Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-12-21
Phys.Rev.D78:024021,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30 pages, LaTeX; v2. 38 pages, Major rewritting including: i) a new realisation of the proposed analogy giving a simple deriva
Scientific paper
10.1103/PhysRevD.78.024021
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. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we show that our approach leads to two-step exact derivation of the Papapetrou force on a gyroscope. We then establish a new proof for a class of tensor identities that define invariants of the type $\vec{E}^2-\vec{B}^2$ and $\vec{E}\cdot\vec{B}$, and we exhibit the invariants built from tidal tensors in both gravity and electromagnetism. We contrast our approach with the two gravito-electromagnetic analogies commonly found in the literature, and argue that it sheds light on the debate about the limit of validity of one of the analogies, and clarifies issues concerning the physical interpretation of the other.
Costa Filipe L.
Herdeiro Carlos A. R.
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