotation is included, but even whenthey exist, there fails to be realized an equivalence ofthe two-form field and the massless scalar one recently claimed by Weinberg.

We argue that quantum-gravitational fluctuations in the space-time background give the vacuum non-trivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light in vacuo. Our proposal is motivated within a Liouville string formulation of quantum gravity that also suggests a frequency-dependent refractive index of the particle vacuum. We construct an explicit realization by treating photon propagation through quantum excitations of D-brane fluctuations in the space-time foam. These are described by higher-genus string effects, that lead to stochastic fluctuations in couplings, and hence in the velocity of light. We discuss the possibilities of constraining or measuring photon diffusion in vacuo via γ-ray observations of distant astrophysical sources.

Bằng cách sử dụng mô hình màng dựa trên mô hình tường gạch, chúng tôi đã tính toán năng lượng tự do và entropi của các lỗ đen đối xứng cầu do spin tùy ý. Kết quả cho thấy entropi của một trường vô hướng và entropi của một trường Fermionic có công thức tương tự nhau. Chỉ có một hệ số nằm giữa chúng.

In this paper, gravitational field within a spherically symmetric star overwhelmed through dynamical de Sitter space is obtained. Indeed, closer situation to reality manifesting effects of the dark energy on the properties of astronomical compact objects is considered. It seems the cosmological constant does not play an outstanding role in astronomical scales, however I showed that mass of a typcal star does vary with time in a way that depends upon the polytropic index of the star. In addition, some of astrophysical limits such as the Buchdahl limit may depend on time. The Oppenheimer–Volkoff mass limit also obeys this rule and although the cosmological constant is too small, the value of the Oppenheimer–Volkoff limit shall be halved after 560 million years under some special conditions.

We propose the method of investigation of radial motions for charged and neutral test particles in the Reissner–Nordström field by means of mass potential. In this context we analyze special features of interaction of charges and their motions in General Relativity and construct the radial motion classification. For test particles and a central source with charges q and Q, respectively, the conditions of attraction (when qQ > 0) and repulsion (when qQ < 0) are obtained. The conditions of motionless test particle states with respect to the central source are investigated and, in addition, stability conditions for such static equilibrium states are found. It is shown that stable states are possible only for the bound states of weakly charged particles in the field of a naked singularity. Frequencies of small oscillations of test particles near their equilibrium positions are also found.

An equation of spinor algebra, which is specified by two positive integers,M andN, is solved by relating it to the problem of integrating a two-dimensional Hamiltonian homogeneous polynomial system of ordinary differential equations, whose degree isN}-1. The case in whichN=1 reduces to a well-known result of spinor algebra. The caseM=N=4 is of relevance in the study of symmetry operators of Maxwell's equations on a curved space-time. It is also shown, using spinor notation, that the first integral for a general two-dimensional Hamiltonian system of ordinary differential equations (whether polynomial or analytic) is determinable in a purely algebraic manner, i.e., by using no integration.

An isotropic spatially inhomogeneous spacetime with the stress tensor satisfying the limiting case of the strong energy condition [T00 + 1/2)T] = 0 in the locally inertial coordinates where the observer's four-velocity is u a = δ0 a satisfying the constraint u a ua = −1 is studied. Special metrics with accelerating expansions of the inhomogeneous spacetime merely controlled by the shear are presented as an alternative model.