McVittie solution in f(T) gravity

TL;DR

This paper demonstrates that the McVittie solution, describing a black hole in an expanding universe, remains valid in f(T) gravity, and explores the conditions under which FLRW geometries are solutions in this modified gravity theory.

Contribution

It shows that the McVittie solution persists in f(T) gravity and identifies multiple conditions under which FLRW solutions are valid, highlighting the theory's additional degrees of freedom.

Findings

McVittie geometry is a non-deformable solution in f(T) gravity.

Flat FLRW geometry is a solution for T=-6H^2 and T=0.

f(T) gravity admits solutions with different torsion scalars, indicating extra degrees of freedom.

Abstract

We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for $T=-6H^{2}$ but also for $T=0$, which could be a manifestation of the additional degrees of freedom involved in f(T) theories.