Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.Comment: 15 pages, v2: typos correcte

The near horizon geometry of the rotating C-metric, describing accelerating Kerr-Newman black holes, is analysed. It is shown that, at extremality, even though not it is isomorphic to the extremal Kerr-Newman, it remains a warped and twisted product of AdS 2 × S 2 . Therefore the methods of the Kerr/CFT correspondence can successfully be applied to build a CFT dual model, whose entropy reproduce, through the Cardy formula, the Bekenstein-Hawking entropy of the accelerating black hole. The mass of accelerating Kerr-Newman black hole, which fulfil the first law of thermodynamics, is presented. Further generalisation in presence of an external Melvin-like magnetic field, used to regularise the conical singularity characteristic of the C-metrics, shows that the Kerr/CFT correspondence can be applied also for the accelerating and magnetised extremal black holes.In the last years there have been a great development of near horizon techniques to study the black hole physics [1]. These methods are being useful in the description of both macroscopic and microscopic properties of black holes in general relativity, especially at extremality. For instance the near horizon analysis was fundamental in the context of the Kerr/CFT correspondence [2], [3], [4] and [5]. While from a more classical point of view, the near horizon limit revealed also useful in determining the energy of magnetised black holes [10] and, through force-free electrodynamics, in modelling the Kerr black hole magnetosphere [6] -[7], its accretion disk and jet dynamics, or describing some radiative processes around extreme Kerr black holes [8], just to cite few relevant applications. Here we will be mainly interested in the Kerr/CFT correspondence. It is based on the symmetries that emerge in the near horizon geometry, which usually are encoded in the U (1) × SL(2, R) group. Thanks to these symmetries it is possible to build a two dimensional conformal model dual to the gravitational one. From the features of the 2D CFT picture, some microscopical details of the black hole entropy can be extrapolated. In particular, through the Cardy formula it is possible to take into account the black hole microstates that generate their entropy. Recently some generalisation of the Kerr/CFT correspondence have been discovered also for extremal black holes embedded in an external magnetic field, such as the Reissner-Nordstrom and Kerr(-Newman) spacetimes immersed in the Melvin magnetic universe [11]- [12]. In that case the near horizon geometry at extremality remains the same of the Kerr-Newman black hole. The scope of this article is to further extend the applicability of the Kerr/CFT methods and to study possible generalisations of the Kerr-Newman near horizon geometry in case of extremal accelerating black holes. In this context the extremality plays a fundamental role because, at that specific parametric point, the event horizon symmetries are enhanced. This will be analysed in section 3 and 4. In particular we will focus on stationary and axisymmetric spacetimes. We w...

The explicit solution for a Kerr-Newman black hole immersed in an external magnetic field, sometimes called the Melvin-Kerr-Newman black hole, has been derived by Ernst and Wild in 1976. In this paper, we clarify the first law and Smarr formula for black holes in a magnetic field. We then define the unique mass which is integrable and reduces to the Kerr-Newman mass in the absence of magnetic field. This defines the thermodynamic potentials of the black hole. Quite strikingly, the mass coincides with the standard Christodoulou-Ruffini mass of a black hole as a function of the entropy, angular momentum and electric charge.

Using the covariant phase space formalism, we compute the conserved charges for a solution, describing an accelerating and electrically charged Reissner-Nordstrom black hole. The metric is regular provided that the acceleration is driven by an external electric field, in spite of the usual string of the standard C-metric. The Smarr formula and the first law of black hole thermodynamics are fulfilled. The resulting mass has the same form of the Christodoulou-Ruffini mass formula. On the basis of these results, we can extrapolate the mass and thermodynamics of the rotating C-metric, which describes a Kerr-Newman-(A)dS black hole accelerated by a pulling string.