arXiv:2504.12370v1 Announce Type: new
Abstract: In our previous work [Van de Moortel, The breakdown of weak null singularities, Duke Mathematical Journal 172 (15), 2957-3012, 2023], we showed that dynamical black holes formed in charged spherical collapse generically feature both a null weakly singular Cauchy horizon and a stronger (presumably spacelike) singularity, confirming a longstanding conjecture in the physics literature. However, this previous result, based on a contradiction argument, did not provide quantitative estimates on the stronger singularity.
In this study, we adopt a new approach by analyzing local initial data inside the black hole that are consistent with a breakdown of the Cauchy horizon. We prove that the remaining portion is spacelike and obtain sharp spacetime estimates near the null-spacelike transition. Notably, we show that the Kasner exponents of the spacelike portion are positive, in contrast to the well-known Oppenheimer-Snyder model of gravitational collapse. Moreover, these exponents degenerate to (1,0,0) towards the null-spacelike transition.
Our result provides the first quantitative instances of a null-spacelike singularity transition inside a black hole. In our companion paper, we moreover apply our analysis to carry out the construction of a large class of asymptotically flat one or two-ended black holes featuring coexisting null and spacelike singularities.
Future Roadmap
Challenges
- Quantitative estimation of the stronger singularity: The previous work did not provide quantitative estimates on the stronger singularity. This poses a challenge in understanding the nature and properties of this singularity.
- Analysis of local initial data: The new approach requires analyzing local initial data inside the black hole that are consistent with a breakdown of the Cauchy horizon. This may require advanced mathematical techniques and computational simulations.
- Construction of a large class of black holes: The companion paper aims to construct a large class of asymptotically flat one or two-ended black holes with coexisting null and spacelike singularities. This task may involve complex mathematical calculations and modeling.
Opportunities
- Confirmation of a longstanding conjecture: The study confirms a longstanding conjecture in the physics literature regarding the presence of both null weakly singular Cauchy horizons and stronger (presumably spacelike) singularities in dynamical black holes formed in charged spherical collapse. This provides an opportunity to further probe the nature of black holes and test existing theories.
- Understanding spacetime estimates near the null-spacelike transition: The new analysis provides sharp spacetime estimates near the null-spacelike transition. This opens up opportunities to investigate the behavior and characteristics of spacetime in the vicinity of this transition.
- Exploring the Kasner exponents: The discovery that the Kasner exponents of the spacelike portion are positive, in contrast to the Oppenheimer-Snyder model, presents an opportunity to study and understand the role of these exponents in black hole formation and evolution.
Conclusion: The future roadmap for readers of this study involves addressing the challenges of quantitatively estimating the stronger singularity, analyzing local initial data, and constructing a large class of black holes with coexisting singularities. These efforts present opportunities to confirm a longstanding conjecture, gain insights into spacetime estimates near the null-spacelike transition, and explore the significance of Kasner exponents in black hole dynamics.