Non-isolated dynamic black holes and white holes

TL;DR

This paper introduces new dynamic black and white hole solutions using a modified Kerr-Schild transformation with a time-dependent scalar field, revealing non-isolated singularities and evolving horizons.

Contribution

It develops a novel class of dynamic black and white hole spacetimes with non-isolated singularities and time-dependent horizons, expanding the understanding of such objects beyond static solutions.

Findings

Black holes shrink over time with localized physical regions.

White holes expand and are physically valid throughout.

Dynamic horizons are confirmed to behave like event horizons.

Abstract

Modifying the Kerr-Schild transformation used to generate black and white hole spacetimes, new dynamic black and white holes are obtained using a time-dependent Kerr-Schild scalar field. Physical solutions are found for black holes that shrink with time and for white holes that expand with time. The black hole spacetimes are physical only in the vicinity of the black hole, with the physical region increasing in radius with time. The white hole spacetimes are physical throughout. Unlike the standard Schwarzschild solution the singularities are non-isolated, since the time-dependence introduces a mass-energy distribution. The surfaces in the metrics where g_{tt}=g^{rr}=0 are dynamic, moving inward with time for the black holes and outward for the white holes, which leads to a question of whether these spacetimes truly have event horizons--a problem shared with Vaidya's cosmological black hole spacetimes. By finding a surface that shrinks or expands at the same rate as the null geodesics move, and within which null geodesics move inward or outward faster than the surfaces shrink or expand respectively, it is verified that these do in fact behave like black and white holes.