Novel ansatzes and scalar quantities in gravitoelectromagnetism
Abstract
In this work, we focus on the theory of gravitoelectromagnetism (GEM)—the theory that describes the dynamics of the gravitational field in terms of quantities met in electromagnetism—and we propose two novel forms of metric perturbations. The first one is a generalisation of the traditional GEM ansatz, and succeeds in reproducing the whole set of Maxwell's equations even for a dynamical vector potential A. The second form, the socalled alternative ansatz, goes beyond that leading to an expression for the Lorentz force that matches the one of electromagnetism and is free of additional terms even for a dynamical scalar potential Φ. In the context of the linearised theory, we then search for scalar invariant quantities in analogy to electromagnetism. We define three novel, 3rdrank gravitational tensors, and demonstrate that the last two can be employed to construct scalar quantities that succeed in giving results very similar to those found in electromagnetism. Finally, the gauge invariance of the linearised gravitational theory is studied, and shown to lead to the gauge invariance of the GEM fields E and B for a general configuration of the arbitrary vector involved in the coordinate transformations.
 Publication:

General Relativity and Gravitation
 Pub Date:
 March 2017
 DOI:
 10.1007/s107140172207x
 arXiv:
 arXiv:1610.09819
 Bibcode:
 2017GReGr..49...44B
 Keywords:

 General relativity;
 Gravitoelectromagnetism;
 Maxwell equations;
 Lorentz force;
 Scalar invariants;
 Gauge invariance;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
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