Abelian–Higgs strings in Rastall gravity

Abstract

In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenological equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to 2π at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map S 1 → S 1 . Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.

Noncommutative geometry inspired black holes in Rastall gravity

“…Rastall gravity has been employed to study the cosmological consequences [11][12][13]. Various exact solutions of Rastall gravity have also been derived in [14][15][16][17][18].…”

A thermodynamics revision of Rastall gravity

“…Despite this represents the main drawback of the model, one alternative to solve this fact could be given by the introduction of an auxiliary (external) field in the Einstein-Hilbert action by means of a Lagrange multiplier. This would provide two possibilities: the Rastall gravity could be naturally seen as an extension of the Einstein model, secondly, one could also assume that this new contribution to the Einstein gravity arises from the quantum effects described by the Rastall equation [28].…”

Neutral regular black hole solution in generalized Rastall gravity *

“…where and is a constant. As a theory of modified gravity, Rastall gravity has received increasing attention lately [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], particularly due to recent findings in cosmology [45][46][47][48][49][50][51][52][53][54].…”