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

TL;DR

This paper investigates how regular black holes and horizonless objects can evade the Penrose singularity theorem by analyzing violations of the null convergence condition during dynamic transitions, revealing that NCC violations are common in such processes.

Contribution

The study demonstrates that NCC violations frequently occur during non-stationary transitions between black hole states, providing new understanding of how regular black holes circumvent singularity formation.

Findings

NCC violations occur during kinematic transitions between black hole states.

Transitions toward horizonless objects and wormholes involve consistent NCC violations.

Stationary regular black holes can satisfy NCC, but dynamic processes often violate it.

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.