Fluid-membrane descriptions of various black holes

Abstract The membrane paradigm of black holes is an effective theory that replaces the event horizon with a fictitious yet tangible fluid. It has provided us with valuable insights, especially in understanding the environment of black holes. The paradigm establishes a fluid/gravity correspondence that allows the computation of the thermal properties of the black hole in terms of the transport coefficients of the fluid. Recently, we showed that this is a van der Waals-type fluid for Kerr and especially for Johannsen–Psaltis black holes. Here, we use the paradigm to study the properties of various black holes in different dimensions to test the predictive capacity of effective theory. Among these, for the BTZ black holes, the paradigm gives a physical bulk viscosity, unlike the generic examples, for which the paradigm works with a negative bulk viscosity. For Lorentz-violating black holes, we demonstrate that the parameter for Lorentz violation is seen as a hair under the paradigm, which shifts the ergoregion where the fluid pressure diverges. It might have a consequence for black hole jets. For asymptotically safe quantum-corrected black holes, the paradigm detects the final state of evaporation, i.e., a remnant with a correct value for the mass that still has an event horizon. Finally, we check the paradigm with stringy black holes that have dilatonic and axionic charges, and the fluid produces the known results.