Thermodynamics of static solutions in (n+1)-dimensional Quintic Quasitopological gravity

TL;DR

This paper constructs and analyzes static black hole solutions in higher-dimensional quintic quasitopological gravity, exploring their thermodynamics and stability, with solutions exhibiting multiple horizons and stability depending on spacetime asymptotics.

Contribution

It introduces a new class of higher-dimensional static solutions in quintic quasitopological gravity and examines their thermodynamic properties and stability.

Findings

Black hole solutions with two horizons in AdS and flat spacetimes.

Existence of three-horizon black holes in dS for certain mass ranges.

Thermal stability varies with spacetime geometry and horizon topology.

Abstract

Based on the fact that some important theories like string and M-theories predict spacetime with higher dimensions, so, in this paper, we aim to construct a theory of quintic quasitopological gravity in higher dimensions ($n\geq5$). This $(n+1)$-dimensional quintic quasitopological gravity can also lead to the most second-order linearized field equations in the spherically symmetric spacetimes. These equations can not be solved exactly and so, we obtain a new class of $(n+1)$-dimensional static solutions with numeric methods. For large values of mass parameter $m$, these solutions yield to black holes with two horizons in AdS and flat spacetimes. For dS solutions, there are two values, $m_{\rm ext}$ and $m_{\rm cri}$, which yield to a black hole with three horizons for $m_{\rm ext}<m<m_{\rm cri}$. We also calculate thermodynamic quantities for this black hole such as entropy and temperature and check the first law of thermodynamics. Finally, we analyze thermal stability of the $(n+1)$-dimensional static black hole at the horizon $r_{+}$. Unlike dS solutions, AdS ones have thermal stability for each values of $k$, but flat solutions are stable with just $k=1$.