# Quantum field backreaction corrections and remnant stable evaporating Schwarzschild-de Sitter dynamical black hole

## Abstract

Time-dependent backreaction corrections of the renormalized expectation value of the stress-energy tensor operator of a massless quantum scalar field, minimally coupled, in the two-dimensional spherically symmetric nondilatonic Schwarzschild-de Sitter dynamical black hole metric, is applied to determine the final state of its thermal radiation. Renormalization theory in the two-dimensional analog of a generally curved space-time reduces to a trace anomaly defined in terms of the Ricci scalar. So the regularized stress-energy tensor, in close relation to the work by Christensen and Fulling, may be obtained by the nonlocal contribution of the trace anomaly and some suitable parameters. Linear-order, time-dependent solutions of the metric backreaction equations, in close relation to the work by Bousso et al., show that the spherically symmetric nondilatonic evaporating Schwarzschild-de Sitter dynamical black hole final state, reduces to a set of remnant, stable, mini black holes where their metric should be described in terms of some permissible discrete Eddington-Finkelstein advance times. Also the results of this article are confirmed by the consequences of time-independent backreaction solutions which were derived recently by the author and may propose a new approach for quantization of gravity, in which the cosmological constant and a distinguished observer have a key role.

- Authors:

- Physics Department, Semnan University, P.O. Box 35195-363 (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 21020378

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084009; (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; BLACK HOLES; CORRECTIONS; COSMOLOGICAL CONSTANT; DE SITTER GROUP; EXPECTATION VALUE; GRAVITATION; MATHEMATICAL SOLUTIONS; QUANTIZATION; QUANTUM FIELD THEORY; RENORMALIZATION; SCALAR FIELDS; SCHWARZSCHILD METRIC; SPACE-TIME; STRESSES; TENSORS; THERMAL RADIATION; TIME DEPENDENCE; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Ghaffarnejad, Hossein.
```*Quantum field backreaction corrections and remnant stable evaporating Schwarzschild-de Sitter dynamical black hole*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.084009.

```
Ghaffarnejad, Hossein.
```*Quantum field backreaction corrections and remnant stable evaporating Schwarzschild-de Sitter dynamical black hole*. United States. doi:10.1103/PHYSREVD.75.084009.

```
Ghaffarnejad, Hossein. Sun .
"Quantum field backreaction corrections and remnant stable evaporating Schwarzschild-de Sitter dynamical black hole". United States.
doi:10.1103/PHYSREVD.75.084009.
```

```
@article{osti_21020378,
```

title = {Quantum field backreaction corrections and remnant stable evaporating Schwarzschild-de Sitter dynamical black hole},

author = {Ghaffarnejad, Hossein},

abstractNote = {Time-dependent backreaction corrections of the renormalized expectation value of the stress-energy tensor operator of a massless quantum scalar field, minimally coupled, in the two-dimensional spherically symmetric nondilatonic Schwarzschild-de Sitter dynamical black hole metric, is applied to determine the final state of its thermal radiation. Renormalization theory in the two-dimensional analog of a generally curved space-time reduces to a trace anomaly defined in terms of the Ricci scalar. So the regularized stress-energy tensor, in close relation to the work by Christensen and Fulling, may be obtained by the nonlocal contribution of the trace anomaly and some suitable parameters. Linear-order, time-dependent solutions of the metric backreaction equations, in close relation to the work by Bousso et al., show that the spherically symmetric nondilatonic evaporating Schwarzschild-de Sitter dynamical black hole final state, reduces to a set of remnant, stable, mini black holes where their metric should be described in terms of some permissible discrete Eddington-Finkelstein advance times. Also the results of this article are confirmed by the consequences of time-independent backreaction solutions which were derived recently by the author and may propose a new approach for quantization of gravity, in which the cosmological constant and a distinguished observer have a key role.},

doi = {10.1103/PHYSREVD.75.084009},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}