Generalized Thermodynamic Properties of Lifshitz black holes

TL;DR

This paper investigates the motion and thermodynamic properties of Lifshitz black holes, deriving generalized effective potentials, analyzing orbit stability, and confirming thermodynamic laws and entropy behavior in these exotic spacetimes.

Contribution

It introduces a generalized effective potential for Lifshitz black holes and derives their thermodynamic properties, including entropy, mass, and temperature, satisfying key thermodynamic principles.

Findings

Bounded orbits are forbidden for positive z and allowed for negative z.

Entropy can still follow the area law in these black holes.

Mass, temperature, and entropy satisfy thermodynamic laws and Smarr formula.

Abstract

The generalized effective potential for motion in Lifshitz geometry (with arbitrary value of both the dynamical exponent $z$ and $f(r)$) is presented. Based on this effective potential energy, we shall show that bounded orbits are forbidden for positive values of $z$ and allowed for negative values of $z$. The stability of these bounded orbits are analysed in full detail. Besides, by comparison, we quote a theorem which should be very helpful in searching thermodynamical properties of these gravitational black holes. Based on this theorem, generalized thermodynamic properties of Lifshitz black holes are computed. Examples are given where the entropy still satisfies the area law. The calculated mass, temperature and entropy satisfy both the first thermodynamic principle of black holes and a Smarr formula.