Magnetised Kerr/CFT correspondence

The tools of Kerr/CFT correspondence are applied to the Kerr black hole embedded in an axial external magnetic field. Its extremal near horizon geometry remains a warped and twisted product of $AdS_2\times S^2$. The central charge of the Virasoro algebra, generating the asymptotic symmetries of the near horizon geometry, is found. It is used to reproduce, via the Cardy formula, the Bekenstein-Hawking entropy of the magnetised Kerr black hole as the statistical microscopic entropy of a dual CFT. The presence of the background magnetic field makes available also a second dual CFT picture, based on the $U(1)$ electromagnetic symmetry, instead of the only rotational one of the standard non-magnetised Kerr spacetime. A Meissner-like effect, where at extremality the external magnetic field is expelled out of the black hole, allows us to infer the value of the mass for these magnetised extremal black holes. The generalisation to the CFT dual for the magnetised extreme Kerr-Newman black hole is also presented.Comment: 16 pages, v4 final versio

CFT Duals for Accelerating Black Holes

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 $AdS_2 \times S^2$. 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 Beckenstein-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.Comment: 21 pages, published versio

Removal of conical singularities from rotating C-metrics and dual CFT entropy

We show how to remove from the rotating C-metric spacetime, which describes accelerating Kerr black holes, both conical singularities. This can be done by embedding the metric into a swirling gravitational universe, through a proper Ehlers transformation. The spin-spin interaction between the external rotational background and the black hole provides the source of the acceleration without the need of rods or strings. The physical properties and entropy of the new solution are studied using near horizon and dual conformal techniques of the Kerr/CFT correspondence. The charged case is also analysed: Accelerating Reissner-Nordstrom and Accelerating Kerr-Newman space-times embedded in a swirling universe are also generated.Comment: 18 pages, no figure

Accelerating and Charged Type I Black Holes

A new, exact and analytical class of accelerating and charged black holes is built, in the Einstein-Maxwell theory, thanks to the Harrison transformation. The diagonal metric does not belong to the Petrov type D classification, therefore it is not part of the Plebanski-Demianski spacetimes. The simplest subcase of this family recovers the Reissner-Nordstrom black hole in the vanishing acceleration limit and the standard C-metric in the limit of null electric charge. More general cases can have two independent electric charges, which can be tuned as desired, even to remain with an uncharged black hole, such as Petrov Type I Schwarzschild, in an accelerating charged Rindler background. Magnetic, dyonic and NUTty extensions are also discussed. Conical singularities can be possibly removed in extremal configurations.Comment: 20 page

Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ\sigma -model system

An exact hairy asymptotically locally AdS black hole solution with a flat horizon in the Einstein-nonlinear sigma model system in (3+1) dimensions is constructed. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and depends explicitly on Killing coordinates, but in such a way that its energy-momentum tensor is compatible with a metric with Killing fields. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. A $U(1)$ gauge field interacting with Einstein gravity can also be included. The thermodynamics is analyzed. Interestingly, the hairy black hole is always thermodynamically favored with respect to the corresponding black hole with vanishing Pionic field.Comment: 15 pages, 1 figure. Accepted for publication in Physics Letters