A Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity

We present a multi-domain spectral method to compute initial data of binary systems in General Relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided up into two subdomains within which the spectral expansion of the field quantities is carried out. If a component of the binary is a neutron star, a further subdomain covering the star's interior is added. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes, binary neutron stars or mixed binaries. In particular, it is possible to describe a black hole component by the puncture ansatz as well as through an excision technique. First examples are given for binary black hole excision data that fulfill the requirements of the quasi-stationary framework, which combines the Conformal Thin Sandwich formulation of the constraint equations with the Isolated Horizon conditions for black holes in quasi-equilibrium. These numerical solutions were obtained to extremely high accuracy with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large mass ratios of the binary components

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

A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.Comment: Contribution to the "Encuentros Relativistas Espanoles - Spanish Relativity Meeting ERE07" Proceedings, Tenerife, Spain (September 2007

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

Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods

We give a detailed description of the recently developed multi-domain spectral method for constructing highly accurate general-relativistic models of rapidly rotating stars. For both "ordinary" and "critical" configurations, it is exhibited by means of representative examples, how the accuracy improves as the order of the approximation increases. Apart from homogeneous fluid bodies, we also discuss models of polytropic and strange stars.Comment: 22 pages, 4 figures, 9 tables, version accepted by A&

Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity

We present a multi-domain spectral method to compute initial data of binary systems in General Relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided up into two subdomains within which the spectral expansion of the field quantities is carried out. If a component of the binary is a neutron star, a further subdomain covering the star's interior is added. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes, binary neutron stars or mixed binaries. In particular, it is possible to describe a black hole component by the puncture ansatz as well as through an excision technique. First examples are given for binary black hole excision data that fulfill the requirements of the quasi-stationary framework, which combines the Conformal Thin Sandwich formulation of the constraint equations with the Isolated Horizon conditions for black holes in quasi-equilibrium. These numerical solutions were obtained to extremely high accuracy with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large mass ratios of the binary components

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

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. 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 a negative Komar mass. Furthermore, there exists a continuous transition from discs to black holes even when their Komar masses are negative

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