Weak field limit and gravitational waves in f(T, B) teleparallel gravity

Abstract We derive the gravitational waves for $$f\left( T, B\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mfenced><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi></mml:mfenced></mml:mrow></mml:math> 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.

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