Related papers: Mass-Angular Momentum Inequality For Black Ring Sp…
We prove the Penrose inequality with angular momentum for asymptotically flat, axisymmetric vacuum initial data sets containing a stable marginally outer trapped surface. This inequality provides a lower bound for the ADM mass in terms of…
A Kerr black hole with mass $M$ and angular momentum $J$ satisfies the extremality inequality $|J| \le M^2$. In the presence of matter and/or gravitational radiation, this bound needs to be reformulated in terms of local measurements of the…
We prove that in Einstein-Maxwell theory the inequality $(8\pi J)^2+(4\pi Q^2)^2 < A^2$ holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here $J, Q$, and $A$ are angular momentum, electric…
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…
We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that $a^2+Q^2=M^2$ always holds provided that a continuous sequence of…
A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate…
The inequality between area and charge $A\geq 4\pi Q^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime…
Near the black hole threshold in phase space, the black hole mass as a function of the initial data shows the "critical scaling" M \simeq C (p-p_*)^\gamma, where p labels a family of initial data, p_* is the value of p at the threshold, and…
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge…
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a…
We consider stationary, axially symmetric toroids rotating around spinless black holes, assuming the general-relativistic Keplerian rotation law, in the first post-Newtonian approximation. Numerical investigation shows that the angular…
We construct a supergravity solution describing a charged rotating black ring with S^2xS^1 horizon in a five dimensional asymptotically flat spacetime. In the neutral limit the solution is the rotating black ring recently found by Emparan…
We propose a new thermodynamic inequality for stationary and asymptotically Anti-de Sitter rotating black holes, $ 4\pi J^2/(3MV)<1 $. This inequality is derived by analyzing the roots of the identity relating the thermodynamic variables,…
We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations…
We note that the recently discovered 450 Hz frequency in the X-ray flux of the black hole candidate GRO J1655-40 is in a 3:2 ratio to the previously known 300 Hz frequency of quasi-periodic oscillations (QPO) in the same source. If the…
The generalization of the black hole in three-dimensional spacetime to include an electric charge Q in addition to the mass M and the angular momentum J is given. The field equations are first solved explicitly when Q is small and the…
We consider perturbative solutions in Einstein gravity with higher-derivative extensions and address some subtle issues of taking extremal limit. As a concrete new result, we construct the perturbative rotating black hole in five dimensions…
Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in…
The Penrose-Gibbons inequality for charged black holes is proved in spherical symmetry, assuming that outside the black hole there are no current sources, meaning that the charge e is constant, with the remaining fields satisfying the…
We prove an inequality between horizon area and angular momentum for a class of axially symmetric black holes. This class includes initial conditions with an isometry which leaves fixed a two-surface. These initial conditions have been…