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

Understand

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.