Black Holes With Complete Asymptotic Throats
Abstract
We investigate whether a spherically symmetric black hole can have a complete inner end at finite, nonzero areal radius while satisfying the standard energy conditions sufficiently far outside its horizon. Retaining two independent metric functions, we treat both null-type and spacelike-type asymptotic throats and derive a necessary and sufficient integral criterion for causal geodesic completeness. Under boundedness and finite-limit assumptions on the independent curvature components, null-type ends have limiting curvature fixed by the throat radius, whereas spacelike-type ends admit an additional nonnegative curvature parameter. We obtain criteria for bounded curvature in timelike and null parallel-propagated frames. Complete spacelike-type examples can have bounded scalar invariants and bounded timelike-frame curvature but unbounded null-frame curvature at infinite affine parameter. We also prove that the radial null energy condition must fail arbitrarily close to every complete inner end in the stated class. Nevertheless, explicit real-analytic constructions with either type of throat satisfy the null, weak, dominant, and strong energy conditions throughout a sufficiently distant exterior region. Smooth constructions can become exactly Schwarzschild beyond a finite radius. These results establish the compatibility of complete asymptotic throats with exterior energy conditions while distinguishing completeness from different levels of curvature regularity.
Related
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- Extremal black hole throats from non extremal near horizon expansions
- Asymptotic expansion of cavity Quasi-Normal Modes in Schwarzschild de-Sitter black hole
- Local scale symmetry and black holes
BibTeX
@misc{liang2026black,
title = {{Black Holes With Complete Asymptotic Throats}},
author = {Yi-Bo Liang and Hong-Rong Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39186},
eprint = {2609.39186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39186},
}
RIS
TY - UNPB
TI - Black Holes With Complete Asymptotic Throats
AU - Yi-Bo Liang
AU - Hong-Rong Li
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39186
UR - https://arxiv.org/abs/2609.39186
AB - We investigate whether a spherically symmetric black hole can have a complete inner end at finite, nonzero areal radius while satisfying the standard energy conditions sufficiently far outside its horizon. Retaining two independent metric functions, we treat both null-type and spacelike-type asymptotic throats and derive a necessary and sufficient integral criterion for causal geodesic completeness. Under boundedness and finite-limit assumptions on the independent curvature components, null-type ends have limiting curvature fixed by the throat radius, whereas spacelike-type ends admit an additional nonnegative curvature parameter. We obtain criteria for bounded curvature in timelike and null parallel-propagated frames. Complete spacelike-type examples can have bounded scalar invariants and bounded timelike-frame curvature but unbounded null-frame curvature at infinite affine parameter. We also prove that the radial null energy condition must fail arbitrarily close to every complete inner end in the stated class. Nevertheless, explicit real-analytic constructions with either type of throat satisfy the null, weak, dominant, and strong energy conditions throughout a sufficiently distant exterior region. Smooth constructions can become exactly Schwarzschild beyond a finite radius. These results establish the compatibility of complete asymptotic throats with exterior energy conditions while distinguishing completeness from different levels of curvature regularity.
ER -