Conformal cosmological black holes: Towards restoring determinism to Einstein 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. However, 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 of this feature, the charged non-rotating Thakurta black hole, which is 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). Furthermore, we show that the charged McVittie spacetime, although not conformal to any GR solution, represents a charged black hole embedded in a cosmological background with varying Hubble parameter that does not exhibit a real Cauchy horizon. These arguments speak in favor of restoring determinism to Einstein theory, which was questioned in recent research.