Static, spherically symmetric solutions in $f(Q)$-gravity and in nonmetricity scalar-tensor theory

TL;DR

This paper derives new static, spherically symmetric solutions in $f(Q)$ gravity and nonmetricity scalar-tensor theory, analyzing their physical properties, conservation laws, and relation to general relativity.

Contribution

It introduces novel solutions within power-law $f(Q)$ gravity and scalar-tensor theory, including the derivation of the point-like Lagrangian and conservation laws.

Findings

New solutions for static, spherically symmetric spacetimes

Analysis of physical properties and GR limit

Construction of conservation laws and analytical solutions

Abstract

We solve the gravitational field equations for a static, spherically symmetric spacetime within the framework of the symmetric teleparallel theory of gravity. Specifically, we derive new solutions within the context of power-law $f(Q)$ gravity and the nonmetricity scalar-tensor theory. For the connection in the non-coincidence gauge, we present the point-like Lagrangian that describes the employed field equations. Furthermore, we construct two conservation laws, and for different values of these conserved quantities, we analytically solve the gravitational field equations. New solutions are obtained, we investigate their physical properties and their general relativistic limit. Finally, we discuss the algebraic properties for the derived spacetimes.