# 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 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 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; SPACE-TIME

### 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 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.},

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}

}