Extremal black hole initial data deformations

We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the $t$-$\phi$ symmetry implies the existence of a family of deformed data having the same horizon structure. This result allows us to measure how close solutions to Lichnerowicz equation are when arising from nearby free data.Comment: 21 pages, no figures, final versio

Small deformations of extreme Kerr black hole initial data

We prove the existence of a family of initial data for Einstein equations which represent small deformations of the extreme Kerr black hole initial data. The data in this family have the same asymptotic geometry as extreme Kerr. In particular, the deformations preserve the angular momentum and the area of the cylindrical end.Comment: 26 pages, 4 figure

Horizon area--angular momentum inequality for a class of axially symmetric black holes

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 extensively used in the numerical evolution of rotating black holes. They can describe highly distorted black holes, not necessarily near equilibrium. We also prove the inequality on extreme throat initial data, extending previous results.Comment: 23 pages, 5 figures. We improved the hypothesis of the main theore

Black hole Area-Angular momentum-Charge inequality in dynamical non-vacuum spacetimes

We show that the area-angular momentum-charge inequality (A/(4\pi))^2 \geq (2J)^2 + (Q_E^2 + Q_M^2)^2 holds for apparent horizons of electrically and magnetically charged rotating black holes in generic dynamical and non-vacuum spacetimes. More specifically, this quasi-local inequality applies to axially symmetric closed outermost stably marginally (outer) trapped surfaces, embedded in non-necessarily axisymmetric black hole spacetimes with non-negative cosmological constant and matter content satisfying the dominant energy condition.Comment: 4 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

Extreme Bowen-York initial data

The Bowen-York family of spinning black hole initial data depends essentially on one, positive, free parameter. The extreme limit corresponds to making this parameter equal to zero. This choice represents a singular limit for the constraint equations. We prove that in this limit a new solution of the constraint equations is obtained. These initial data have similar properties to the extreme Kerr and Reissner-Nordstrom black hole initial data. In particular, in this limit one of the asymptotic ends changes from asymptotically flat to cylindrical. The existence proof is constructive, we actually show that a sequence of Bowen-York data converges to the extreme solution.Comment: 21 page