Newtonian Potential in Weyl Gravitoelectromagnetism

Abstract

The gauge structure of the Weyl Gravitoelectromagnetic (GEM) formalism has been investigated, showing that although the theory admits additional propagating modes, only an effective spin-2 sector contributes to physical observables. Building on this result, the formalism is applied to Bhabha scattering mediated by the tensor field $A_{μν}$, and the Newtonian gravitational potential is derived in the zero-temperature limit. Finite-temperature effects are incorporated through the Thermo Field Dynamics (TFD) formalism. While the Newtonian interaction is recovered at low temperatures, it becomes progressively suppressed in the high-temperature regime, revealing a thermal screening mechanism. The physical origin of this behavior and its possible dependence on the underlying scattering process are briefly discussed.