Spherically symmetric gravitational collapse of general fluids
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 nonnull 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 freeboundaries 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 TolmanOppenheimerVolkoff equations for hydrostatic equilibrium to include anisotropic stresses inmore »
 Authors:
 Centre for Stellar and Planetary Astrophysics, School of Mathematical Sciences, Monash University, Wellington Rd, Melbourne 3800 (Australia)
 Publication Date:
 OSTI Identifier:
 21010901
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024031; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; COSMOLOGY; EINSTEIN FIELD EQUATIONS; EQUATIONS OF STATE; GRAVITATIONAL COLLAPSE; HEAT FLUX; SCHWARZSCHILD METRIC; SPACETIME
Citation Formats
Lasky, P. D., and Lun, A. W. C. Spherically symmetric gravitational collapse of general fluids. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.024031.
Lasky, P. D., & Lun, A. W. C. Spherically symmetric gravitational collapse of general fluids. United States. doi:10.1103/PHYSREVD.75.024031.
Lasky, P. D., and Lun, A. W. C. Mon .
"Spherically symmetric gravitational collapse of general fluids". United States.
doi:10.1103/PHYSREVD.75.024031.
@article{osti_21010901,
title = {Spherically symmetric gravitational collapse of general fluids},
author = {Lasky, P. D. and Lun, A. W. C.},
abstractNote = {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 nonnull 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 freeboundaries 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 TolmanOppenheimerVolkoff equations for hydrostatic equilibrium to include anisotropic stresses in general coordinates.},
doi = {10.1103/PHYSREVD.75.024031},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

Final fate of spherically symmetric gravitational collapse of a dust cloud in EinsteinGaussBonnet gravity
We give a model of the higherdimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n({>=}5)dimensional action with the GaussBonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M{approx_equal}M{sup 2}xK{sup n2} with a perfect fluid and a cosmological constant. This is a generalization of the MisnerSharp formalism of the fourdimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5more » 
Gravitational collapse of spherically symmetric plasmas in EinsteinMaxwell spacetimes
We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energymomentum tensor [Phys. Rev. D 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of electromagnetic matter. We show the system reduces to the ReissnerNordstrom spacetime in general, spherically symmetric coordinates in the vacuum limit. Furthermore, we show reduction to the charged Vaidya spacetime in nonnull coordinates when certain equations of states are chosen. A model of gravitational collapse is discussed whereby a charged fluid resides within a boundary of finite radial extent on the initial hypersurface, and is allowed to radiatemore »