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We analyze stationary self-gravitating disks around spinning black holes that satisfy the recently found general-relativistic Keplerian rotation law. There is a numerical evidence that the angular velocity, circumferential radius and…
Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.
We study an exact solution of Einstein's equations describing a self-gravitating system, made of dust, distributed with axial symmetry and in stationary rotation, and we prove that this type of system has no Newtonian analogue. In a…
We study stationary and axially symmetric black hole-disk systems, assuming a combination of the DD2 and Timmes-Swesty equations of state and a three-parameter family of rotation laws. There exist two branches of solutions that are shown to…
We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and…
The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities phi: R^3\Sigma -> H^2_C, where Sigma is a subset of the axis of symmetry, and H^2_C is the complex hyperbolic…
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to…
We present analytic stationary and axially-symmetric black hole solutions to the semiclassical Einstein equations that are sourced by the trace anomaly. We also find that the same spacetime geometry satisfies the field equations of a subset…
A class of metrics solving Einstein's equations with negative cosmological constant and representing rotating, topological black holes is presented. All such solutions are in the Petrov type-$D$ class, and can be obtained from the most…
From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional gravity the uniqueness of wide families of exact solutions is established, among them, all…
In this report the exact rotating charged black hole solution to the Einstein--nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic…
We present the spectrum of stationary black hole solutions associated with the first non-trivial member of the Dym family of boundary conditions. The analysis combines the holonomy conditions provided by the Chern-Simons formulation of…
We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact ($S^{3}$) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
The first fully integrated explicit exact solution of the Einstein field equations corresponding to the superposition of a counterrotating dust disk with a central black hole is presented. The obtained solution represents an infinite…
Investigating the rigidly rotating disc of dust with constant specific charge, we find that it leads to an extreme Kerr-Newman black hole in the ultra-relativistic limit. A necessary and sufficient condition for a black hole limit is, that…