# Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity

## Abstract

**:**

## 1. Introduction

## 2. Black Hole Solution in the Einstein–GB-Λ System

#### 2.1. Model

#### 2.2. Solutions

#### 2.3. Properties of the Solutions

**Figure 1.**The $\tilde{M}$-${r}_{h}$ diagrams of the static solutions in the six-dimensional Einstein–GB-Λ system. We set $1/{\ell}^{2}=1$ (negative cosmological constant), $k=-1$, $\u03f5=+1$ (the non-GR branch) and $\tilde{\alpha}=0.2$. For $0<\tilde{M}<{\tilde{M}}_{ex}$, the solution has a black hole horizon (the upper one) and an inner horizon (the lower one). The dot with character “E" implies the degenerate horizon.

## 3. Equation of Motion of the Thin Dust Shell

## 4. Motion of the Shell in 6-dimensional Spacetime

**Figure 2.**“Potential" of the thin shell around the black hole. We set $\tilde{\alpha}=0.2$, ${\ell}^{2}=1$, $k=-1$, $\u03f5=1$, and ${\tilde{M}}_{s}=0.1{\tilde{M}}_{ex}$ (red solid curve), ${\tilde{M}}_{s}=2.0{\tilde{M}}_{ex}$ (blue dashed curve). The shell can move the region where $V\left(R\right)\le 0$.

## 5. Conclusions

## Acknowledgments

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## Appendix

## A. Asymptotic Motion of the Shell

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Torii, T.
Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity. *Entropy* **2012**, *14*, 2291-2301.
https://doi.org/10.3390/e14112291

**AMA Style**

Torii T.
Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity. *Entropy*. 2012; 14(11):2291-2301.
https://doi.org/10.3390/e14112291

**Chicago/Turabian Style**

Torii, Takashi.
2012. "Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity" *Entropy* 14, no. 11: 2291-2301.
https://doi.org/10.3390/e14112291