The Geometry of Black Hole Singularities

2014/01/01 by Ovidiu Cristinel Stoica
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology and Gravitation Theories #General relativity #Geometry #Gravitational singularity #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #Singularity #Theoretical physics #gr-qc #hep-th #math-ph #math.DG #math.MP

paper · pdf · doi:10.1155/2014/907518

published as Advances in High Energy Physics, Volume 2014 (2014), Article ID 907518 · To appear in Advances in High Energy Physics

openalex publication_date 2014/01/01 · arxiv created 2014/01/24 · arxiv updated 2014/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

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