Dyonic Kerr Newman Black Holes Research Articles

The dark (BPS) side of thermodynamics in Minkowski4

We explore the BPS limit of asymptotically flat black hole thermodynamics, drawing analogies with recent studies of black holes in anti-de Sitter space. Although ultimately motivated by supersymmetry and quantum gravity, the BPS limit is classically well-defined for the dyonic Kerr-Newman black holes in pure Einstein-Maxwell theory and various generalizations with additional scalars and gauge fields that admit embedding in mathcal{N} = 2 supergravity (for concreteness we consider the STU model). This limit is manifestly different from extremality as it includes a family of rotating Euclidean saddles that represent a (fictitious) thermal branch, smoothly connected with the extremal static Reissner-Nordström black hole and its generalizations with extra matter. We are able to evaluate unambiguously all BPS chemical potentials, finding constant imaginary angular velocity as a consequence of Wick rotation. In the mixed ensemble of fixed magnetic and varying electric charges, we derive the OSV formula that is crucial for the microscopic understanding of the system, and provide evidence that it should be interpreted as a fixed-point formula.

Gluing gravitational blocks for AdS black holes

We provide a unifying entropy functional and an extremization principle for black holes and black strings in AdS4 × S7 and AdS5 × S5 with arbitrary rotation and generic electric and magnetic charges. This is done by gluing gravitational blocks, basic building blocks that are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. We also provide an explicit realization of the attractor mechanism by identifying the values of the scalar fields at the horizon with the critical points of the entropy functional. We give examples based on dyonic rotating black holes with a twist in AdS4 × S7, rotating black strings in AdS5 × S5, dyonic Kerr-Newman black holes in AdS4 × S7 and Kerr-Newman black holes in AdS5 × S5. In particular, our entropy functional extends existing results by adding rotation to the twisted black holes in AdS4 and by adding flavor magnetic charges for the Kerr-Newman black holes in AdS4. We also discuss generalizations to higher-dimensional black objects.

On the Smarr formula for rotating dyonic black holes

We revisit the derivation by Tomimatsu of the generalized Komar integrals giving the mass and angular momentum of rotating Einstein–Maxwell black holes. We show that, contrary to Tomimatsu's claim, the usual Smarr formula relating the horizon mass and angular momentum still holds in the presence of both electric and magnetic charges. The simplest case is that of dyonic Kerr–Newman black holes, for which we recover the modified Smarr formula relating the asymptotic mass and angular momentum, the difference between asymptotic and horizon masses being equal to the sum of the two Dirac string masses. Our results apply in particular to the case of dyonic dihole solutions which have been investigated recently.

Weak cosmic censorship, dyonic Kerr–Newman black holes and Dirac fields

It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr–Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of the conversion is a direct consequence of the fact that the Einstein–Hilbert energy-momentum tensor of the classical Dirac field does not satisfy the null energy condition, and is therefore not in contradiction with the weak cosmic censorship conjecture. We give a derivation of the absence of superradiance of the Dirac field without making use of the complete separability of the Dirac equation in the dyonic Kerr–Newman background, and we determine the range of superradiant frequencies of the scalar field. The range of frequencies of the Dirac field that can be used to convert a black hole into a naked singularity partially coincides with the superradiant range of the scalar field. We apply horizon-penetrating coordinates, as our arguments involve calculating quantities at the event horizon. We describe the separation of variables for the Dirac equation in these coordinates, although we mostly avoid using it.

Supergravity, complex parameters and the Janis–Newman algorithm

The Demiański–Janis–Newman (DJN) algorithm is an original solution generating technique. For a long time it has been limited to producing rotating solutions, restricted to the case of a metric and real scalar fields, despite the fact that Demiański extended it to include more parameters such as a NUT charge. Recently two independent prescriptions have been given for extending the algorithm to gauge fields and thus electrically charged configurations. In this paper we aim to end setting up the algorithm by providing a missing but important piece, which is how the transformation is applied to complex scalar fields. We illustrate our proposal through several examples taken from N = 2 supergravity, including the stationary BPS solutions from Behrndt et al and Senʼs axion–dilaton rotating black hole. Moreover we discuss solutions that include pairs of complex parameters, such as the mass and the NUT charge, or the electric and magnetic charges, and we explain how to perform the algorithm in this context (with the example of Kerr–Newman–Taub–NUT and dyonic Kerr–Newman black holes). The final formulation of the DJN algorithm can possibly handle solutions with five of the six Plebański–Demiański parameters along with any type of bosonic fields with spin less than two (exemplified with the stationary Israel–Wilson–Perjes solutions). This provides all the necessary tools for applications to general matter-coupled gravity and to (gauged) supergravity.

Test of the weak cosmic censorship conjecture with a charged scalar field and dyonic Kerr–Newman black holes

A thought experiment considered recently in the literature, in which it is investigated whether a dyonic Kerr-Newman black hole can be destroyed by overcharging or overspinning it past extremality by a massive complex scalar test field, is revisited. Another derivation of the result that this is not possible, i.e. the weak cosmic censorship is not violated in this thought experiment, is given. The derivation is based on conservation laws, on a null energy condition, and on specific properties of the metric and the electromagnetic field of dyonic Kerr-Newman black holes. The metric is kept fixed, whereas the dynamics of the electromagnetic field is taken into account. A detailed knowledge of the solutions of the equations of motion is not needed. The approximation in which the electromagnetic field is fixed is also considered, and a derivation for this case is also given. In addition, an older version of the thought experiment, in which a pointlike test particle is used, is revisited. The same result, namely the non-violation of the cosmic censorship, is rederived in a way which is simpler than in earlier works.

Dyonic Kerr–Newman black holes, complex scalar field and cosmic censorship

We construct a gedanken experiment, in which a weak wave packet of the complex massive scalar field interacts with a four-parameter (mass, angular momentum, electric and magnetic charges) Kerr-Newman black hole. We show that this interaction cannot convert an extreme the black hole into a naked sigularity for any black hole parameters and any generic wave packet configuration. The analysis therefore provides support for the weak cosmic censorship conjecture.