Rotating black holes in higher dimensions with a cosmological constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and the Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S(D-2) bundles over S2, infinitely many for each odd D>/=5. Applications to string theory and M-theory are indicated.     

Charged black holes and additional dimensions

A multidimensional generalization is obtained for the Reissner-Nordstrom solution of general relativity theory for the case of n Ricci-plane internal spaces with inclusion of the dilaton field. A two-parameter family of solutions that describe black holes of arbitrary dimensionality D is identified. It is shown that nontrivial black holes with dimensionality D > 4 exist only for nonzero electric charge. The observational consequences, particularly a violation of Coulomb's law, are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 24–28, July, 1991.     

Charged BTZ-like black holes in higher dimensions

Motivated by many worthwhile papers about (2+1)-dimensional BTZ black hole solutions, we generalize them to (n+1)-dimensional solutions, the so-called BTZ-like solutions. We show that the electric field of BTZ-like solutions is the same as that of (2+1)-dimensional BTZ black holes, and also their lapse functions are approximately the same, too. By these similarities, it is also interesting to investigate the geometric and thermodynamics properties of the BTZ-like solutions. We find that, depending on the metric parameters, the BTZ-like solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons, an extreme black hole or naked singularity. Then, we obtain the conserved and thermodynamic quantities, and we show that they satisfy the first law of thermodynamics. Next, we perform a thermodynamic stability analysis in the canonical ensemble and find that the BTZ-like solutions are stable in the whole phase space.     

Tunnelling with a negative cosmological constant

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.     

Charged black holes in phantom cosmology

In the classical relativistic regime, the accretion of phantom-like dark energy onto a stationary black hole reduces the mass of the black hole. We have investigated the accretion of phantom energy onto a stationary charged black hole and have determined the condition under which this accretion is possible. This condition restricts the mass-to-charge ratio in a narrow range. This condition also challenges the validity of the cosmic-censorship conjecture since a naked singularity is eventually produced due to accretion of phantom energy onto black hole.     

Charged boson stars and black holes

We consider boson stars and black holes in scalar electrodynamics with a V-shaped scalar potential. The boson stars come in two types, having either ball-like or shell-like charge density. We analyze the properties of these solutions and determine their domains of existence. When mass and charge become equal, the space–times develop a throat. The shell-like solutions need not be globally regular, but may possess a horizon. The space–times then consist of a Schwarzschild-type black hole in the interior, surrounded by a shell of charged matter, and thus a Reissner–Nordström-type space–time in the exterior. These solutions violate black hole uniqueness. The mass of the black hole solutions is related to the mass of the regular shell-like solutions by a mass formula of the type first obtained within the isolated horizon framework.     

Revisiting the ADT mass of the five-dimensional rotating black holes with squashed horizons

We evaluate the Abbott–Deser–Tekin (ADT) mass of the five-dimensional rotating black holes with squashed horizons on two different on-shell reference backgrounds, which are the flat background and the boundary matched Kaluza–Klein (KK) monopole. The mass on the former, identified with the one on the background of the asymptotic geometry, differs from the mass on the latter by that of the KK monopole. However, each mass satisfies the first law of black hole thermodynamics. To test the results in five dimensions, we compute the mass in the context of the dimensionally reduced theory. Finally, in contrast with the original ADT formulation, its off-shell generalisation is applied to calculate the mass as well.     

Charged balanced black rings in five dimensions

We present balanced black ring solutions of pure Einstein–Maxwell theory in five dimensions. The solutions are asymptotically flat, and their tension and gravitational self-attraction are balanced by the repulsion due to rotation and electrical charge. Hence the solutions are free of conical singularities and possess a regular horizon which exhibits the ring topology S¹×S²$S^1\times S^2$. We discuss the global charges and the horizon properties of the solutions and show that they satisfy a Smarr relation. We construct these black rings numerically, restricting to the case of black rings with a rotation in the direction of the S¹$S^1$ and large black rings. We compare these to the blackfold results.     

Charged fermions tunneling from regular black holes

We study Hawking radiation of charged fermions as a tunneling process from charged regular black holes, i.e., the Bardeen and ABGB black holes. For this purpose, we apply the semiclassical WKB approximation to the general covariant Dirac equation for charged particles and evaluate the tunneling probabilities. We recover the Hawking temperature corresponding to these charged regular black holes. Further, we consider the back-reaction effects of the emitted spin particles from black holes and calculate their corresponding quantum corrections to the radiation spectrum. We find that this radiation spectrum is not purely thermal due to the energy and charge conservation but has some corrections. In the absence of charge, e = 0, our results are consistent with those already present in the literature.     

Charged torus-like black holes as heat engines

We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle,and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole cannot be arbitrary. Last,we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.