In 2008-2009, F. Costa and C. Herdeiro proposed a new gravito-electromagnetic analogy, based on tidal tensors. We show that connections on the tangent bundle of the space-time manifold can help not only in finding a covnenient geometrization of their ideas, but also a common mathematical description of the main equations of gravity and electromagnetism.
By considering Hadamard vacuum states, we first construct the two-point functions associated with Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes. Then, from the general formalism developed in [A. Belokogne and A. Folacci, Phys. Rev. D \textbf{93}, 044063 (2016)], we obtain an exact analytical expression for the vacuum expectation value of the renormalized stress-energy tensor of the massive vector field propagating in these maximally symmetric spacetimes.
We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime (gauge invariance of the classical theory and covariant quantization, wave equations for the massive spin-1 field $A_μ$, for the auxiliary Stueckelberg scalar field $Φ$ and for the ghost fields $C$ and $C^\ast$, Ward identities, Hadamard representation of the various Feynman propagators and covariant Taylor series expansions of the corresponding coefficients). This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with…
We present a framework in which the projective symmetry of the Einstein-Hilbert action in metric-affine gravity is used to induce an effective coupling between the Dirac lagrangian and the Maxwell field. The effective $U(1)$ gauge potential arises as the trace of the non-metricity tensor $Q_{μa}{}^a$ and couples in the appropriate way to the Dirac fields to in order to allow for local phase shifts. On shell, the obtained theory is equivalent to Einstein-Cartan-Maxwell theory in presence of Dirac spinors.
We first investigate the form the General Relativity Theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to each particle with a different electric charge-to-mass ratio in superimposed gravitational and electromagnetic fields there corresponds a spacetime manifold whose metric tensor $g_{μν}$ describes the dynamical actions of gravitation and electromagnetism. The electric field outside a charged sphere ass…
