The Geometry of Black Hole singularities

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 non-singular 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 don't 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 making Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

To appear in Advances in High Energy Physics

References in corpus (10)

• Quantum Gravity at a Lifshitz Point
• Singularity Theorems and Their Consequences
• Fractional Action-Like Variational Problems
• Effective temperature, Hawking radiation and quasinormal modes
• Spacetime Singularities
• Primordial Black Hole Evaporation and Spontaneous Dimensional Reduction
• Coupling running through the Looking-Glass of dimensional Reduction
• Solutions of the Klein-Gordon equation on manifolds with variable geometry including dimensional reduction
• Riemannian $(1+\mathbf{d})$-Dim Space-Time Manifolds with Nonstandard Topology which Admit Dimensional Reduction to Any Lower Dimension and Transformation of the Klein-Gordon Equation to the $1$-Dim Schrödinger Like Equation
• Hawking radiation and Quasinormal modes

Cited by in corpus (8)

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• Black Bounces with multiple throats and anti-throats
• Vacuum fluctuation, micro-cyclic "universes" and the cosmological constant problem
• Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings
• Horizon of quantum black holes in various dimensions
• On Black Hole Thermodynamics, Singularity, and Gravitational Entropy
• Gauge theory at singularities