Violations of the null convergence condition in kinematical transitions between singular and regular black holes, horizonless compact objects, and bounces

Abstract

How do regular black holes evade the Penrose singularity theorem? Various models of stationary regular black holes globally satisfy the null convergence condition (NCC). At first glance this might seem puzzling, as the NCC must generically be violated to avoid the focusing point implied by the Penrose theorem. In fact, the Penrose singularity theorem depends on subtle global assumptions and does not provide information about where and when the singularity actually forms. In particular inner horizons are typically reached at finite affine parameter, before null geodesic focusing occurs, and the region inside the inner horizon is not itself a trapped region. Specifically, the Bardeen, Dymnikova, Hayward models of stationary regular black holes feature an inner Cauchy horizon which violates global hyperbolicity, hence violating one of the key assumptions of Penrose's singularity theorem, and furthermore challenging their viability as long-living end-points of gravitational collapse. In contrast, during non-stationary processes describing kinematic transitions between standard singular black holes and regular black holes or horizonless compact objects, the inner horizon -- when present -- need not act as a Cauchy horizon. This raises the intriguing possibility that the NCC might instead be violated during intermediate stages of such transitions. Our detailed analysis confirms that NCC violations occur frequently during such kinematic transitions, even when the stationary end-point spacetimes respect the NCC. We also investigate analogous transitions toward black-bounce spacetimes and their horizonless compact counterparts, wormholes, where the NCC is always violated. These findings offer new insights into how regular black holes and related objects evade the constraints imposed by the Penrose singularity theorem.

v3: 22 pages; discussion extended; published version

References in corpus (25)

• Formation and evaporation of non-singular black holes
• Isolated and dynamical horizons and their applications
• Black-bounce to traversable wormhole
• Twilight for the energy conditions?
• The 1965 Penrose singularity theorem
• A Primer on Energy Conditions
• Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure
• On the viability of regular black holes
• Geodesically complete black holes
• Regular black holes with asymptotically Minkowski cores
• Charged black-bounce spacetimes
• Quantum Instability of the Cauchy Horizon in Reissner-Nordström-deSitter Spacetime
• Inner horizon instability and the unstable cores of regular black holes
• Physical observability of horizons
• Dynamic thin-shell black-bounce traversable wormholes
• Opening the Pandora's box at the core of black holes
• Black Holes, AdS, and CFTs
• The Generalized Second Law implies a Quantum Singularity Theorem
• Semiclassical energy conditions for quantum vacuum states
• Classical and quantum flux energy conditions for quantum vacuum states
• Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT
• Hawking radiation inside a rotating black hole
• Backreaction from quantum fluxes at the Kerr inner horizon
• The Unruh vacuum and the in-vacuum in the Reissner-Nordström spacetime
• Fully extremal black holes: a black hole graveyard?

Cited by in corpus (11)

• Regular Black Hole Models in the Transition from Baryonic Matter to Quark Matter
• Regular black holes from pure gravity in four dimensions
• On Schwarzschild black hole singularity formation
• How Much NEC Breaking Can the Universe Endure?
• From de Sitter to anti-de Sitter singularity regularization: Theory and phenomenology
• Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities
• Roche limit and stellar disruption in the Simpson--Visser spacetime
• Energy conditions in static, spherically symmetric spacetimes and effective geometries
• Interior evolution of regular Schwarzschild black holes
• Quantum dynamics and thermodynamics of a Minkowski-Minkowski wormhole
• The spacetime geodesy of perfect fluid spheres