Scale-dependent three-dimensional charged black holes in linear and non-linear electrodynamics

Abstract

In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein-Maxwell as well as in Einstein-powerMaxwell theories in (2 + 1)-dimensional spacetimes without a cosmological constant. We allow for scale dependence of the gravitational and electromagnetic couplings, and we solve the corresponding generalized field equations imposing the null energy condition. Certain properties, such as horizon structure and thermodynamics, are discussed in detail.

Scale-dependent planar anti-de Sitter black hole

“…This choice seems peculiar, since one usually expects k ∼ 1/z for dimensional reasons. Similar results have been found in [46][47][48][49][50][51][52][53][54][55][56][57][58][59] but the deeper reason behind this result is still unknown . An important hint for solving this riddle could come from considering the dimensionless product G(k) ·Λ (k) instead of the individual dimensionful quantities as discussed in [73].…”

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

“…It is the aim of this work to study the scale dependence at the level of the effective action of three-dimensional charged black holes in the presence of the Einstein-power-Maxwell non-linear electrodynamics for any value of the power parameter, extending and generalizing previous work [49], where we imposed the traceless condition β = 3/4. We will use the formalism and notation of [49].…”

“…As a benchmark point, we will revisit the solution for α = 2 which was previously discussed in Ref. [49]. Note that, although we are able to produce physical solutions for α ≥ 2, only a single case will be shown here explicitly.…”

“…The idea and notation follows [49][50][51][52][53][54][55][56][57][58]. The scaledependent couplings of the theory are (i) the Newton's coupling G k (which can be related with the gravitational coupling by κ k ≡ 8π G k ), and (ii) the electromagnetic coupling 1/e 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].…”