New Analogies Between Electromagnetic and Gravitational Fields Through the Bel-Robinson Tensor / Nuevas analogías entre los campos electromagnético y gravitacional a través del tensor de Bel-Robinson
Resumen
Abstract
Based on the 3+1 formalism for the formulation of an arbitrary reference frame and using the concept of electric and magnetic Weyl’s tensors, profound analogies between gravitational and electromagnetic field, its invariants, and specifically, among the energy-momentum field tensor in electromagnetic theory and Bel-Robinson’s (BR) or “super-energy” tensor in gravitation are established and discussed. In order to do that, original expressions for Weyl’s and BR’s tensors in terms of quasi-electric and quasi-magnetic fields were obtained. Furthermore, some theoretical consequences on the implications of the development of those analogies are outlined within the context of the yet to be directly proven experimental reality of gravitational waves.
Resumen
Basados en el formalism 3+1, con el cual es posible formular un sistema de referencia arbitrario en la
Teoría General de la Relatividad TGR, establecemos profundas analogías entre los campos gravitacional
y electromagnético. Para lograrlo se obtuvieron nuevas expresiones para los invariantes gravitacionales y del tensor de Bel Robinson a través de los campos de los tensores cuasi-eléctricos y cuasi-magnéticos de Weyl en gravitación. Adicionalmente, son brevemente discutidas algunas implicaciones teóricas de estas analogías en el contexto de la aún no verificada realidad experimental de las ondas gravitacionales.
Palabras clave
TGR’s interpretation, BR’s tensor, gravitoelectromagnetic stress-energy tensor, gravitational waves
Referencias
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