Rotating and spatially twisting Locally Rotationally Symmetric Spacetimes in f(R)-Gravity: a No-Go theorem

TL;DR

This paper investigates whether rotating and twisting locally rotationally symmetric spacetimes can exist in f(R)-gravity, concluding that such spacetimes enforce the theory to reduce to general relativity due to symmetry constraints.

Contribution

It demonstrates that the symmetries of these spacetimes restrict f(R)-gravity to be equivalent to general relativity, highlighting how spacetime geometry constrains gravitational theories.

Findings

Symmetries force f(R)-gravity to reduce to GR.

Rotating and twisting LRS spacetimes cannot exist in generic f(R)-gravity.

Higher order curvature effects do not generate entropy flux in these spacetimes.

Abstract

Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and dynamic astrophysical bodies. However, these spacetimes necessarily require imperfect fluids with entropy flux. Therefore, in this paper, we investigate the existence of these spacetimes in generic f(R)-gravity models, where the entropy flux is generated purely by higher order curvature effects, while the standard matter still remains a perfect fluid. However, we transparently demonstrate here, that the symmetries of these spacetimes force the theory to be general relativity. This is a novel study that shows how the geometrical properties of a spacetime can be used to restrict the theories of gravity.