Conformal cosmological black holes: 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. 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.