The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory

We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8\pi J)2+(4\pi Q2)2=A+ A-, where A+ and A- denote the areas of event and Cauchy horizon respectively

Universal properties of distorted Kerr-Newman black holes

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 (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr-Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.Comment: 7 page

The interior of axisymmetric and stationary black holes: Numerical and analytical studies

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms of a single-domain fully pseudo-spectral scheme. Thereafter, a rigorous mathematical approach is given, in which soliton methods are utilized to derive an explicit relation between the event horizon and an inner Cauchy horizon. This horizon arises as the boundary of the future domain of dependence of the event horizon. Our numerical studies provide strong evidence for the validity of the universal relation \Ap\Am = (8\pi J)^2 where \Ap and \Am are the areas of event and inner Cauchy horizon respectively, and $J$ denotes the angular momentum. With our analytical considerations we are able to prove this relation rigorously.Comment: Proceedings of the Spanish Relativity Meeting ERE 2010, 10 pages, 5 figure

Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity

We study the transition from inspiral to plunge in general relativity by computing gravitational waveforms of non-spinning, equal-mass black-hole binaries. We consider three sequences of simulations, starting with a quasi-circular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, prior to coalescence of the holes. For each sequence, the binding energy of the system is kept constant and the orbital angular momentum is progressively reduced, producing orbits of increasing eccentricity and eventually a head-on collision. We analyze in detail the radiation of energy and angular momentum in gravitational waves, the contribution of different multipolar components and the final spin of the remnant. We find that the motion transitions from inspiral to plunge when the orbital angular momentum L=L_crit is about 0.8M^2. For L<L_crit the radiated energy drops very rapidly. Orbits with L of about L_crit produce our largest dimensionless Kerr parameter for the remnant, j=J/M^2=0.724. Generalizing a model recently proposed by Buonanno, Kidder and Lehner to eccentric binaries, we conjecture that (1) j=0.724 is the maximal Kerr parameter that can be obtained by any merger of non-spinning holes, and (2) no binary merger (even if the binary members are extremal Kerr black holes with spins aligned to the orbital angular momentum, and the inspiral is highly eccentric) can violate the cosmic censorship conjecture.Comment: Added sequence of long inspirals to the study. To match published versio

Numerical implementation of isolated horizon boundary conditions

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasiequilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the conformal thin sandwich equations. As main results, we first establish the consistency of including in the set of boundary conditions a constant surface gravity prescription, interpretable as a lapse boundary condition, and second we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the conformal transverse traceless equations with quasiequilibrium horizon conditions extend to the conformal thin sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon

A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter

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 spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity $a=J/M$ is the black hole's intrinsic angular momentum per unit mass, $Q$ its electric charge and $M$ the well known black hole mass parameter introduced by Christodoulou and Ruffini.Comment: 19 pages, 2 figures, replaced with published versio

A single-domain spectral method for black hole puncture data

We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these methods exhibit rapid convergence of the conformal factor and lead to highly accurate solutions. As an application we investigate small mass ratios of binary black holes and compare these with the corresponding test mass limit that we obtain through a semi-analytical limiting procedure. In particular, we compare the binding energy of puncture data in this limit with that of a test particle in the Schwarzschild spacetime and find that it deviates by 50% from the Schwarzschild result at the innermost stable circular orbit of Schwarzschild, if the ADM mass at each puncture is used to define the local black hole masses.Comment: 13 pages, 6 figures; published version with one important change, see Fig. 4 and the corresponding changes to the tex

Black Holes Surrounded by Uniformly Rotating Rings

Highly accurate numerical solutions to the problem of Black Holes surrounded by uniformly rotating rings in axially symmetric, stationary spacetimes are presented. The numerical methods developed to handle the problem are discussed in some detail. Related Newtonian problems are described and numerical results provided, which show that configurations can reach an inner mass-shedding limit as the mass of the central object increases. Exemplary results for the full relativistic problem for rings of constant density are given and the deformation of the event horizon due to the presence of the ring is demonstrated. Finally, we provide an example of a system for which the angular momentum of the central Black Hole divided by the square of its mass exceeds one.Comment: 12 pages, 14 figures, revtex, v4: minor changes, Eq. (17) corrected, corresponds to version in PR

Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin-spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-G\'omez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.Comment: 15 pages, 3 figures; Contribution to Juergen Ehlers Memorial Issue (GeRG journal

Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes

We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. The one type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of dust surrounded by such a ring. Both types of spacetime are regular everywhere (outside of the horizon in the case of the black hole) and fulfil the requirements of the positive energy theorem. However, it is shown that both the black hole and the disc can have negative Komar mass. Furthermore, there exists a continuous transition from discs to black holes even when their Komar masses are negative.Comment: 7 pages, 2 figures, document class iopart. v2: changes made (including title) to coincide with published versio