Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality

Abstract

We investigate a Schwarzschild metric exhibiting a signature change across the event horizon, which gives rise to what we term a Lorentzian-Euclidean black hole. The resulting geometry is regularized by employing the Hadamard partie finie technique, which allows us to prove that the metric represents a solution of vacuum Einstein equations. In this framework, we introduce the concept of atemporality as the dynamical mechanism responsible for the transition from a regime with a real-valued time variable to a new one featuring an imaginary time. We show that this mechanism prevents the occurrence of the singularity and, by means of the regularized Kretschmann invariant, we discuss in which terms atemporality can be considered as the characteristic feature of this black hole.

arXiv comment22 pages, 5 figures, accepted for publication in Phys. Rev. D

References in corpus (40)

• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Formation and evaporation of non-singular black holes
• Foundations of Black Hole Accretion Disk Theory
• Rotating regular black holes
• Problem of Time in Quantum Gravity
• On Gravitational Shock Waves in Curved Spacetimes
• Hadamard Regularization
• Dynamical renormalization of black-hole spacetimes
• Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes
• Selection Rules in Minisuperspace Quantum Cosmology
• The Origin of Time Asymmetry
• Kleinian Geometry and the N=2 Superstring
• The wave function discord
• Regularized Stable Kerr Black Hole: Cosmic Censorships, Shadow and Quasi-Normal Modes
• Geodesic motion in Euclidean Schwarzschild geometry
• Signature Change on the Brane
• Gravity and Signature Change
• Nonsingular bouncing cosmology in general relativity: physical analysis of the spacetime defect
• Signature change in loop quantum gravity: General midisuperspace models and dilaton gravity
• Regularized big bang singularity
• Nonsingular bouncing cosmology from general relativity
• Einstein's Equations in the Presence of Signature Change
• Sub-leading contributions to the black hole entropy in the brick wall approach
• Ordered magnetic fields around the 3C 84 central black hole
• Signature change in matrix model solutions
• Comment on "Failure of standard conservation laws at a classical change of signature"
• More on the regularized big bang singularity
• A new type of nonsingular black-hole solution in general relativity
• Signature change induces compactification
• Light-like Signals in General relativity and Cosmology
• Loop quantum gravity, signature change, and the no-boundary proposal
• Black-hole solution without curvature singularity
• Cut-and-paste for impulsive gravitational waves with $\Lambda$: The geometric picture
• On boosted space-times with cosmological constant and their ultrarelativistic limit
• Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita--Bertotti--Robinson
• Riemann curvature of a boosted spacetime geometry
• Unitary and Vilenkin's wave functions
• Geometrogenesis in GFT: An Analysis
• Particle dynamics in spherically symmetric electro-vacuum instantons
• Signature transition and compactification

Cited by in corpus (36)

• Static neutral black holes in Kalb-Ramond gravity
• Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
• Atemporality from Conservation Laws of Physics in Lorentzian-Euclidean Black Hole
• Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes
• Preserving quantum information in $f(Q)$ cosmology
• Formation of regular black hole from baryonic matter
• Primordial regular black holes as all the dark matter. III. Covariant canonical quantum gravity models
• Frolov Black Hole Surrounded by Quintessence -- I: Thermodynamics, Geodesics and Shadows
• Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
• Extremely small stars in scalar-tensor gravity: when stellar radius is less than Schwarzschild one
• Grey-body factors of higher dimensional regular black holes in quasi-topological theories
• Testing black holes with cosmological constant in Einstein-bumblebee gravity through the black hole shadow using EHT data and deflection angle
• Conundrum of regular black holes with nonlinear electromagnetic fields
• Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes
• Acceleration Radiation of Freely Falling Atoms: Nonlinear Electrodynamic Effects
• Dyonic regular black bounce solutions in General Relativity
• Gauss-Bonnet lensing of spinning massive particles in static spherically symmetric spacetimes
• Boundary-only weak deflection angles from isothermal optical geometry
• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• Extension of Buchdahl's Theorem on Reciprocal Solutions
• General Framework for the Spontaneous Scalarization of Regular Black Holes
• Shadows of a Non-Commutative Black Hole under the Influence of a Magnetized Plasma
• Lorentzian-Euclidean black holes and Lorentzian to Riemannian metric transitions
• Overcharging a nonsingular black hole in general relativity: the nonlinear electrodynamic field effects
• The Hybrid Euclidean-Lorentzian Universe: Stability Considerations and the Point of Transition
• Charge constraint on M87* with twisted light
• Uncertainty Principles and Non-local Black Holes
• Energy conditions in static, spherically symmetric spacetimes and effective geometries
• Gravitational waveforms from periodic orbits around a novel regular black hole
• Horizon-Brightened Acceleration Radiation and Optical Signatures of Generic Regular Black Holes from Nonlinear Electrodynamics
• Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model
• Thermodynamic Phase Transitions and Quantum Entropy Corrections in the Simpson-Visser Regular Black Hole
• Analytical approach for calculating shadow of dynamical black hole
• Lorentz-violating modifications to particle dynamics, thermodynamics and vacuum energy in bumblebee gravity
• Lorentzian-Euclidean singularity-free solutions to gravitational collapse
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations