Ĭosta, L.F.O., Natário, J., Wylleman, L.: Work in progress (for a brief summary of the main results). Jantzen, R.T., Carini, P., Bini, D.: GEM: The User Manual (2004). Jantzen, R.T., Carini, P., Bini, D.: Ann. Thorne, Kip S., Price, R.H., Macdonald, D.A.: Black Holes, the Membrane Paradigm. Landau, L., Lifshitz, E.: The Classical Theory of Fields, 4th edn. (eds.) Reference Frames and Gravitomagnetism, p. Mashhoon, B.: In: Pascual-Sanchez, J.-F., Floria, L., San Miguel, A. Gralla, S., Harte, A.I., Wald, R.M.: Phys. (eds.) Near Zero: New Frontiers of Physics. Thorne, Kip S.: In: Fairbank, J.D., Deaver Jr., B.S., Everitt, C.W.F., Michelson, P.F. 4.4Ĭarroll, S.M.: Spacetime and Geometry. University of Chicago Press, Chicago (1984). Ruggiero, M.L., Tartaglia, A.: Il Nuovo Cimento B 117, 743 (2002) Ohanian, H.C., Ruffini, R.: Gravitation and Spacetime, 2nd ed. Princeton University, Princeton, NJ (1995) Paris 246, 3015 (1958)Ĭosta, L.F., Natário, J., Zilhão, M.: Ĭiufolini, I., Wheeler, J.A.: Gravitation and Inertia, Princeton Series in Physics. That means that (1.1b) holds for infinitesimally close curves belonging to an arbitrary geodesic congruence (it is in this sense that in e.g., \(\delta U\) is portrayed as “arbitrary”-it is understood to be infinitesimal therein, as those treatments deal with congruences of curves).Ĭosta, L.F., Herdeiro, C.A.R.: Phys. (1.1b) allows for an infinitesimal \(\delta U\propto \delta x\), as can be seen from Eq. (1.1a) requires strictly \(\delta \mathbf =0\), see , Eq. There is however a difference: whereas Eq. When the particles have arbitrary velocities, both in electromagnetism and gravity, their relative acceleration is not given by a simple contraction of a tidal tensor with a separation vector the equations include more terms, see. Equations (1.1) apply to the instant where the two particles have the same (or infinitesimally close, in the gravitational case) tangent vector. We want to emphasize this point, which, even today, is not clear in the literature. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. New results within each approach are unveiled. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. Both are reformulated, extended and generalized. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called “1+3 formalism”, and the analogy based on tidal tensors. Arrows along the lines point away from the circles.We reexamine and further develop different gravito-electromagnetic analogies found in the literature, and clarify the connection between them. Lines come out of each circle, begin to curve toward the point labeled P, then bend away from it as they get farther away from the circles. Between the circles is a point labeled P. The fourth type of field includes two circles, both with a positive sign. On the left side of the positive circle and right side of the negative circle, the lines curve away from the circles rather than connecting them together as they do in the second type. The third type of field also includes a positive and negative circle connected by lines in a similar pattern as the second type of field, but has over twice the number of lines. All arrows point away from the positive circle and toward the negative circle. One horizontal line runs between them, then curved lines come out from all around each circle and form concentric loops that connect the circles. The second type of field includes a circle with a positive sign on the left and a circle with a negative sign on the right. Several horizontal lines run between the bars and each has an arrow that points right. The first has two vertical bars, the left labeled with a positive sign and the right a negative sign.
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