Singularity and differentiability at the origin of static and spherically symmetric black holes
arXiv:2509.15477 · doi:10.1103/hf4r-19xh
Abstract
The divergence of curvature invariants at a given point signals the impossibility of extending the spacetime to that point, with the derivative order of these diverging invariants determining the differentiability class of the considered spacetime. We hereby focus on a general static and spherically symmetric geometry and determine, in the full non-linear regime and in a model-independent way, the conditions that the metric functions must satisfy in order to achieve finiteness of all curvature invariants at the origin. Our findings have direct implications regarding the extendibility of such spacetimes, which we illustrate by making explicit examples of various black hole geometries. This work is structured around a central theorem, which relates the finiteness of curvature invariants at the origin to the leading order behavior and parity properties of the metric functions. The detailed proof of this theorem constitutes the main result of the paper.
25 pages
References in corpus (46)
- Formation and evaporation of non-singular black holes
- Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics
- The Bardeen Model as a Nonlinear Magnetic Monopole
- Noncommutative geometry inspired Schwarzschild black hole
- Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics
- Super-renormalizable Quantum Gravity
- Renormalization group improved black hole spacetimes
- Rotating regular black holes
- Construction of Regular Black Holes in General Relativity
- Regular phantom black holes
- Regular black holes with a nonlinear electrodynamics source
- Black-bounce to traversable wormhole
- Cosmological term as a source of mass
- Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure
- Regular black holes: Electrically charged solutions, Reissner-Nordström outside a de Sitter core
- Regular black holes with asymptotically Minkowski cores
- Field sources for Simpson-Visser space-times
- On a regular charged black hole with a nonlinear electric source
- Charged black-bounce spacetimes
- Quantum Corrected Black Holes from String T-Duality
- Spacetime completeness of non-singular black holes in conformal gravity
- Quantum radiation from an evaporating non-singular black hole
- On the Effective Metric of a Planck Star
- Singularities and the Finale of Black Hole Evaporation
- Matter and gravitons in the gravitational collapse
- On the fate of singularities and horizons in higher derivative gravity
- Towards a Non-singular Paradigm of Black Hole Physics
- Geodesic incompleteness of some popular regular black holes
- Quantum corpuscular corrections to the Newtonian potential
- Regular hairy black holes through Minkowski deformation
- Space-Times with Integrable Singularity
- Regular Black Holes: Towards a New Paradigm of Gravitational Collapse
- A Safe Beginning for the Universe?
- Action principle selection of regular black holes
- Cosmological consequences of a principle of finite amplitudes
- Schwarzschild black hole revisited: Before the complete collapse
- Higher-order regularity in local and nonlocal quantum gravity
- Instability of nonsingular black holes in nonlinear electrodynamics
- Finite Action Principle Revisited
- A critical appraisal of the singularity theorems
- Suppression of spacetime singularities in quantum gravity
- Physical and Theoretical Challenges to Integrable Singularities
- A non-local way around the no-global-symmetries conjecture in quantum gravity?
- Singularities in Quantum Corrected Space-times
- What happens to topological invariants (and black holes) in singularity-free theories?
- Coherent electrically-charged quantum black holes