Abstract
We consider Einstein gravity with a negative cosmological constant endowed with distinct matter sources. The different models analyzed here share the following two properties: (1) they admit static symmetric solutions with planar base manifold characterized by their mass and some additional Noetherian charges, and (2) the contribution of these latter in the metric has a slower falloff to zero than the mass term, and this slowness is of logarithmic order. Under these hypothesis, it is shown that, for suitable bounds between the mass and the additional Noetherian charges, the solutions can represent black holes with two horizons whose locations are given in term of the real branches of the Lambert W functions. We present various examples of such black hole solutions with electric, dyonic or axionic charges with AdS and Lifshitz asymptotics. As an illustrative example, we construct a purely AdS magnetic black hole in five dimensions with a matter source given by three different Maxwell invariants.
Highlights
CFTs in presence of an external magnetic field
The emergence of a magnetic charge is shown to be possible for a flat horizon and by considering at least three different Maxwell invariants
For suitable bounds between the mass and the magnetic charge, the purely magnetic GR solution can be shown to admit an inner and outer horizons. These latter are given in terms of the two real branches of the Lambert W functions
Summary
CFTs in presence of an external magnetic field. For example, four-dimensional dyonic black holes have been proved to be relevant for a better comprehension of planar condensed matter phenomena such as the quantum Hall effect [1], the superconductivity-superfluidity [2] or the Nernst effect [3]. We will show that, as for the Reissner–Nordstrom solution, the absence of naked singularity can be guaranteed for a suitable bound relation between the mass and the magnetic charge In this case, the location of the inner and outer horizons are expressed analytically in term of the real branches of so-called Lambert W function. A particular attention will be devoted to the purely magnetic GR solution for which a bound relation between the mass and the magnetic charge ensures the existence of an event horizon covering the naked singularity In this case, the inner and outer horizons are expressed in term of the two real branches of the Lambert W functions. The last section is devoted to our conclusion and an appendix is provided where some useful properties of the Lambert W functions are given
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