Evolving black holes from conformal transformations of static solutions

TL;DR

This paper constructs and analyzes a class of dynamic black hole solutions derived from conformal transformations of Schwarzschild metrics, exploring their horizons, causal structure, and energy properties depending on the conformal factor.

Contribution

It introduces a new family of nonstationary spacetimes via conformal transformations, detailing their horizon structure and causal properties, and analyzing their physical characteristics.

Findings

Spacetimes can have event horizons or not depending on the conformal factor.

Black-hole or white-hole regions emerge when the conformal factor stabilizes.

Null singularities may occur in models with unbounded conformal factors.

Abstract

A class of nonstationary spacetimes is obtained by means of a conformal transformation of the Schwarzschild metric, where the conformal factor $a(t)$ is an arbitrary function of the time coordinate only. We investigate several situations including some where the final state is a central object with constant mass. The metric is such that there is an initial big-bang type singularity and the final state depends on the chosen conformal factor. The Misner-Sharp mass is computed and a localized central object may be identified. The trapping horizons, geodesic and causal structure of the resulting spacetimes are investigated in detail. When $a(t)$ asymptotes to a constant in a short enough time scale, the spacetime presents an event horizon and its analytical extension reveals black-hole or white-hole regions. On the other hand, when $a(t)$ is unbounded from above as in cosmological models, the spacetime presents no event horizons and may present null singularities in the future. The energy-momentum content and other properties of the respective spacetimes are also investigated.