12 research outputs found
Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin
This dissertation explores numerical models of the orbit, inspiral, and merger phases of black hole binaries. We focus on the astrophysically realistic case of black holes with nearly extremal spins, and on high energy black hole collisions. To study the evolution of such systems, we form puncture initial data by solving the four general relativity constraint equations using pseudospectral methods on a compactified collocation point domain. The solutions to these coupled, nonlinear, elliptic differential equations represent the desired configuration at an initial moment. They are then propagated forward through time using a set of hyperbolic evolution equations with the moving punctures approach in the BSSNOK and CCZ4 formalisms. To generate realistic initial data with reduced spurious gravitational wave content, the background ansatz is taken to be a conformal superposition of Schwarzschild or Kerr spatial metrics. We track the punctures during evolution, measure their horizon properties, extract the gravitational waveforms, and examine the merger remnant. These new initial data are compared with the well known Bowen-York solutions, producing up to an order of magnitude reduction in the initial unphysical gravitational radiation signature. We perform a collision from rest of two black holes with spins near to the extremal value, in a region of parameter space inaccessible to Bowen-York initial data. We simulate nonspinning black holes in quasi-circular orbits, and perform high energy head-on collisions of nonspinning black holes to estimate the magnitude of the radiated gravitational energy in the limit of infinite momentum. We also evolve spinning black holes in quasi-circular orbits with unequal masses and different spin orientations. These models provide insight into the dynamics and signals generated by compact binary systems. This is crucial to our understanding of many astrophysical phenomena, especially to the interpretation of gravitational waves, which are expected to be detected directly for the first time within the next few years
High Energy Collisions of Black Holes Numerically Revisited
We use fully nonlinear numerical relativity techniques to study high energy
head-on collision of nonspinning, equal-mass black holes to estimate the
maximum gravitational radiation emitted by these systems. Our simulations
include improvements in the construction of initial data, subsequent full
numerical evolutions, and the computation of waveforms at infinity. The new
initial data significantly reduces the spurious radiation content, allowing for
initial speeds much closer to the speed of light, i.e. . Using
these new techniques, We estimate the maximum radiated energy from head-on
collisions to be . This value
differs from the second-order perturbative and zero-frequency-limit
analytic computations, but is close to those obtained by thermodynamic
arguments and by previous numerical estimates .Comment: 11 pages, 10 figure
Evolutions of Nearly Maximally Spinning Black Hole Binaries Using the Moving Puncture Approach
We demonstrate that numerical relativity codes based on the moving punctures
formalism are capable of evolving nearly maximally spinning black hole
binaries. We compare a new evolution of an equal-mass, aligned-spin binary with
dimensionless spin chi=0.99 using puncture-based data with recent simulations
of the SXS Collaboration. We find that the overlap of our new waveform with the
published results of the SXS Collaboration is larger than 0.999. To generate
our new waveform, we use the recently introduced HiSpID puncture data, the CCZ4
evolution system, and a modified lapse condition that helps keep the horizon
radii reasonably large.Comment: Version accepted to PRD. 7 pages, 8 figure
Puncture Initial Data for Black-Hole Binaries with High Spins and High Boosts
We solve the Hamiltonian and momentum constraints of general relativity for
two black holes with nearly extremal spins and relativistic boosts in the
puncture formalism. We use a non-conformally-flat ansatz with an attenuated
superposition of two Lorentz-boosted, conformally Kerr or conformally
Schwarzschild 3-metrics and their corresponding extrinsic curvatures. We
compare evolutions of these data with the standard Bowen-York conformally flat
ansatz (technically limited to intrinsic spins
and boosts ), finding, typically, an order of magnitude
smaller burst of spurious radiation and agreement with inspiral and merger. As
a first case study, we evolve two equal-mass black holes from rest with an
initial separation of and spins , compute the
waveforms produced by the collision, the energy and angular momentum radiated,
and the recoil of the final remnant black hole. We find that the black-hole
trajectories curve at close separations, leading to the radiation of angular
momentum. We also study orbiting nonspinning and moderate-spin black-hole
binaries and compare these with standard Bowen-York data. We find a substantial
reduction in the nonphysical initial burst of radiation which leads to cleaner
waveforms. Finally, we study the case of orbiting binary black-hole systems
with spin magnitude in an aligned configuration and compare
waveform and final remnant results with those of the SXS Collaboration, finding
excellent agreement. This represents the first moving punctures evolution of
orbiting and spinning black holes exceeding the Bowen-York limit. Finally, we
study different choices of the initial lapse and lapse evolution equation in
the moving punctures approach to improve the accuracy and efficiency of the
simulations.Comment: 23 pages, 32 figures. Version accepted to PR
Spinning Black Holes in Numerical Relativity
In nature, it is believed that astrophysical black holes will be nearly neutral and highly spinning. The first condition is due to the fact that, if the black hole were charged, it would preferentially attract opposing charges. The second follows from considerations of matter accreting onto the black hole. By conservation of angular momentum, it is expected that it might be common for black hole spins to approach their theoretical maximal value. In this regime, the non-linearity of Einstein\u27s equations comes into play, and effects such as frame dragging become strong. This becomes particularly interesting in the case of a black hole binary, in which emission of gravitational waves and black hole kicks become important. To date, the simulations with the largest black hole spins fail to probe the top ~35% of the maximal rotational energy. Thus, there is a substantial unexplored energy range that is of real astrophysical and theoretical interest. We use numerical methods to solve Einstein\u27s equations, which enable us to describe the motions of black holes under the influence of gravitation