Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity

TL;DR

This paper derives gravitational wave solutions in $f(T,B)$ gravity, revealing three polarization modes including a novel massive scalar mode, and demonstrates its equivalence to $f(R)$ gravity.

Contribution

It introduces the gravitational wave polarizations in $f(T,B)$ gravity and shows the emergence of a massive scalar polarization mode.

Findings

Three polarization modes: plus, cross, and a massive scalar.

The scalar mode is a mix of longitudinal and breathing modes.

The theory is equivalent to $f(R)$ gravity in terms of gravitational wave solutions.

Abstract

We derive the gravitational waves for $f\left(T, B\right)$ gravity, an extension of teleparallel gravity containing the torsion scalar $T$ and the boundary term $B$, and demonstrate that it is equivalent to $f(R)$ gravity. Gravitational waves, in this theory, show three polarizations: the two standard, plus and cross, of General Relativity, which are purely transverse, massless tensor polarization modes with two-helicity, and an additional massive scalar mode with zero-helicity. The last one is a mix of a longitudinal mode and a transverse breathing mode. The boundary term $B$ excites the extra scalar polarization and the mass of scalar field breaks the symmetry of the TT gauge by adding a new degree of freedom, namely a single mixed scalar polarization.