Entropy of black holes in topologically massive gravity

Abstract

We study the issue of black hole entropy in the topologically massive gravity. Assuming that the presence of gravitational Chern-Simons term with the coupling $1/\mu$ does modify the horizon radius ${\tilde{r}}_{+}$, we propose ${\tilde{S}}_{BH}=\pi {\tilde{r}}_{+}/2G_3$ as the Bekenstein-Hawking entropy. This entropy of CS-BTZ black hole satisfies the first-law of thermodynamics and the area-law but it is slightly different from the shifted-entropy $S_c=\pi r_{+}/2G_3+(1/\mu l)\pi r_{-}/2G_3$ based on the BTZ black hole with outer $r_{+}$ and inner horizon $r_{-}$. In the case of $r_{-}=0$, ${\tilde{S}}_{BH}$ represents the entropy of non-rotating BTZ black hole with the Chern-Simons term (NBTZ-CS), while $S_c$ reduces to the entropy of NBTZ black hole. It shows that ${\tilde{S}}_{BH}$ may be a candidate for the entropy of the CS-BTZ black hole.

11 pages, an expanded version to discuss thermodynamic aspects of BTZ-CS and CS-BTZ black holes

References in corpus (8)

• Geometry of the 2+1 Black Hole
• Chiral Gravity in Three Dimensions
• Cosmological Topologically Massive Gravitons and Photons
• Holography with Gravitational Chern-Simons Term
• Entropy function and attractors for AdS black holes
• Brown-Henneaux's Canonical Approach to Topologically Massive Gravity
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Phase transition between the BTZ black hole and AdS space

Cited by in corpus (5)

• On complexity growth in massive gravity theories, the effects of chirality and more
• Hawking radiation from covariant anomalies in 2+1 dimensional black holes
• Three dimensional rotating hairy black holes, asymptotics and thermodynamics
• Quasinormal modes for topologically massive black hole
• Higher spin swampland conjecture for massive AdS${}_3$ gravity