For general relativistic, inviscid, axisymmetric flow around Kerr black hole one may choose different flow thickness. The stationary flow equations can be solved using methods of dynamical system to get transonic accretion flows , i.e, flow infalling in the blackhole that turns supersonic from subsonic with decreasing radial distance, or vice versa. This transonic flows are obtained by choosing the particular flow passing through critical points of phase portrait. For certain flow thickness like the one maintaining conical shape, the sonic point coincide with the critical point. But there are certain flows maintaining hydrostatic equilibrium, such as the one described by Novikov-Thorne, where the sonic point is not same as the critical point. We perturb the flow for both kind of flow and study the behaviour of linear perturbation which behaves like massless scalar field in some curved spacetime, known as, analogue space time. We draw the compactified causal structure, i.e, Penrose Carter diagram for both kind of analogue metric and prove that for both cases critical points are the acoustic horizons, whereas in the case where sonic points do not coincide with critical points, the sonic points are not the acoustic horizon, as one may expect from the definition of sound speed.
Causal Space-Time Structure and non-Hausdorff Extension of Schwarzschild Black Hole Interior
Landau Phystech-School, Moscow Institute of Physics and Technology（兰道物理技术学院，莫斯科物理技术学院）；Institute for High Energy Physics of National Research Centre "Kurchatov Institute"（库尔恰托夫国家研究中心高能物理研究所）
The space-time structure of an untouchable naked singularity in superstrings theory
Centro de Investigación y de Estudios Avanzados del Intituto Politécnico Nacional（墨西哥国立自治大学高级研究中心）；Departamento de Física, Centro de Investigación y de Estudios Avanzados del Intituto Politécnico Nacional（墨西哥国立自治大学高级研究中心物理系）
All fundamental electrically charged thin shells in general relativity: From star shells to tension shell black holes and regular black holes and beyond
First-Law Entropy and a Degenerate Extremal Remnant in a Minimal-Length Simpson--Visser-Type Regular Black Hole: Geometrothermodynamics, Phase Structure, and Observational Discriminants
University Moulay Ismail（穆莱·伊斯梅尔大学）；Cadi Ayyad University（卡迪·阿亚德大学）
