# Reconstructed black hole solutions in the scalar-tensor theory with nonminimal coupling

Source: [Reconstructed black hole solutions in the scalar-tensor theory with nonminimal coupling](<https://www.sota2.com/research/paper/69c36bf40636e5bf4afc63ba>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-26T05:00:04.122Z

Authors: K.K. Ernazarov

Published: 2026-03-23T19:25:45.000Z

## Abstract

We consider the scalar-tensor theory witn non-minimal coupling in the Jordan frame. The action of the model contains a potential term $U(\\varphi)$, a coupling function $f(\\varphi)$. We explore a reconstruction procedure for a generic static spherically symmetric metric written in the Buchdahl parametrization: $ds^2 = \\left(A(u)\\right)^{-1}du^2 - A(u)dt^2 + C(u)d\\Omega^2$, with given $A(u) \> 0$ and $C(u) \> 0$. The procedure gives the relations for $U(\\varphi(u))$, $f(\\varphi(u))$ and $d\\varphi/du$, which lead to exact solutions to equations of motion with a given metric. A key role in this approach is played by the solutions to a first order linear differential equation for the function $f(\\varphi(u))$. The formalism is illustrated by two examples when: a) the Reissner-Nordstr\\"om-(Anti-)de Sitter metric and b) the Bocharova-Bronnikov-Melnikov-Bekenstein-(Anti)de-Sitter metric are chosen as a starting point.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.22517>)

[PDF](<https://arxiv.org/pdf/2603.22517.pdf>)