2006/09/30 by Rosa Doran, Francisco S. N. Lobo, Paulo Crawford · 85 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #Event horizon #General relativity #Geodesic #Geometry #Gravitational singularity #Kerr metric #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Schwarzschild geodesics #Schwarzschild metric #Schwarzschild radius #Spacetime #Theoretical physics #gr-qc
paper · pdf · doi:10.1007/s10701-007-9197-6
published in Foundations of Physics 38(2), 160-187 (Springer Science+Business Media) · 15 pages, 7 figures, Revtex4. V2: Version to appear in Foundations of Physics
arxiv created 2007/11/22 · openalex publication_date 2007/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.