Bounds on the force between black holes

We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta, the distances and the forces between the black holes. The second one relates the angular momentum and area of each black hole with the forces acting on it.Comment: 13 pages, no figure

Conformally flat black hole initial data, with one cylindrical end

We give a complete analytical proof of existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and extreme Bowen-York's initial data. This extends and refines a previous result \cite{dain-gabach09} to a general case of conformally flat, maximal initial data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published version in Class. Quantum Grav. (2010). Results unchange

Proof of the area-angular momentum-charge inequality for axisymmetric black holes

We give a comprehensive discussion, including a detailed proof, of the area-angular momentum-charge inequality for axisymmetric black holes. We analyze the inequality from several viewpoints, in particular including aspects with a theoretical interest well beyond the Einstein-Maxwell theory.Comment: 31 pages, 2 figure

Horizon area-angular momentum inequality in higher dimensional spacetimes

We consider $n$-dimensional spacetimes which are axisymmetric--but not necessarily stationary (!)--in the sense of having isometry group $U(1)^{n-3}$, and which satisfy the Einstein equations with a non-negative cosmological constant. We show that any black hole horizon must have area A \ge 8\pi |J_+ J_-|^\half, where $J_\pm$ are distinguished components of the angular momentum corresponding to linear combinations of the rotational Killing fields that vanish somewhere on the horizon. In the case of $n=4$, where there is only one angular momentum component $J_+=J_-$, we recover an inequality of 1012.2413 [gr-qc]. Our work can hence be viewed as a generalization of this result to higher dimensions. In the case of $n=5$ with horizon of topology $S^1 \times S^2$, the quantities $J_+=J_-$ are the same angular momentum component (in the $S^2$ direction). In the case of $n=5$ with horizon topology $S^3$, the quantities $J_+, J_-$ are the distinct components of the angular momentum. We also show that, in all dimensions, the inequality is saturated if the metric is a so-called ``near horizon geometry''. Our argument is entirely quasi-local, and hence also applies e.g. to any stably outer marginally trapped surface.Comment: 16 pages, Latex, no figure