A regular scale-dependent black hole solution

Abstract

In this work we present a regular black hole solution, in the context of scale-dependent General Relativity, satisfying the weak energy condition. The source of this solution is an anisotropic effective energy-momentum tensor which appears when the scale dependence of the theory is turned-on. In this sense, the solution can be considered as a semiclassical extension of the Schwarzschild one.

Scale-dependent ( $$2+1$$ 2 + 1 )-dimensional electrically charged black holes in Einstein-power-Maxwell theory

“…To apply the variational procedure (21), however, the knowledge of the exact beta functions of the problem is required. Since in many cases the precise form of these functions is unknown (or at least uncertain) one can, for the case of simple black holes, impose a null energy condition and solve for the couplings G(r ), Λ(r ), e(r ) directly [50,51,53,54,[80][81][82]. This philosophy of assuring the consistency of the equations by imposing a null energy condition will also be applied in the following study on Einstein-Maxwell and Einstein-powerMaxwell black holes.…”

“…when we include the running of the coupling constants, just like their scale-independent counterpart. It would be interesting to investigate how and to which extent those singularities could be cancelled by an additional contribution from the effective stress energy tensor as discussed in [53].…”

Interior solutions of relativistic stars in the scale-dependent scenario

“…The idea is largely inspired by the asymptotic safety program and related approaches as the well-known Renormalization group improvement method [28][29][30][31]. Taking them as inspiration, some authors introduced the now known scale-dependent gravity which has been systematically used in black holes physics [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], and recently, in cosmological problems [48,49]. The crucial point of scale-dependent gravity is to promote the classical parameter {A 0 , B 0 , (· · · ) 0 } to functions which depends on the energy scale k, namely {A k , B k , (· · · ) k }.…”

Stability of cosmic structures in scalar–tensor theories of gravity

“…In general all dark energy models fall into two broad classes, namely on the one hand dynamical dark energy models, in which one has to introduce a new dynamical field assuming Einstein's general relativity (GR) [4][5][6][7], and on the other hand geometrical dark energy models, in which one assumes an alternative theory of gravity that modifies GR at cosmological scales. In the latter category we find the well-known examples of f (R) theoa e-mail: grigorios.panotopoulos@tecnico.ulisboa.pt b e-mail: arrincon@uc.cl ries of gravity [8][9][10][11], the Dvali-Gabadadze-Porrati brane model [12] or scalar-tensor theories of gravity (ST), with the Brans-Dicke [13] model being the archetypal one and recently the scale dependent approach previously applied to certain black holes problems [14][15][16][17][18].…”