227 research outputs found
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
Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity
Using a multi domain spectral method, we investigate systematically the
general-relativistic model for axisymmetric uniformly rotating, homogeneous
fluid bodies generalizing the analytically known Maclaurin and Schwarzschild
solutions. Apart from the curves associated with these solutions and a further
curve of configurations that rotate at the mass shedding limit, two more curves
are found to border the corresponding two parameter set of solutions. One of
them is a Newtonian lens shaped sequence bifurcating from the Maclaurin
spheroid sequence, while the other one corresponds to highly relativistic
bodies with an infinite central pressure. The properties of the configuration
for which both the gravitational and the baryonic masses, moreover angular
velocity, angular momentum as well as polar red shift obtain their maximal
values are discussed in detail. In particular, by comparison with the static
Schwarzschild solution, we obtain an increase of 34.25% in the gravitational
mass. Moreover, we provide exemplarily a discussion of angular velocity and
gravitational mass on the entire solution class.Comment: 4 pages, 4 figures, 1 table, submitted to A&A, corrected eq. for W,
W' in 3.
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
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
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 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 Masses in Regular Stationary Spacetimes
A highly accurate multi-domain spectral method is used to study axially symmetric and stationary spacetimes containing a black hole or disc of dust surrounded by a ring of matter. It is shown that the matter ring can affect the properties of the central object drastically. In particular, by virtue of the ring's frame dragging, the so-called Komar mass of the black hole or disc can become negative. A continuous transition from such discs to such black holes can be found
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