https://doi.org/10.1140/epjp/i2019-12796-5
Regular Article
Conformal cosmological black holes: Towards restoring determinism to Einstein theory
1
Department of Physics and Astronomy & STAR Research Cluster, Bishop’s University, 2600 College Street, J1M 1Z7, Sherbrooke, QC, Canada
2
Physics Department, Champlain College-Lennoxville, 2580 College Street, J1M 0C8, Sherbrooke, QC, Canada
3
Département de Physique, Université de Montréal, 2900 Boulevard Édouard-Montpetit, H3T 1J4, Montréal, QC, Canada
4
Department of Physics, Namık Kemal University, Tekirdağ, Turkey
* e-mail: dkazici@nku.edu.tr
Received:
21
March
2019
Accepted:
31
May
2019
Published online:
2
October
2019
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-Nordström, 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019
