No further gravitational wave modes in $F(T)$ gravity

TL;DR

This paper demonstrates that $F(T)$ gravity does not introduce additional gravitational wave modes beyond those predicted by General Relativity, confirmed through Minkowskian limit calculations and weak field analysis.

Contribution

The study explicitly shows that $F(T)$ gravity's gravitational wave modes are equivalent to those in General Relativity, clarifying the theory's predictions for gravitational waves.

Findings

Gravitational wave modes in $F(T)$ gravity match those in General Relativity.

Minkowskian limit analysis confirms no extra modes.

Weak field analysis supports the equivalence of wave modes.

Abstract

We explore the possibility of further gravitational wave modes in $F(T)$ gravity, where $T$ is the torsion scalar in teleparallelism. It is explicitly demonstrated that gravitational wave modes in $F(T)$ gravity are equivalent to those in General Relativity. This result is achieved by calculating the Minkowskian limit for a class of analytic function of $F(T)$. This consequence is also confirmed by the preservative analysis around the flat background in the weak field limit with the scalar-tensor representation of $F(T)$ gravity.