arXiv:1805.09422v2 [gr-qc] 8 Sep 2019 Conformal cosmological black holes: Towards restoring determinism to Einstein theory Fayçal Hammad, 1, 2, 3, ∗ Dilek K. Çiftci, 1,4, † and Valerio Faraoni 1, ‡ 1 Department of Physics and Astronomy & STAR Research Cluster, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7 Canada 2 Physics Department, Champlain College-Lennoxville, 2580 College Street, Sherbrooke, QC, J1M 0C8 Canada 3 Département de Physique, Université de Montréal, 2900 Boulevard Édouard-Montpetit, Montréal, QC, H3T 1J4 Canada 4 Department of Physics, Namık Kemal University, Tekirdağ, Turkey A widespread solution-generating technique of general relativity consists of confor- mally 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 effec- tive 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. * Electronic address: fhammad@ubishops.ca † dkazici@nku.edu.tr