Static and spherically symmetric solutions in f(Q) gravity

Abstract

$f(Q)$ gravity is the extension of symmetric teleparallel general relativity (STGR), in which both curvature and torsion vanish and gravity is attributed to nonmetricity. This work performs theoretical analyses of static and spherically symmetric solutions with an anisotropic fluid for general $f(Q)$ gravity. We find that the off-diagonal component of the field equation due to a coincident gauge leads to stringent restrictions on the functional form of $f(Q)$ gravity. In addition, although the exact Schwarzschild solution only exists in STGR, we obtain Schwarzschild-like solutions in nontrivial $f(Q)$ gravity and study its asymptotic behavior and deviation from the exact one.