Gravitoelectromagnetic analogy based on tidal tensors
Abstract
We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we show that our approach leads to a twostep exact derivation of Papapetrou’s equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.
 Publication:

Physical Review D
 Pub Date:
 July 2008
 DOI:
 10.1103/PhysRevD.78.024021
 arXiv:
 arXiv:grqc/0612140
 Bibcode:
 2008PhRvD..78b4021C
 Keywords:

 04.20.Cv;
 03.50.De;
 04.80.Cc;
 Fundamental problems and general formalism;
 Classical electromagnetism Maxwell equations;
 Experimental tests of gravitational theories;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 30 pages, LaTeX