Generating Static Spherically Symmetric Black-holes in Lovelock Gravity

TL;DR

This paper generalizes a theorem to generate static, spherically symmetric black-hole solutions in higher-dimensional Lovelock gravity, including special cases like Gauss-Bonnet and Einstein-Hilbert, and explores their properties and singularities.

Contribution

It introduces a unified method to generate black-hole solutions in Lovelock gravity, extending previous results and analyzing solutions with matter fields and topological features.

Findings

Derived new classes of solutions in third order Lovelock gravity.

Analyzed asymptotic behaviors and singularity structures.

Found quantum regularity of spacetime with quantum test particles.

Abstract

Generalization of a known theorem to generate static, spherically symmetric black-hole solutions in higher dimensional Lovelock gravity is presented. Particular limits, such as Gauss-Bonnet (GB) and/or Einstein-Hilbert (EH) in any dimension $N$ yield all the solutions known to date with an energy-momentum. In our generalization, with special emphasis on the third order Lovelock gravity, we have found two different class of solutions characterized by the matter field parameter. Several particular cases are studied and properties related to asymptotic behaviours are discussed. Our general solution which covers topological black holes as well, splits naturally into distinct classes such as Chern-Simon (CS) and Born-Infeld (BI) in higher dimensions. The occurence of naked singularities are studied and it is found that, the spacetime behaves nonsingular in quantum mechanical sense when it is probed with quantum test particles. The theorem is extended to cover Bertotti-Robinson (BR) type solutions in the presence of the GB parameter alone. Finally we prove also that extension of the theorem for a scalar-tensor source of higher dimensions $(N>4)$ fails to work.