Black hole entropy in string-generated gravity models

Abstract

The Euclidean action and entropy are computed in string-generated gravity models with quadratic curvatures, and used to argue that a negative mass extremal metric is the background for hyperbolic (k=-1) black hole spacetimes, k being the curvature constant of the event horizon. The entropy associated with a black hole is always positive for k=(0,1) family. The positivity of energy condition also ensures that the k=-1 (extremal) entropy is non-negative.

Figures (1)

• Figure 1: The specific heat ($C=dE/dT$) vs. horizon radii. The parameters are fixed as $l=1$, $V_{n-1}/4G_{n+1}=1$, $n=4$, (a) $k=-1$ (upper plot): $\alpha=1/4$ (big single cusp), $\alpha=1/12$ (two cusps), and $\alpha=1/120$ (small single cusp). (b) $k=1$ (lower plot): the curve with $\alpha=0$ develops singularity at $r_+=1/\sqrt{2}$, so a small (large) black hole has negative (positive) specific heat, and two other curves correspond to $\alpha=1/12$ and $\alpha=1/4$ (up to down).