Generalized Lemaitre-Tolman-Bondi solutions with pressure

Utilizing the ADM equations, we derive a metric and reduced field equations describing a general, spherically symmetric perfect fluid. The metric describes both the interior perfect fluid region and exterior vacuum Schwarzschild spacetime in a single coordinate patch. The exterior spacetime is in generalized Painleve-Gullstrand coordinates which is an infinite class of coordinate systems. In the static limit the system reduces to a Tolman-Oppenheimer-Volkoff equation on the interior with the exterior in Schwarzschild coordinates. We show the coordinate transformation for the nonstatic cases to comoving coordinates, where the metric is seen to be a direct generalization of the Lemaitre-Tolman-Bondi spacetime to include pressures.

[1]  J. Bjorken,et al.  Simple analytical models of gravitational collapse , 2005, gr-qc/0502040.

[2]  G. Magli,et al.  Naked Singularities Formation in the Gravitational Collapse of Barotropic Spherical Fluids , 2003, gr-qc/0303043.

[3]  G. Magli,et al.  Naked singularities formation in perfect fluids collapse , 2003 .

[4]  Neil Ashby,et al.  Relativity in the Global Positioning System , 2003, Living reviews in relativity.

[5]  B. Nolan.  Dynamical extensions for shell-crossing singularities. , 2003, gr-qc/0301028.

[6]  C. Uggla,et al.  The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models , 1999, gr-qc/9902070.

[7]  Hellaby.  On the Vaidya limit of the Tolman model. , 1994, Physical review. D, Particles and fields.

[8]  T. Piran,et al.  Naked singularities and other features of self-similar general-relativistic gravitational collapse. , 1990, Physical review. D, Particles and fields.

[9]  R. Newman.  Strengths of naked singularities in Tolman-Bondi spacetimes , 1986 .

[10]  D. Christodoulou.  Violation of cosmic censorship in the gravitational collapse of a dust cloud , 1984 .

[11]  K. Lake.  COLLAPSE OF RADIATING IMPERFECT FLUID SPHERES , 1982 .

[12]  K. Lake,et al.  Collapse of radiating fluid spheres , 1981 .

[13]  George F. R. Ellis,et al.  The Large Scale Structure of Space-Time , 2023 .

[14]  A. Taub,et al.  Spherically symmetric similarity solutions of the Einstein field equations for a perfect fluid , 1971 .

[15]  H. Bondi.  Spherically Symmetrical Models in General Relativity , 1947 .

[16]  R. Tolman.  Effect of Inhomogeneity on Cosmological Models. , 1934, Proceedings of the National Academy of Sciences of the United States of America.