Scale dependence at the level of the effective action is a generic result of quantum field theory. Allowing for scale dependence of the gravitational couplings leads to a generalization of the corresponding field equations. In this work, those equations are solved by imposing the "null energy condition" in three-dimensional space time with stationary spherical symmetry. The constants of integration are given in terms of the classical BTZ parameters plus one additional constant, that parametrizes the strength of the scale dependence. The properties such as asymptotics, horizon structure, and thermodynamics are discussed. It is found that the black hole entropy shows a remarkable transition from the usual "area law" to an "area × radius" law.PACS numbers: 04.60., 04.70. I. INTRODUCTIONGravity in (2 + 1) dimensions is a vibrant field of research. This is in part due to the fact that the absence of propagating degrees of freedom makes things simpler than in (3 + 1) dimensions, in particular when dealing with the challenge of formulating a quantization of this theory. Another important feature of gravity in (2 + 1) dimensions is the deep connection to Chern-Simons theory [1][2][3]. This by itself makes the black hole solution [4,5] found by Bañados, Teitelboim, and Zanelli (BTZ) an extremely interesting research object, which has been generalised in many directions. An additional component that motivates the research on black holes in three dimensions is their prominent role in the context of the AdS/CFT correspondence [6][7][8][9].Despite of some progress, the consistent formulation of quantum gravity remains an open task which is attacked in many different ways [10-26] (for a review see [27]). Even though many approaches to quantum gravity are very different, most of them have the common feature that the resulting effective action of gravity acquires a scale dependence. This means that the couplings appearing in the quantum-effective action (such as Newtons coupling G 0 , or the cosmological term Λ 0 ) become scale dependent quantities (G 0 → G k , Λ 0 → Λ k ). There is quite some evidence that this scaling behavior is in agreement with Weinberg's Asymptotic Safety program [28][29][30][31][32][33][34][35]. In particular, the effective action and running couplings in three dimensions have been studied in [36,37]. In any case, scale dependent couplings can be expected to produce differences to classical general relativity, such as modifications of classical black hole backgrounds .In this paper the possible effects of scale dependence on the black hole in three dimensional gravity will be investigated in the light of the effective action approach. We will use the scale-field method applied to the Einstein-Hilbert truncation, which allows to derive generalized Einstein equations for the case of scale dependent couplings [59][60][61][62]. The theoretical uncertainty concerning the functional form of the scale dependence of G k and Λ k will be avoided. Instead, the most general stationary spherically symmetric solution w...

In the present work we study the scale-dependence of polytropic non-charged black holes in (3+1)-dimensional space-times assuming a cosmological constant. We allow for scale-dependence of the gravitational and cosmological couplings, and we solve the corresponding generalized field equations imposing the null energy condition. Besides, some properties, such as horizon structure and thermodynamics, are discussed in detail.

Simple generic extensions of isotropic DurgapalFuloria stars to the anisotropic domain are presented. These anisotropic solutions are obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors by means of the minimal geometric deformation approach are satisfied. Hence the anisotropic field equations are isolated resulting a more treatable set. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, observational effects of such anisotropies when measuring the surface redshift are discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations is shown. In this manner, different anisotropic sectors can be isolated of each other and modeled in a simple and systematic way.

In the present work a generalization of the BTZ black hole is studied, for the case of scale dependent couplings. One starts by using the effective action for scale dependence couplings to get a generalization of the Einstein field equations. Self consistent solutions for lapse function, cosmological coupling and Newtons coupling are found. The effect of scale dependent couplings with respect to the classical solution is shown. Moreover, asymptotic behavior as well as thermodynamic properties were investigated. Finally, an alternative way to get the scale dependent Newton coupling, from the so-called "Null Energy Condition" is presented.

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.

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.

We find new exact analytical solutions in three-dimensional gravity applying the Minimal Geometric Deformation approach in a cloud of strings.PACS. PACS-key discribing text of that key -PACS-key discribing text of that key

The effect of a scale dependent newton coupling, which is a crucial ingredient of many quantum gravity theories, is investigated in this paper. For case of non-rotating black holes, and using the null energy condition, we show that Newtons scale dependent coupling can actually be obtained without solving the full quantum gap equations.