Abstract
We derive the gravitational waves for fleft( T, Bright) gravity which is an extension of teleparallel gravity and demonstrate that it is equivalent to f(R) gravity by linearized the field equations in the weak field limit approximation. f(T, B) gravity shows three polarizations: the two standard of general relativity, plus and cross, which are purely transverse with two-helicity, massless tensor polarization modes, and an additional massive scalar mode with zero-helicity. The last one is a mix of longitudinal and transverse breathing scalar polarization modes. 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.
Highlights
[1,2,3], is equivalent to GR and was named Teleparallel Equivalent General Relativity (TEGR), in the sense that it describes the same physics because it gives the same field equations of GR
The f (T ) teleparallel gravity differs from f (R) gravity because the former leads to second-order field equations while the latter leads to fourth order field equations in metric formalism
We investigate gravitational waves (GWs) generated in theories containing the torsion scalar T and the boundary term B and show, from this point of view, their equivalence with f (R) gravity
Summary
[1,2,3], is equivalent to GR and was named Teleparallel Equivalent General Relativity (TEGR), in the sense that it describes the same physics because it gives the same field equations of GR. The teleparallel theory of gravity f (T, B) is the teleparallel equivalent of f (R) as the TEGR is the teleparallel equivalent of GR as we will show below by considering the weak field limit and the gravitational wave modes. In generic metric theories of gravity, it is possible to show that the GWs polarizations can give, at maximum of six modes in 4D spacetimes. In order to study the further GW polarizations, beyond the two standards plus and cross modes, it is useful to extend GR to more general theories. We investigate GWs generated in theories containing the torsion scalar T and the boundary term B and show, from this point of view, their equivalence with f (R) gravity.
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