Spherically-symmetric solutions with internal Ricci-flat spaces in Brans-Dicke theory
Abstract
We construct a new family of exact spherically symmetric solutions in D-dimensional Brans-Dicke theory with n internal Ricci-flat spaces. The spacetime is assumed to be a product of a four-dimensional spherical sector and n Ricci-flat internal manifolds. By performing a conformal transformation to the Einstein frame, the problem is reduced to Einstein gravity with a minimally coupled scalar field, for which the exact solution is already known. Applying the inverse transformation to the Jordan frame yields explicit expressions for the metric and the Brans-Dicke scalar field, together with a generalized algebraic constraint on the exponents. The obtained solutions generalize the four-dimensional Brans solutions and the multidimensional solutions with Ricci-flat internal spaces. We analyze the causal structure of the four-dimensional section and derive the necessary condition for the surface R=L to be an event horizon, ν≡ |a+b+1/2∑i aiNi| ≥ 1. A Kretschmann-scalar analysis shows that, apart from the Schwarzschild limit and the case of frozen internal spaces, a regular horizon is generically absent when the extra dimensions are dynamical. For the four-dimensional section we also obtain the photon-sphere and ISCO radii and discuss their Schwarzschild limits. The results clarify the role of nonminimal Brans-Dicke coupling in multidimensional black-hole geometries with Ricci-flat internal factors.
Related
- Exact solutions for static spherically symmetric spacetime with a perfect fluid in Rastall theory
- Spherically symmetric solutions in quasi-local Einstein-Weyl gravity
- On spherically symmetric Berwald vacuum solutions in Finsler gravity
- Spherically symmetric solutions with dust and radiation sources in Schouten-Codazzi Gravity
- Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities
BibTeX
@misc{ernazarov2026sphericallysymmetric,
title = {{Spherically-symmetric solutions with internal Ricci-flat spaces in Brans-Dicke theory}},
author = {K. K. Ernazarov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01691},
eprint = {2611.01691},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01691},
}
RIS
TY - UNPB
TI - Spherically-symmetric solutions with internal Ricci-flat spaces in Brans-Dicke theory
AU - K. K. Ernazarov
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01691
UR - https://arxiv.org/abs/2611.01691
AB - We construct a new family of exact spherically symmetric solutions in D-dimensional Brans-Dicke theory with n internal Ricci-flat spaces. The spacetime is assumed to be a product of a four-dimensional spherical sector and n Ricci-flat internal manifolds. By performing a conformal transformation to the Einstein frame, the problem is reduced to Einstein gravity with a minimally coupled scalar field, for which the exact solution is already known. Applying the inverse transformation to the Jordan frame yields explicit expressions for the metric and the Brans-Dicke scalar field, together with a generalized algebraic constraint on the exponents. The obtained solutions generalize the four-dimensional Brans solutions and the multidimensional solutions with Ricci-flat internal spaces. We analyze the causal structure of the four-dimensional section and derive the necessary condition for the surface R=L to be an event horizon, ν≡ |a+b+1/2∑_i a_iN_i| ≥ 1. A Kretschmann-scalar analysis shows that, apart from the Schwarzschild limit and the case of frozen internal spaces, a regular horizon is generically absent when the extra dimensions are dynamical. For the four-dimensional section we also obtain the photon-sphere and ISCO radii and discuss their Schwarzschild limits. The results clarify the role of nonminimal Brans-Dicke coupling in multidimensional black-hole geometries with Ricci-flat internal factors.
ER -