Marcus Ansorg

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 pseudospectral 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 semianalytical 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.

Recoil velocities from equal-mass binary black-hole mergers: A systematic investigation of spin-orbit aligned configurations

The final evolution of a binary-black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for nonspinning binaries with unequal masses have pointed out that kick velocities approximately 175 km/s can be reached for a mass ratio approximately 0.36. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as approximately 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.

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 (8piJ);{2}+(4piQ;{2});{2}=A;{+}A;{-}, where A+ and A- denote the areas of event and Cauchy horizon, respectively.

Highly accurate calculation of rotating neutron stars

A new spectral code for constructing general–relativistic models of rapidly rotating stars with an unprecedented accuracy is presented. As a first application, we reexamine uniformly rotating homogeneous stars and compare our results with those obtained by several previous codes. Moreover, representative relativistic examples corresponding to highly flattened rotating bodies are given.

A universal inequality between the angular momentum and horizon area for axisymmetric and stationary black holes with surrounding matter

We prove that for sub-extremal axisymmetric and stationary black holes with arbitrary surrounding matter the inequality 8π|J| < A holds, where J is the angular momentum and A the horizon area of the black hole.

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 (J{sub c}/M{sub c}{sup 2}>1)

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 is the well-known black hole mass parameter introduced by Christodoulou and Ruffini.

Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids

We present a thorough investigation of sequences of uniformly rotating, homogeneous axisymmetric Newtonian equilibrium configurations that bifurcate from highly flattened Maclaurin spheroids. Each one of these sequences possesses a mass-shedding limit. Starting at this point, the sequences proceed towards the Maclaurin sequence and beyond. The first sequence leads to the well-known Dyson rings, whereas the end-points of the higher sequences are characterized by the formation of a two-body system, either a core‐ring system (for the second, the fourth, etc., sequence) or a two-ring system (for the third, the fifth, etc., sequence). Although the general qualitative picture drawn by Eriguchi and Hachisu in the 1980s has been confirmed, slight differences arise in the interpretation of the origin of the first two-ring sequence and in the general appearance of fluid bodies belonging to higher sequences.

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.

Numerical evolutions of a black hole-neutron star system in full general relativity: Head-on collision

We present the first simulations in full general relativity of the head-on collision between a neutron star and a black hole of comparable mass. These simulations are performed through the solution of the Einstein equations combined with an accurate solution of the relativistic hydrodynamics equations via high-resolution shock-capturing techniques. The initial data is obtained by following the York-Lichnerowicz conformal decomposition with the assumption of time symmetry. Unlike other relativistic studies of such systems, no limitation is set for the mass ratio between the black hole and the neutron star, nor on the position of the black hole, whose apparent horizon is entirely contained within the computational domain. The latter extends over