Constraints on the Nieh-Yan modified teleparallel gravity with gravitational waves

The equations for gravitational plane waves produced by a typical binary system as a solution of linear approximation of Einstein equations are derived. The dynamics of the corresponding gravitational field is analyzed in a four-dimensional space-time manifold, endowed with a metric and taking into account torsion. In this context, the geometrical reason of the existence of torsion due to the presence of gravitational waves (GW) is highlighted and the geodesic deviation is obtained taking into account both curvature and torsion. In a laser interferometer gravitational detector, the delay time between the arrivals of the two laser beams traveling back and forth along the two arms in presence of gravitational waves is interpreted from this point of view. This delay is calculated for the NS–NS binary pulsar (1913 + 16) in two specific orientations with respect to the experimental device, corresponding to different polarizations of gravitational waves. In the specific case of this example, it is shown that the results obtained in the context of the standard general relativity (GR) and in the framework of teleparallel gravity are equivalent.

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

The European Physical Journal C ◽

10.1140/epjc/s10052-020-7737-9 ◽

2020 ◽

Vol 80 (2) ◽

Cited By ~ 18

Author(s):

Salvatore Capozziello ◽

Maurizio Capriolo ◽

Loredana Caso

Keyword(s):

Gravitational Waves ◽

Teleparallel Gravity ◽

Weak Field ◽

Massive Scalar ◽

Tensor Polarization ◽

Field Equations ◽

Field Limit ◽

Weak Field Limit ◽

Limit Approximation ◽

Scalar Mode

Abstract We derive the gravitational waves for $$f\left( T, B\right) $$fT,B 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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ENERGY CONTENTS OF GRAVITATIONAL WAVES IN TELEPARALLEL GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732310031488 ◽

2010 ◽

Vol 25 (03) ◽

pp. 221-232 ◽

Cited By ~ 9

Author(s):

M. SHARIF ◽

SUMAIRA TAJ

Keyword(s):

General Relativity ◽

Angular Momentum ◽

Gravitational Waves ◽

Teleparallel Gravity ◽

Gravitational Energy ◽

Conserved Quantities ◽

Hamiltonian Approach ◽

Momentum Fluxes

The conserved quantities, that are, gravitational energy–momentum and its relevant quantities are investigated for cylindrical and spherical gravitational waves in the framework of teleparallel equivalent of General Relativity using the Hamiltonian approach. For both cylindrical and spherical gravitational waves, we obtain definite energy and constant momentum. The constant momentum shows consistency with the results available in General Relativity and teleparallel gravity. The angular momentum for cylindrical and spherical gravitational waves also turn out to be constant. Further, we evaluate their gravitational energy–momentum fluxes and gravitational pressure.

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