Gravito-electromagnetism

We propose a step-by-step manual for the construction of alternative theories of gravity, perturbatively as well as nonperturbatively. The construction is guided by no more than two fundamental principles that we impose on the gravitational dynamics: invariance under spacetime diffeomorphisms and causal compatibility with given matter dynamics, provided that spacetime is additionally endowed with matter fields. The developed framework then guides the computation of the most g...

Drawing an analogy between gravity dynamical equation of motion and that of Maxwell electrodynamics with an electric source we outline a way of appearance of a dual to graviton field. We propose a dimensional reduction ansatz for the field strength of this field which reproduces the correct duality relations between fields arising in the dimensional reduction of D-dimensional gravity action to D-1 dimensions. Modifying the PST approach we construct a new term entering the act...

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. F...

Two modern programs involving analogies between general relativity and electromagnetism, gravito-electromagnetism (GEM) and the classical double copy (CDC), induce electromagnetic potentials from specific classes of spacetime metrics. We demonstrate such electromagnetic potentials are gauge equivalent to Killing vectors present in the spacetime, long known themselves to be analogous to electromagnetic potentials. We utilize this perspective to relate the Type D Weyl double co...

We develop a gauge theory of the combined gravitational-electromagnetic field by expanding the Poincar\'e group to include clock synchronization transformations. We show that the electromagnetic field can be interpreted as a local gauge theory of the synchrony group. According to this interpretation, the electromagnetic field equations possess nonlinear terms and electromagnetic gauge transformations acquire a space-time interpretation as local synchrony transformations. The ...

There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers whether Mother Nature may have used the same basic pattern for her laws of gravitation and electrodynamics, in which case the CEs might be viewed as the field equations of gravitation in place of Einstein's equation. This is not a new theory o...

We discuss the linear gravitoelectromagnetic approach used to solve Einstein equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the Solar System, where the approximation holds true. In particular, we discuss the analogy according to which Einstein equations can be written as Maxwell-like equations and focus on the definition of the gravitoelectromagnetic fields in n...

I review electric-magnetic duality from the perspective of extended supergravity theories in four spacetime dimensions

The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an attempt to generalize to gravitation the energy-momentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which are remarkably similar to those of the energy-momentum tensor of electromagnetism. However, the physical role of these tensors in General Relativity has remained obscure and no interpretat...

We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the electromagnetic waves.