# Two Black Hole Initial Data

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### The Evolution of Distorted Rotating Black Holes III: Initial Data

Black hole initial data sets, based on the Einstein-Rosen bridge construction [13], have been developed over the last few decades. In the early 1960 s a series of time symmetric, conformally at wormhole data sets cor-responding to two black holes were developed by Mis-ner [14] and Brill and Lindquist [15]. At about the same

### PHYSICAL REVIEW D 024012 (2011) Simple method to set up low

realistic binary black hole systems that have been inspiral-ing already for a long time, we expect the two black holes to be in quasicircular orbits around each other with a radius which shrinks on a timescale much larger than the orbital timescale. This means that the initial data should be such that the orbit has no or at least very small

### ROTATING BLACK HOLE SPACETIMES BY STEVEN ROBERT BRANDT B.S

A new family of initial data sets, along with a study of their evolutions including apparent horizons, event horizons and gravitational radiation, is presented. These initial data sets represent distorted rotating black holes, and two types of non-rotating black holes with odd-parity radiation distortions. The first has the equatorial plane

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### Kerr-Schild type of initial data in the close limit approximation

Initial slice at a snapshot of a binary black hole merger In this regime, spacetime can be treated as a distorted single black hole Astrophysical realistic data? Very difﬁcult! Instead, use mathematical guidance Advantage of close limit approximation: (semi-) analytic insight; one can easily compute the radiated energy

### Black Holes in General Relativity - projecteuclid.org

In Section 2 a black hole is defined in terms of a event horizon and it is shown that the surface area of a black hole cannot decrease with time. In Section 3 it is shown that a rotating stationary black hole must be axisymmetric, and in Section 4 it is shown that any stationary black hole must have a topologically spherical boundary.

### Black Holes, Singularity Theorems, and All That

The goal of these last two lectures is to provide an introduction to global properties of General Relativity. We want to understand, for example (1) why formation of a singularity is inevitable once a trapped surface forms (2) why the area of a classical black hole can only increase (3) why, classically, one cannot traverse a wormhole ( topological

### A Two-Domain Spectral Method for Solving the Constraint

Two-Domain Spectral Grid General method for computing initial data for binaries We choose: Two-Domains for Excised Binary Black Holes Developed by Marcus Ansorg as a way to Compactify spatial infinity to a finite grid Resolve data at infinity Deal with puncture singularities (If using Puncture data) 7 of 18

### Initial Data for the Two-Body Problem of General Relativity

initial-data sets is developed by posing the apparent-horizon equation as a boundary-value problem. This method is applied to the single-hole, initial-data sets leading to a new understanding of the physical content of these initial hypersurfaces. The physical content of the two-hole, initial-data sets is also explored.

### arXiv:2106.01436v1 [gr-qc] 2 Jun 2021

In order to simulate black hole hyperbolic encounters in full GR, we have made use of the latest (2020) version of the Einstein Toolkit software [14, 15]. In particular, the Cactus Computational Toolkit [16, 17] was used, as well as the adaptive mesh re nement (AMR) grid infrastructure provided by Carpet [18, 19]. The initial two black hole data

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### Hirotaka Yoshino - ResearchGate

two-black-hole initial data, and the result suggests that the Penrose inequalities are satisﬁed in this system. This is the ﬁrst step for simulating black hole collisions in higher-curvature

### Initial Data for Black Holes and Rough Spacetimes

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### The mathematical analysis of black holes in general relativity

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### Approximate analytical solutions to the initial data problem

Initial data setting for multiple black hole spacetimes us-ing the method described by Matzner, Huq, and Shoemaker [email protected]# begins by specifying a conformal spatial metric which is a straightforward superposition of two Kerr-Schild single hole ~spatial! metrics: ˜g ijdx idx j5d ijdx idx 12 1H~xa!~ 1ljdxj!2 12 2H~xa!~ 2ljdxj!2. ~5!

### PHYSICAL REVIEW D 084054 (2012) Are different approaches to

astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using superposed Kerr-Schild initial data and compare with an analogous simulation using CF initial data. We ﬁnd that the resultant

### Puncture Initial Data and Evolution of Black Hole Binaries

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### A Variational Principle for Black Holes

It is shown that the initial data which gives rise to stationary black hole solutions extremizes the mass for a given angular momentum and area of the horizon. The only extremum of the mass for a given area of the horizon but arbitrary angular momentum is the Schwarzschild solution. In this case, and when the angular momentum

### Abstract References Constructing more astrophysically

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### Comparing initial-data sets for binary black holes

content of initial-data sets, and how to specify astrophysi-cally relevant initial data with the appropriate gravitational wave content, e.g., for two black holes orbiting each other. Unfortunately, assessing and controlling the gravitational wave content of initial-data sets is not well understood at all.

### Improved Initial Lapse and Shift for Binary Black Hole

Numerical Relativity simulations of binary black hole mergers in order to study the e ects of a new set of initial data for two equations used during the calculation of gravitational waveforms.

### INITIAL DATA FOR BLACK HOLE EVOLUTIONS

INITIAL DATA FOR BLACK HOLE EVOLUTIONS Harald Paul Pfeiﬀer, Ph.D. Cornell University 2003 We discuss the initial value problem of general relativity in its recently uniﬁed La-grangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the resulting coupled nonlinear partial diﬀerential equations.

### Beyond Conformally-Flat Black-Hole Initial Data

Beyond Conformally-Flat Black-Hole Initial Data Author: Jason D. Grigsby, Wake Forest University, Dept. of Physics Subject: Ref.Met. Keywords: black hole, initial data, astrophysical Created Date: 5/10/2008 9:07:00 PM

### Strong cosmic censorship in spherical symmetry for two-ended

Mar 07, 2017 at initial data I. The interior of the black hole region By Jonathan Luk and Sung-Jin Oh Abstract This is the rst and main paper of a two-part series, in which we prove the C2-formulation of the strong cosmic censorship conjecture for the Einstein{Maxwell-(real)-scalar- eld system in spherical symmetry for two-ended asymptotically at data.

### 084017 (2008) Binary-black-hole initial data with nearly

structing black-hole initial data with nearly extremal spin. First, we revisit puncture initial data and inversion-symmetric Bowen-York initial data. We show that for a single, spinning black hole at rest, both approaches are identical, and we determine spin limits based purely on initial data more accurately than before:

### Trumpet initial data for boosted black holes

position of single hole data. There is room within the scheme for later improvement to resolve (iterate) the constraint equations in the multiple black hole case. The approach is shown to yield an initial trumpet slice for one black hole that is close to, and rapidly settles to, a stationary trumpet geometry. By avoiding the

### Two black holes with axisymmetric parallel spins: initial data

The extrinsic curvature on an initial spacelike hypersurface of two black holes with axisymmetric parallel spins is derived in terms of an analytic infinite series. This curvature constitutes an important piece of the initial data required to solve completely the Cauchy problem of a head-on collision of two holes with spin.

### Embedding Negatively Curved Initial Data on Black-Hole

Embedding Negatively Curved Initial Data on Black-Hole Collisions in R3 Hsungrow Chan Abstract Visualizing the evolution of gravitating systems can be of considerable conceptual value, be-cause it provides important physical information about those systems such as initial data for the problem of the head-on collision of two black holes.

### Embedding negatively curved initial data of black- hole

an initial datum that describes the starting conﬁguration of black holes. All solutions must be discussed in multiply connected topology [15, 16]. According to the properties of black-hole collisions, the slice is supposed to be a surface with the general shape of a pair of trousers.

### Jonathan Winghong Luk - web.stanford.edu

at initial data II. The exterior of the black hole region, arXiv:1702.05716, Annals of PDE, 5(6), 2019. J. Luk and S.-J. Oh. Strong cosmic censorship in spherical symmetry for two-ended asymptoti-cally at initial data I. The interior of the black hole region, arXiv:1702.05715, Annals of Math 190(1):1{111, 2019. J. Luk and J. Speck.

### Multi-Domain Spectral Method for Initial Data of Arbitrary

the black hole is assumed which can be taken into account by a speciﬁc ansatz for the initial data. Therefore the relevant space for the constraint equations is all of R 3 k The excision techniques solve the constraints only in the exterior of an excised spheroid within which

### Close limit evolution of Kerr-Schild type initial data for

to each other. This brings to the forefront the problem of specifying initial data for the binary black hole collisions. Ideally, one would like to have initial data representing astrophysically relevant situations, that is, resembling the situation the two black holes would be in when they are in a realistic collision at the given separation.

### NUMERICAL STUDIES OF BLACK HOLE INITIAL DATA BY

currently the most commonly used binary black hole initial data, and Thin Sandwich data (TSD) based on a helical killing vector ansatz, that are thought to be very close to Post-Newtonian results. The two di erent sets are compared in terms of the phys-ical quantities that can be measured from the numerical data, and in terms of their

### The Use of PN Diagnostics in Evaluating Initial-Data Sets

Three-dimensional initial data for the collision of two black holes II: Quasicircular orbits Excision boundary conditions for black hole initial data. Phys. Rev

### Initial data for black hole collisions

of apparent horizon gives as a practical criteria to distinguish a black hole data. However, it is important to recall that in principle it is possible to have a black hole without any apparent horizon. A space time contains two black black hole if the event horizon has two discon-nected components.

### New Numerical Code for Black Hole Initial Data

New Numerical Code for Black Hole Initial Data HyperSolID Maria Babiuc Hamilton and Je Winicour 20th Eastern Gravity Meeting Penn State, University Park, PA June 9, 2017.

### Toward Astrophysical Black-Hole Binaries

Toward Astrophysical Black-Hole Binaries Gregory B. Cook Wake Forest University Mar. 29, 2002 Abstract A formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. If each black hole is assumed to be in quasi-equilibrium, then a complete set of

### Initial data transients in binary black hole evolutions

Initial data transients in binary black hole evolutions Nigel T. Bishop Department of Mathematics (Pure & Applied), Rhodes University, Grahamstown 6140, South Africa This poster is based on N. T. Bishop, D. Pollney, C. Reisswig, Initial data transients in binary black hole evolutions, arXiv:1101.5492.

### Black hole initial data by numerical integration of the

Black hole initial data by numerical struction of initial data for distorted black holes which, in certain cases, have homologous two-surfaces S