Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame

A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation scheme can be transformed to one in which perturbations all take place within the co-frame. A covariant definition of a teleparallel Minkowski geometry is proposed. We compute the perturbed field equations for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> teleparallel gravity and discuss the stability of the teleparallel Minkowski geometry within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> teleparallel gravity.

# Elementary particle physics # teleparallel gravity # teleparallel perturbation # constant torsion spacetimes # teleparallel Minkowski spacetime # perturbed teleparallel field equations # orthonormal perturbation

Alexandre Landry, Robert J. van den Hoogen (2023). "Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame". Universe. https://doi.org/10.3390/universe9050232