Conformal cosmological black holes: restoring determinism to Einstein theory

TL;DR

This paper investigates how conformal transformations of known solutions in general relativity lead to new solutions that reveal instabilities in black hole horizons within cosmological backgrounds, supporting the idea of restoring determinism to Einstein's theory.

Contribution

It demonstrates that conformally transformed solutions solve a Brans-Dicke theory and exhibit horizon instabilities, challenging the stability of black holes in cosmological settings and advocating for deterministic Einstein theory.

Findings

Conformal transformations produce solutions solving a pathological Brans-Dicke theory.

Embedded black holes lose their Cauchy horizons in cosmological backgrounds.

Results support restoring determinism to Einstein's theory.

Abstract

A widespread solution-generating technique of general relativity consists of conformally transforming known `seed' solutions. It is shown that these new solutions always solve the field equations of a pathological Brans-Dicke theory. Furthermore, when interpreted as effective Einstein equations,those field equations exhibit, in the case of a cosmological `background', an induced imperfect fluid as an additional effective source besides the original sources of the `seed' solutions. As an application, the charged non-rotating Thakurta black hole conformal to Reissner-Nordstrom is used to demonstrate the fragility of the inner Cauchy horizon when this black hole is embedded in the universe (even accounting for the separation of black hole and Hubble scales). Similarly, the charged McVittie spacetime representing a charged black hole embedded in a cosmological `background' with varying Hubble parameter does not exhibit a real Cauchy horizon. These arguments speak in favor of restoring determinism to Einstein theory, which was questioned in recent research.