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We construct exact black hole solutions to Einstein gravity with nonlinear electrodynamic field. In these solutions, there are in general four parameters. They are physical mass, electric charge, cosmological constant and the coupling…

This paper deals with the thermodynamical properties of black hole formulated in Einstein theory of relativity and associated with a nonlinear electromagnetic field. The transition of the black hole is analyzed using the parameters mass,…

Singularities in the metric of the classical solutions to the Einstein equations (Schwarzschild, Kerr, Reissner -- Nordstr\"om and Kerr -- Newman solutions) lead to appearance of generalized functions in the Einstein tensor that are not…

The interaction of a Reissner-Nordstr\"om black hole and a charged massive particle is studied in the framework of perturbation theory. The particle backreaction is taken into account, studying the effect of general static perturbations of…

If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present…

Despite the fact that modified theories of gravity, in particular the f(R) gravity models have attracted much attention in the last years, the problem of the energy localization in the framework of these models has not been addressed. In…

In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, M{\o}ller, and Weinberg. In this review, we firstly explored…

We perform fully non-linear numerical simulations of charged-black-hole collisions, described by the Einstein-Maxwell equations, and contrast the results against analytic expectations. We focus on head-on collisions of non-spinning black…

The mass--energy formula of black holes implies that up to 50% of the energy can be extracted from a static black hole. Such a result is reexamined using the recently established analytic formulas for the collapse of a shell and expression…

The neutral particle motion around rotating regular black hole that was derived from the Ay\'{o}n-Beato-Garc\'{i}a black hole solution by the Newman-Janis algorithm in the preceding paper [Phys. Rev. D 89, 104017, (2014)] has been studied.…

A model of nonlinear electrodynamics with two parameters, coupled with general relativity, is investigated. We study the magnetized black hole and obtain solutions. The asymptotic of the metric and mass functions at $r\rightarrow\infty$ and…

In their seminal 1992 paper, Ba\~{n}ados, Teitelboim and Zanelli (BTZ) proposed a simple charged generalization of what is now known as the spinning BTZ black hole, the proposal being that a rotating metric can be supported by a `static…

The first objective of this work is to obtain practical prescriptions to calculate the absorption of mass and angular momentum by a black hole when external processes produce gravitational radiation. These prescriptions are formulated in…

The generalization of the black hole in three-dimensional spacetime to include an electric charge Q in addition to the mass M and the angular momentum J is given. The field equations are first solved explicitly when Q is small and the…

In this paper, we will use the coincident gauge to investigate new solutions of the f(Q) theory applied in the context of black holes, regular black holes, and the black-bounce spacetime. For each of these approaches, we compute the linear…

An approach to computing, withing the framework of distribution theory, the distributional valued energy-momentum tensor for the Schwarzschild spacetime is disscused. This approach avoids the problems associated with the regularization of…

We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular…

Using a nonlinear electrodynamics coupled to General Relativity a new regular exact black hole solution is found. The nonlinear theory reduces to the Maxwell one in the weak limit, and the solution corresponds to a charged black hole for…

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of…

We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein equations. We focus on the theory in four dimensions, in presence of negative cosmological constant,…