Asymptotically flat black holes with a singular Cauchy horizon and a spacelike singularity
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910064194879488 |
|---|---|
| author | Van de Moortel, Maxime |
| author_facet | Van de Moortel, Maxime |
| contents | In our recent work [Van de Moortel, The coexistence of null and spacelike singularities inside spherically symmetric black holes], we analyzed the transition between null and spacelike singularities in spherically symmetric dynamical black holes and demonstrated that the spacelike portion is described by a Kasner metric with positive varying exponents that degenerate to $(1,0,0)$ near the null-spacelike transition. In the present paper, we provide examples of global spacetimes satisfying the assumptions of this previous result and apply its analysis to obtain a large class of asymptotically flat (spherically symmetric) black hole spacetimes that exhibit coexisting null and spacelike singularities. Our main results include:
_The construction of one-ended asymptotically flat black hole spacetimes solving the Einstein-Maxwell-charged-scalar-field equations. The proof relies on a new spacelike-characteristic gluing method between any uncharged spherically symmetric solution and the event horizon of a charged dynamical black hole.
_The construction of a large class of two-ended asymptotically flat black hole spacetimes solving the Einstein-Maxwell-(uncharged)-scalar-field equations.
In both cases, we show that the terminal boundary in the black hole interior only has two distinct components: a weakly singular (null) Cauchy horizon $\mathcal{CH}_{i^+}$ where curvature blows up and a strong singularity $\mathcal{S}=\{r=0\}$.
Our construction provides the first examples of black holes with coexisting null and spacelike singularities. These examples hold particular significance in the one-ended case as a model of gravitational collapse, where this phenomenon is conjecturally generic for the Einstein-scalar-field model, even beyond spherical symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically flat black holes with a singular Cauchy horizon and a spacelike singularity Van de Moortel, Maxime General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Differential Geometry In our recent work [Van de Moortel, The coexistence of null and spacelike singularities inside spherically symmetric black holes], we analyzed the transition between null and spacelike singularities in spherically symmetric dynamical black holes and demonstrated that the spacelike portion is described by a Kasner metric with positive varying exponents that degenerate to $(1,0,0)$ near the null-spacelike transition. In the present paper, we provide examples of global spacetimes satisfying the assumptions of this previous result and apply its analysis to obtain a large class of asymptotically flat (spherically symmetric) black hole spacetimes that exhibit coexisting null and spacelike singularities. Our main results include: _The construction of one-ended asymptotically flat black hole spacetimes solving the Einstein-Maxwell-charged-scalar-field equations. The proof relies on a new spacelike-characteristic gluing method between any uncharged spherically symmetric solution and the event horizon of a charged dynamical black hole. _The construction of a large class of two-ended asymptotically flat black hole spacetimes solving the Einstein-Maxwell-(uncharged)-scalar-field equations. In both cases, we show that the terminal boundary in the black hole interior only has two distinct components: a weakly singular (null) Cauchy horizon $\mathcal{CH}_{i^+}$ where curvature blows up and a strong singularity $\mathcal{S}=\{r=0\}$. Our construction provides the first examples of black holes with coexisting null and spacelike singularities. These examples hold particular significance in the one-ended case as a model of gravitational collapse, where this phenomenon is conjecturally generic for the Einstein-scalar-field model, even beyond spherical symmetry. |
| title | Asymptotically flat black holes with a singular Cauchy horizon and a spacelike singularity |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2510.07431 |