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A gravito-electromagnetic analogy based on tidal tensors by Luís Filipe P. O. Costa

Dec. 04 - 20:30 - 2008

<p>According to General Relativity, the way mass curves spacetime depends<br />on its motion. Just like the gravitational field of a mass at rest<br />resembles, under certain conditions, the Coulomb electric field, mass<br />currents give rise to effects which strongly resemble magnetism.<br /><br />In this talk we present a new approach (Phys. Rev. D 78 024021, 2008)<br />to explore the physical analogy between General Relativity and<br />Electromagnetism, based on tidal tensors of both theories. Our<br />proposal goes well beyond the previous approaches found in literature,<br />since it leads to an exact, covariant, and fully general form for the<br />physical gravitational analogues of Maxwell's equations. It also leads<br />to an exact and physically enlightening derivation of Papapetrou's<br />equation for the gravitational force exerted on a gyroscope.<br /><br />The tidal tensor formalism allows for a comparison between gravity and<br />electromagnetism in terms of quantities common to both theories,<br />making transparent the similarities and key differences between the<br />two interactions. Among the latter the absence of gravitational<br />induction effects (that have been predicted in the literature)<br />analogous to the electromagnetic ones, which is shown to explain<br />Hawking's [Phys Rev. Lett.  26, 1344 (1971)] spin-dependent upper<br />bound for the energy released when two black holes collide.<br /><br />Two special cases of matching between gravitational and<br />electromagnetic tidal tensors are discussed: one matches linearized<br />gravitational tidal tensors to exact electromagnetic tidal tensors in<br />Minkowski spacetime; in the other we reveal an exact matching between<br />magnetic gravitational tidal tensors from ultra-stationary spacetimes<br />and magnetic tidal tensors from electromagnetism in curved spaces.<br /><br />Analogous scalar invariants built from tidal tensors of both theories<br />are also discussed.<br /><br />Our approach clarifies some issues concerning other<br />gravito-electromagnetic analogies commonly found in the literature: it<br />sheds light on the debate about the limit of validity of the analogy<br />based on linearised theory (eg.  [arXiv: gr-qc/0207065]), and solves<br />conceptual difficulties in the physical interpretation of the analogy<br />based on the splitting of the Weyl tensor in electric and magnetic<br />parts (eg. [arXiv: gr-qc/9704059]), clarifying at the same time the<br />relationship between these two analogies.<br /><br />It also achieves an unification within gravito-electromagnetism, by<br />revealing that the analogy known from the linearized theory originates<br />from the same fundamental principle as the exact mapping (via the<br />Klein-Gordon equation) between ultra-stationary spacetimes and<br />magnetic fields in curved manifolds [arXiv: hep-th/0309199]. </p><p> </p><p>A gravito-electromagnetic analogy based on tidal tensors</p><p>Luís Filipe P. O. Costa - Centro de Física do Porto, Universidade do Porto<br /><br />4 Dezembro (quinta-feira) 14:30<br />Sala P6</p>

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