A computer assisted existence proof for a non-Schwarzschild black hole in Einstein--Weyl gravity
Abstract
Static, asymptotically flat, non-Schwarzschild black holes in four-dimensional Einstein--Weyl gravity have previously been constructed by numerical shooting, while the local field equations admit horizon and asymptotic expansions to all orders. We give a computer assisted existence proof for a non-Schwarzschild solution whose dimensionless horizon radius is one in units of the massive spin-two scale, with parameters close to the previously reported numerical branch. The exterior is divided into a convergent horizon series domain, a compact core enclosed by a parameter dependent Taylor model with directed rounding, and an infinite asymptotic domain treated as a centered stable manifold fixed point problem. The resulting five-dimensional matching map between the core and tail is continuous on a rigorously specified box. After exact rational preconditioning, the signs on opposite faces satisfy the hypotheses of the Poincaré--Miranda theorem and therefore certify a matching zero. The solution has a regular nondegenerate horizon, no additional exterior horizon, vanishing Ricci scalar, and nonvanishing Ricci tensor. The strict bounds also imply existence at every sufficiently nearby horizon radius and a local continuous family at fixed coupling. The proof establishes existence, but not uniqueness of the matching zero.
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BibTeX
@misc{goldstein2026computer,
title = {{A computer assisted existence proof for a non-Schwarzschild black hole in Einstein--Weyl gravity}},
author = {Kevin Goldstein and Vishnu Jejjala},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.21797},
eprint = {2609.21797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21797},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A computer assisted existence proof for a non-Schwarzschild black hole in Einstein--Weyl gravity
AU - Kevin Goldstein
AU - Vishnu Jejjala
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.21797
UR - https://arxiv.org/abs/2609.21797
AB - Static, asymptotically flat, non-Schwarzschild black holes in four-dimensional Einstein--Weyl gravity have previously been constructed by numerical shooting, while the local field equations admit horizon and asymptotic expansions to all orders. We give a computer assisted existence proof for a non-Schwarzschild solution whose dimensionless horizon radius is one in units of the massive spin-two scale, with parameters close to the previously reported numerical branch. The exterior is divided into a convergent horizon series domain, a compact core enclosed by a parameter dependent Taylor model with directed rounding, and an infinite asymptotic domain treated as a centered stable manifold fixed point problem. The resulting five-dimensional matching map between the core and tail is continuous on a rigorously specified box. After exact rational preconditioning, the signs on opposite faces satisfy the hypotheses of the Poincaré--Miranda theorem and therefore certify a matching zero. The solution has a regular nondegenerate horizon, no additional exterior horizon, vanishing Ricci scalar, and nonvanishing Ricci tensor. The strict bounds also imply existence at every sufficiently nearby horizon radius and a local continuous family at fixed coupling. The proof establishes existence, but not uniqueness of the matching zero.
ER -