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Title:
Spherically symmetric gravitational collapse of general fluids
Authors:
Lasky, P. D.; Lun, A. W. C.
Affiliation:
AA(Centre for Stellar and Planetary Astrophysics, School of Mathematical Sciences, Monash University, Wellington Rd, Melbourne 3800, Australia), AB(Centre for Stellar and Planetary Astrophysics, School of Mathematical Sciences, Monash University, Wellington Rd, Melbourne 3800, Australia)
Publication:
Physical Review D, vol. 75, Issue 2, id. 024031 (PhRvD Homepage)
Publication Date:
01/2007
Origin:
APS
PACS Keywords:
Initial value problem, existence and uniqueness of solutions, Exact solutions, Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
Abstract Copyright:
(c) 2007: The American Physical Society
DOI:
10.1103/PhysRevD.75.024031
Bibliographic Code:
2007PhRvD..75b4031L

Abstract

We express Einstein’s field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null radiation such that a region of Vaidya spacetime develops. Therefore, on any subsequent spacelike slice there exists three regions; general fluid, Vaidya and Schwarzschild, all expressed in a single coordinate patch with two free-boundaries determined by the equations. This implies complicated matching schemes are not required at the interfaces between the regions, instead, one simply requires the matter variables tend to the appropriate equations of state. We also show the reduction of the system of equations to the static cases, and show staticity necessarily implies zero “heat flux.” Furthermore, the static equations include a generalization of the Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium to include anisotropic stresses in general coordinates.
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