# Quantized fields and temperature in charged dilatonic black hole spacetimes

TL;DR: In this paper, the stress energy tensor of a quantized scalar field is computed in the reduced two-dimensional charged dilatonic black hole spacetime of Garfinkle, Horowitz, and Strominger.

Abstract: The stress-energy tensor of a quantized scalar field is computed in the reduced two-dimensional charged dilatonic black hole spacetime of Garfinkle, Horowitz, and Strominger. In order for the stress-energy of quantized fields to be regular on the event horizon in both the extreme string metric and the conformally associated physical metric, it is necessary to assign a nonzero temperature, T = (8 pi e^{phi_0} M)^{-1}, to the extreme string metric, contrary to the expectation that this horizonless spacetime would have a natural temperature of zero.

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TL;DR: In this paper, the authors apply the scheme of Hiscock and Weems to model the evaporation of an asymptotically flat dilatonic charge black hole known as the Garfinkle-Horowitz-Strominger (GHS) black hole.

Abstract: Hiscock and Weems showed that under Hawking evaporation, an isolated asymptotically flat Reissner-Nordstrom (RN) black hole evolves in a surprising manner: if it starts with a relatively small value of charge-to-mass ratio Q/M, then said value will temporarily increase along its evolutionary path, before finally decreases towards zero. This contrasts with highly charged ones that simply radiate away its charge steadily. The combination of these two effects is the cosmic censor at work: there exists an attractor that flows towards the Schwazschild limit, which ensures that extremality — and hence naked singularity — can never be reached under Hawking evaporation. We apply the scheme of Hiscock and Weems to model the evaporation of an asymptotically flat dilatonic charge black hole known as the Garfinkle-Horowitz-Strominger (GHS) black hole. We found that upholding the cosmic censorship requires us to modify the charged particle production rate, which remarkably agrees with the expression obtained independently via direct computation of charged particle production rate on curved spacetime background. This not only strengthens the case for cosmic censorship, but also provides an example in which cosmic censorship can be a useful principle to deduce other physics. We also found that the attractor behavior is not necessarily related to the specific heat, contrary to the claim by Hiscock and Weems.

20 citations

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TL;DR: In this article, Zhang's de Broglie wave method was used to obtain the unthermal spectrum of the massive particles' tunneling from Garfinkle-Horowitz-Strominger black hole.

Abstract: Hawking radiation is viewed as a process of quantum tunneling. The massive particles' tunneling from Garfinkle–Horowitz–Strominger black hole is investigated. Using Jingyi Zhang's de Broglie wave method, we get the unthermal spectrum, and the result is consistent with the underlying unitary theory.

8 citations

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TL;DR: In this article, the authors studied the thermodynamic properties of the Garfinkle-Horowitz-Strominger dilaton black hole from the viewpoint of geometry and calculated the heat capacity and the temperature of the black hole, Weinhold metric and Ruppeiner metric.

Abstract: This paper studies the thermodynamic properties of the Garfinkle–Horowitz–Strominger dilaton black hole from the viewpoint of geometry. It calculates the heat capacity and the temperature of the black hole, Weinhold metric and Ruppeiner metric are also obtained respectively. It finds that they are both curved and the scalar curvature of the Weinhold geometry consists with the first-order transition point reproduced from the capacity, while the Ruppeiner one is both in accordance with the first-order and the second-order phase transition points reproduced from the capacity.

8 citations

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TL;DR: In this paper, the authors apply the scheme of Hiscock and Weems to model the evaporation of an asymptotically flat dilatonic charge black hole known as the Garfinkle-Horowitz-Strominger (GHS) black hole.

Abstract: Hiscock and Weems showed that under Hawking evaporation, an isolated asymptotically flat Reissner-Nordstrom (RN) black hole evolves in a surprising manner: if it starts with a relatively small value of charge-to-mass ratio Q/M, then said value will temporarily increase along its evolutionary path, before finally decreases towards zero. This contrasts with highly charged ones that simply radiate away its charge steadily. The combination of these two effects is the cosmic censor at work: there exists an attractor that flows towards the Schwazschild limit, which ensures that extremality -- and hence naked singularity -- can never be reached under Hawking evaporation. We apply the scheme of Hiscock and Weems to model the evaporation of an asymptotically flat dilatonic charge black hole known as the Garfinkle-Horowitz-Strominger (GHS) black hole. We found that upholding the cosmic censorship requires us to modify the charged particle production rate, which remarkably agrees with the expression obtained independently via direct computation of charged particle production rate on curved spacetime background. This not only strengthens the case for cosmic censorship, but also provides an example in which cosmic censorship can be a useful principle to deduce other physics. We also found that the attractor behavior is not necessarily related to the specific heat, contrary to the claim by Hiscock and Weems.

7 citations

### Cites background from "Quantized fields and temperature in..."

...extremal form T = ~c/(8πGkBM) – would result in a divergent stress-energy [56]....

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...[56] Daniel J....

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TL;DR: In this paper, the GHS black hole's quantum horizon is constructed by treating macro-black hole as quantum states, and using Brown-York's quasi-local gravitational energy definition and Heisenberg uncertainty principle.

Abstract: Treating macro-black hole as quantum states, and using Brown–York's quasi-local gravitational energy definition and Heisenberg uncertainty principle, the GHS black hole's quantum horizon is constructed. The Hawking temperature is computed naturally, and the entropy can also be figured out without introducing the cutoff factor h. The Φ-field mode number is predicted too. The result is consistent with that of the Schwarzschild and R-N black hole.

4 citations

### Cites background from "Quantized fields and temperature in..."

...The metric of the more complex GHS black hole is as follows [ 8 , 9]...

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##### References

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01 Jan 1982

TL;DR: A comprehensive review of the subject of gravitational effects in quantum field theory can be found in this paper, where special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe.

Abstract: This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

6,564 citations

01 Apr 1984

TL;DR: A comprehensive review of the subject of gravitational effects in quantum field theory can be found in this paper, where special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe.

Abstract: This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

6,464 citations