Stationary dilatons with arbitrary electromagnetic field

Abstract

We present two new classes of axisymmetric stationary solutions of the Einstein-Maxwell-Dilaton equations with coupling constant α 2 = 3. Both classes are written in terms of two harmonic maps λ and τ . λ determines the gravitational potential and τ the electromagnetic one in such a form that we can have an arbitrary electromagnetic field. As examples we generate two solutions with mass (M ), rotation (s) and scalar (δ) parameters, one with electric charge (q) another one with magnetic dipole (Q) parameter. The first solution contains the Kerr metric for q = δ = 0.

Duality covariant non-BPS first order systems

“…Combined with (2.9), this equation permits to relate the expression of the Maurer-Cartan form to the derivative of the section V in the tangent frame. Similarly, we also define 23) which transforms in the same C nv representation of K 4 .…”

“…The over-rotating (or ergo) branch is characterised by the presence of an ergo-region and includes the extremal Kerr solution. In contrast, we will focus on the under-rotating (or ergo-free) black holes, which then admit a flat three-dimensional base, and include the static extremal black holes [22][23][24]. Single centre under-rotating non-BPS black holes have been studied throughout the last decade or so, from various aspects and using various techniques, see for example [10,12,15,[17][18][19][25][26][27][28] and references therein for some JHEP09 (2012)100 developments.…”

A Kaluza–Klein subtractor

“…Rotating KaluzaKlein black holes were first constructed in [12,13,14]. In the non-extremal case, on top of a mass parameter M k and the charges Q 1 and Q 2 , now we have a rotation parameter a k in the metric [15].…”

“…Once we turn on rotation, the system is substantially more complicated. The black hole solutions of this theory were written down in [12,13,14]. There are two kinds of extremal limits that these black holes have, the so called ergo-branch and the ergo-free branch [15].…”

“…The branch that allows a natural generalization from the static case is the ergo-free branch, and that is the one we will study. As it turns out, the black hole solutions of [12,13,14] are not general enough to discuss the attraction basin that generalizes the static basin of section 2. Fortunately, despite the complications of the rotating case, using some symmetries of the equations of motion we are able to generate precisely such solutions.…”