First Law of Inner Mechanics of Black Holes in Generalized Minimal Massive Gravity

TL;DR

This paper investigates the validity of the first law of inner mechanics for black holes within Generalized Minimal Massive Gravity, confirming its applicability to BTZ and warped black holes and analyzing entropy relations influenced by Chern-Simons terms.

Contribution

It demonstrates the first law's validity for specific black holes in Generalized Minimal Massive Gravity and explores entropy product dependencies on mass due to Chern-Simons effects.

Findings

First law holds for BTZ and warped black holes in the model.

Entropy product depends on mass because of Lorentz Chern-Simons term.

Inner and outer horizon entropy relations are affected by topological terms.

Abstract

In this paper, we examine the validity of the first law of inner mechanics of black holes in Generalized Minimal Massive Gravity. We consider BTZ and spacelike warped black holes and show that the first law of inner mechanics is valid for given black holes in Generalized Minimal Massive Gravity. As we expect, due to the presence of the Lorentz Chern-Simons term in Lagrangian of considered model, the product of the entropies of the inner and outer horizons depends on the mass as it happens in Topologically Massive Gravity.