Einstein’s hole argument and Schwarzschild singularities

• Published in: Annals of physics Vol. 452; p. 169274
• Main Author: Gogberashvili, Merab
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-05-2023
• Subjects: Einstein’s hole argument; Schwarzschild black holes; Singular coordinates; Singular coordinates; Schwarzschild black holes; Einstein’s hole argument
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2023.169274

According to the Einstein hole argument, vacuum metric solutions are equivalent only if they correspond to the same energy–momentum tensor in the source region. In this paper it is shown that singular coordinates that are used to show Schwarzschild geodesics completeness, introduce the fictive delta-like sources at the horizon. Then, metric tensors obtained by such singular transformations, cannot be considered as solutions of the same Einstein equations with the central source.
•Schwarzschild metrics obtained by singular transformations are solutions of different Einstein equations.•The Regge–Wheeler radial variable should contain Heaviside function at the Schwarzschild horizon.•Particles do not cross Schwarzschild sphere, but are absorbed and some reflected by the horizon.