Black hole and wormhole branches in gravitational decoupling
Abstract
Minimal Geometric Deformation (MGD) applied to a static Schwarzschild black hole seed generates a single decoupler function h(r), obtained by solving the θ-sector field equations together with an equation of state. Once h(r) is fixed, the resulting one-parameter family is controlled by the coupling strength k through F(r;k)=1+k h(r). We show that, whenever the deformation develops a simple outermost root that crosses the seed horizon, the same fixed decoupler leads to two mutually exclusive branches associated with different global completions: on one side of the critical coupling the deformed metric preserves the seed horizon as a black hole, whereas on the other side the root r*>2M lies in the exterior and cannot be interpreted as an interior modification of the black hole geometry. We prove that this root forces a loss of Lorentzian signature on the interval (2M,r*), so that no smooth extension of the exterior metric through the seed horizon r=2M exists once r* lies outside it. Within the static, spherically symmetric class considered here, the corresponding smooth Lorentzian completion is a two-ended wormhole obtained by excising (2M,r*) and doubling the region r≥ r* across the minimal sphere 𝒯={r=r*}. No topology change of any single spacetime is claimed or required: k>kc and k<kc simply correspond to two different, non-diffeomorphic manifolds, and Lemma~1 below shows that the metric itself dictates which of the two is the admissible completion for a given k. We compute the second homology group of both completions explicitly, H2(ΣBH,ℋ)=0 for the black hole exterior relative to its horizon and H2(ΣWH)≅ℤ for the completed wormhole manifold, giving a discrete invariant that distinguishes the two branches.
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BibTeX
@misc{telloortiz2026black,
title = {{Black hole and wormhole branches in gravitational decoupling}},
author = {Francisco Tello-Ortiz and Y. Gomez-Leyton and Vitalii Vertogradov and Jean Baez Cuevas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10102},
eprint = {2609.10102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10102},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Black hole and wormhole branches in gravitational decoupling
AU - Francisco Tello-Ortiz
AU - Y. Gomez-Leyton
AU - Vitalii Vertogradov
AU - Jean Baez Cuevas
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10102
UR - https://arxiv.org/abs/2609.10102
AB - Minimal Geometric Deformation (MGD) applied to a static Schwarzschild black hole seed generates a single decoupler function h(r), obtained by solving the θ-sector field equations together with an equation of state. Once h(r) is fixed, the resulting one-parameter family is controlled by the coupling strength k through F(r;k)=1+k h(r). We show that, whenever the deformation develops a simple outermost root that crosses the seed horizon, the same fixed decoupler leads to two mutually exclusive branches associated with different global completions: on one side of the critical coupling the deformed metric preserves the seed horizon as a black hole, whereas on the other side the root r_*>2M lies in the exterior and cannot be interpreted as an interior modification of the black hole geometry. We prove that this root forces a loss of Lorentzian signature on the interval (2M,r_*), so that no smooth extension of the exterior metric through the seed horizon r=2M exists once r_* lies outside it. Within the static, spherically symmetric class considered here, the corresponding smooth Lorentzian completion is a two-ended wormhole obtained by excising (2M,r_*) and doubling the region r≥ r_* across the minimal sphere 𝒯={r=r_*}. No topology change of any single spacetime is claimed or required: k>k_c and k<k_c simply correspond to two different, non-diffeomorphic manifolds, and Lemma~1 below shows that the metric itself dictates which of the two is the admissible completion for a given k. We compute the second homology group of both completions explicitly, H_2(Σ_BH,ℋ)=0 for the black hole exterior relative to its horizon and H_2(Σ_WH)≅ℤ for the completed wormhole manifold, giving a discrete invariant that distinguishes the two branches.
ER -