Static and Radiating Solutions of Lovelock Gravity in the Presence of a Perfect Fluid

TL;DR

This paper derives general static and radiating solutions in third order Lovelock gravity with a specific perfect fluid, revealing new black hole configurations and singularity properties that extend previous solutions.

Contribution

It provides a comprehensive class of solutions for third order Lovelock gravity with a linear equation of state, including new static and radiating black hole solutions with diverse horizon structures.

Findings

Solutions include black holes with one or two horizons, extremal black holes, and naked singularities.

Asymptotic behaviors are flat or (anti)-de Sitter depending on parameters.

New features such as black holes with two horizons at zero mass are identified.

Abstract

We present a general solution of third order Lovelock gravity in the presence of a specific type II perfect fluid. This solution for linear equation of state, $p=w(\rho-4B)$ contains all the known solutions of third order Lovelock gravity in the literature and some new static and radiating solutions for different values of $w$ and $B$. Specially, we consider the properties of static and radiating solutions for $w=0$ and $w=(n-2)^{-1}$ with B=0 and $B\neq0$. These solutions are asymptotically flat for B=0, while they are asymptotically (anti)-de Sitter for $B\neq0$. The new static solutions for these choices of $B$ and $w$ present black holes with one or two horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. The static solution with $w=0$ and vanishing geometrical mass ($m=0$) may present a black hole with two inner and outer horizons. This is a peculiar feature of the third order Lovelock gravity, which does not occur in lower order Lovelock gravity. We also, investigate the properties of radiating solutions for these values of $B$ and $w$, and compare the singularity strengths of them with the known radiating solutions of third order Lovelock gravity.