Exact Relativistic Treatment of Stationary Counter-Rotating Dust Disks: Axis, Disk, and Limiting Cases
Tóm tắt
We continue to study the construction of explicit solutions of the stationary axisymmetric Einstein equations, interpretable as counterrotating disks of dust. We discuss the previously constructed class of solutions for disks with constant angular velocity and constant relative density. The metric for these space–times is given in terms of theta functions on a Riemann surface of genus two. We discuss the metric functions at the axis of symmetry and on the disk. Interesting limiting cases are the Newtonian, static, and ultrarelativistic limits (in the latter limit, the central red shift diverges).
Tài liệu tham khảo
citation_journal_title=Phys. Rev; citation_author=F. J. Ernst; citation_volume=167; citation_publication_date=1968; citation_pages=1175; citation_id=CR1
citation_journal_title=Phys. R ev. Lett.; citation_author=D. Maison; citation_volume=41; citation_publication_date=1978; citation_pages=521; citation_id=CR2
citation_journal_title=Sov. Phys.-JETP; citation_author=V. A. Belinski, V. E. Zakharov; citation_volume=48; citation_publication_date=1978; citation_pages=985; citation_id=CR3
citation_journal_title=J. Phys. A; citation_author=G. Neugebauer; citation_volume=12; citation_publication_date=1979; citation_pages=L67; citation_id=CR4
citation_journal_title=Astrophys. J. Lett.; citation_author=G. Neugebauer, R. Meinel; citation_volume=414; citation_publication_date=1993; citation_pages=L97; citation_id=CR5
citation_journal_title=Theor. Math. Phys.; citation_author=D. A. Korotkin; citation_volume=77; citation_publication_date=1988; citation_pages=1018; citation_id=CR6
citation_journal_title=Phys. Rev. Lett.; citation_author=C. Klein, O. Richter; citation_volume=79; citation_publication_date=1997; citation_pages=565; citation_id=CR7
C. Klein and O. Richter, Phys. Rev. D, 58, CID 124018 (1998).
citation_journal_title=Phys. Rev. Lett.; citation_author=C. Klein, O. Richter; citation_volume=83; citation_publication_date=1999; citation_pages=2884; citation_id=CR9
citation_journal_title=Phys. Rev. D; citation_author=C. Klein; citation_volume=63; citation_publication_date=2001; citation_pages=064033; citation_id=CR10
citation_title=Exact Solutions of Einstein's Field Equations; citation_publication_date=1980; citation_id=CR11; citation_author=D. Kramer; citation_author=H. Stephani; citation_author=E. Herlt; citation_author=M. MacCallum; citation_publisher=Cambridge Univ. Press
citation_title=Theta Functions on Riemann Surfaces; citation_publication_date=1973; citation_id=CR12; citation_author=J. Fay; citation_publisher=Springer
citation_journal_title=Nucl. Phys. B; citation_author=D. Korotkin, H. Nicolai; citation_volume=475; citation_publication_date=1996; citation_pages=397; citation_id=CR13
D. Korotkin and V. Matveev, “Solutions of Schlesinger system and Ernst equation in terms of theta functions,” gr-qc/9810041 (1998); Funct. Anal. Appl., 34, 252 (2000).
citation_journal_title=Kodai Math. J.; citation_author=A. Yamada; citation_volume=3; citation_publication_date=1980; citation_pages=114; citation_id=CR15
citation_title=General Relativity; citation_publication_date=1984; citation_id=CR16; citation_author=R. Wald; citation_publisher=Univ. of Chicago Press
citation_journal_title=Astrophys. J.; citation_author=J. M. Bardeen, R. V. Wagoner; citation_volume=167; citation_publication_date=1971; citation_pages=359; citation_id=CR17
citation_journal_title=Phys. Rev.; citation_author=T. Morgan, L. Morgan; citation_volume=183; citation_publication_date=1969; citation_pages=1097; citation_id=CR18
citation_title=Tata Lectures on Theta II; citation_publication_date=1993; citation_id=CR19; citation_author=D. Mumford; citation_publisher=Birkhäuser
citation_journal_title=Class. Q. Grav.; citation_author=C. Klein; citation_volume=14; citation_publication_date=1997; citation_pages=2267; citation_id=CR20
R. Meinel, “The rigidly rotating disk of dust and its black hole limit,” gr-qc/9703077 (1997).
citation_journal_title=J. Math. Phys.; citation_author=I. Hauser, F. Ernst; citation_volume=21; citation_publication_date=1980; citation_pages=1126; citation_id=CR22
citation_title=Algebro-Geometric Approach to Nonlinear Integrable Equations; citation_publication_date=1994; citation_id=CR23; citation_author=E. D. Belokolos; citation_author=A. I. Bobenko; citation_author=V. Z. Enolskii; citation_author=A. R. Its; citation_author=V. B. Matveev; citation_publisher=Springer