Kasner Singularity of Black Holes in Einstein-scalar Gravity

TL;DR

This paper investigates the nature of Kasner singularities inside black holes in Einstein-scalar gravity, revealing how asymptotic parameters influence singularity properties and identifying bounds on particle survival times.

Contribution

It introduces a detailed analysis of the Kasner singularity structure in Einstein-scalar black holes, linking near-singularity constants to asymptotic parameters and discovering bounds on particle infall times.

Findings

The integration constant near the singularity relates to mass and scalar charge.

A general pattern shows the constant asymptotes to a linear combination of mass and scalar charge.

A maximum survival time for particles inside the black hole is identified, with Schwarzschild black holes saturating this bound.

Abstract

We study the spacelike Kasner singularity of spherically-symmetric, static and asymptotically flat black holes in Einstein gravity minimally coupled to a massless scalar with a suitable self-interacting scalar potential. We focus on how the asymptotic information such as the mass and scalar charge affect the properties of the Kasner singularity, including the Kasner exponents. We show how a nontrivial integration constant can be extracted from the near-singularity geometry and find a general pattern that this integration constant asymptotes to a linear combination of the mass and scalar charge at large mass limit. We also find that there may be a black hole upper bound on the maximum surviving time of a massive particle inside such a black hole before it falls into the Kasner singularity, and the Schwarzschild black hole saturate this bound.