Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.27125

Diffeomorphism-Like Symmetry in Gravitoelectromagnetism

L. A. S. Evangelista·A. F. Santos
View original source ↗Read source document ↗Export metadata ↓

Abstract

Gravitoelectromagnetism in the Weyl formalism is investigated through an analysis of the consequences of a restricted gauge symmetry acting on the tensor field $A_{μν}$. The propagator associated with the GEM field is explicitly derived and decomposed within the Barnes--Rivers formalism, revealing contributions from the spin-2, spin-1, and scalar spin-0 sectors. By coupling the theory to conserved sources, it is shown that only the spin-2 and scalar sectors contribute to physical processes, while the spin-1 component decouples. The resulting effective propagator can then be written in a compact metric form closely resembling the graviton propagator of linearized General Relativity. The role of gauge fixing is also analyzed by considering both Lorentz-like and de Donder-type gauge conditions. It is shown that the Lorentz-like gauge is consistent with the restricted gauge symmetry of the theory and leads to gauge-independent physical amplitudes, whereas the de Donder gauge introduces residual gauge-dependent scalar contributions, signaling an incompatibility with the underlying symmetry structure. The gauge symmetry is further extended to the fermionic and electromagnetic sectors through diffeomorphism-like transformations. In both cases, conserved currents are derived and shown to coincide with the corresponding energy-momentum tensors, implying that the GEM field couples to matter in the same manner as in linearized gravity. Finally, the associated Ward identities are verified, providing a nontrivial consistency check of the gauge structure and interaction vertices of the theory.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

L. A. S. Evangelista, A. F. Santos. 2026-05-26. Diffeomorphism-Like Symmetry in Gravitoelectromagnetism. https://arxiv.org/abs/2605.27125

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Dirac Observables for Gowdy Cosmologies regular at the Big Bang

Gowdy cosmologies are exact, spatially inhomogeneous solutions of the vacuum Einstein equations which describe nonlinear gravitational waves coalescing at the Big Bang singularity. With toroidal spatial sections they provenly have the Asymptotic Velocity Domination property, in that close to the Big Bang dynamical spatial gradients fade out and the dynamics is governed by a Carroll-type gravity theory. Here we construct an infinite set of Dirac observables for Gowdy cosmologies, valid off-shell, strongly, and without gauge fixing. These observables stay regular at the Big Bang and can be matched to much simpler Dirac observables of the Carroll-type gravity theory. Conversely, in an adapted foliation there is a systematic anti-Newtonian expansion (in inverse powers of the reduced Newton constant) of the full Dirac observables whose leading terms are the Carroll ones. In particular, this provides an off-shell generalization of the Asymptotic Velocity Domination property.

gr-qc↗
arXiv2026

Global causality constraints in rotating scalar-tensor spacetimes

Modified gravity is often formulated as an effective field theory (EFT), where higher-order corrections parametrize departures from General Relativity. We argue that such corrections should be constrained by the global causal structure of curved spacetime, in addition to the usual flat-space requirements such as positivity and unitarity. We propose that within the domain of validity of the EFT, the onset of closed timelike curves should not happen in a parametrically more accessible region than in the corresponding GR background. We test this diagnostic in the quadratic k-essence sector of scalar-tensor gravity. For stationary and axisymmetric spacetimes, the invariant test for closed axial orbits is the sign of the azimuthal component of the metric \(g_{φφ}\). We supplement this test by requiring a local time function in the space of Killing vectors. We apply these conditions to quadratic k-essence on Kerr--(A)dS backgrounds, with and without scalar charge. The zero-charge branch is exact Kerr--(A)dS, and we treat the charged branch perturbatively in scalar charge and in Hartle--Thorne slow rotation. Expanding for small spin \(χ=a/(GM)\ll1\), frame dragging begins at \(\mathcal O(χ)\), while the quadrupolar backreaction relevant for circular closed timelike curves enters at second order in both rotation and charge. We find that, in the truncation used here, any occurrence of \(g_{φφ}<0\) also lies outside EFT control. A higher-order calculation or a fully nonlinear treatment is therefore needed. Finally, we discuss how quasinormal modes and black-hole echoes could probe such causal structure.

gr-qc↗