Interior of a Schwarzschild black hole revisited

TL;DR

This paper revisits the interior Schwarzschild black hole solution, analyzing its metric, geodesics, and coordinate systems to clarify misconceptions and explore its cosmological interpretations, highlighting unresolved issues about black hole interiors.

Contribution

It provides a detailed analysis of the interior Schwarzschild solution using time-dependent metrics and explores its implications, addressing misconceptions and examining coordinate systems from the interior perspective.

Findings

Interior metric derived without exterior biases

Conserved quantities for geodesics analyzed

Coordinate systems examined from interior viewpoint

Abstract

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.