William E. East

Publications (9)7.37 Total impact

• Article: Ultrarelativistic black hole formation.

  William E East, Frans Pretorius
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  ABSTRACT: We study the head-on collision of fluid particles well within the kinetic energy dominated regime (γ=8 to 12) by numerically solving the Einstein-hydrodynamic equations. We find that the threshold for black hole formation is lower (by a factor of a few) than simple hoop conjecture estimates, and, moreover, near this threshold two distinct apparent horizons first form postcollision and then merge. We argue that this can be understood in terms of a gravitational focusing effect. The gravitational radiation reaches luminosities of 0.014 c^{5}/G, carrying 16±2% of the total energy.
  Physical Review Letters 03/2013; 110(10):101101. · 7.37 Impact Factor
• Article: Simulating extreme-mass-ratio systems in full general relativity

  William E. East, Frans Pretorius
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  ABSTRACT: We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract off its contribution to the truncation error, thereby more efficiently achieving a desired level of accuracy. We demonstrate the method by applying it to the radial infall of a solar-type star into supermassive black holes with mass ratios $\geq 10^6$. The self-gravity of the star is thus consistently modeled within the context of general relativity, and the star's interaction with the black hole computed with moderate computational cost, despite the over five orders of magnitude difference in gravitational potential (as defined by the ratio of mass to radius). We compute the tidal deformation of the star during infall, and the gravitational wave emission, finding the latter is close to the prediction of the point-particle limit.
  03/2013;
• Article: Observing complete gravitational wave signals from dynamical capture binaries

  William E. East, Sean T. McWilliams, Janna Levin, Frans Pretorius
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  ABSTRACT: We assess the detectability of the gravitational wave signals from highly eccentric compact binaries. We use a simple model for the inspiral, merger, and ringdown of these systems. The model is based on mapping the binary to an effective single black hole system described by a Kerr metric, thereby including certain relativistic effects such as zoom-whirl-type behavior. The resultant geodesics source quadrupolar radiation and, in turn, are evolved under its dissipative effects. At the light ring, we attach a merger model that was previously developed for quasicircular mergers but also performs well for eccentric mergers with little modification. We apply this model to determine the detectability of these sources for initial, Enhanced, and Advanced LIGO across the parameter space of nonspinning close capture compact binaries. We conclude that, should these systems exist in nature, the vast majority will be missed by conventional burst searches or by quasicircular waveform templates in the advanced detector era. Other methods, such as eccentric templates or, more practically, a stacked excess power search, must be developed to avoid losing these sources. These systems would also have been missed frequently in the initial LIGO data analysis. Thus, previous null coincidence results with detected gamma-ray bursts cannot exclude the possibility of coincident gravitational wave signals from eccentric binaries.
  12/2012;
• Article: Dynamical Capture Binary Neutron Star Mergers

  William E. East, Frans Pretorius
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  ABSTRACT: We study dynamical capture binary neutron star mergers as may arise in dense stellar regions such as globular clusters. Using general-relativistic hydrodynamics, we find that these mergers can result in the prompt collapse to a black hole or in the formation of a hypermassive neutron star, depending not only on the neutron star equation of state but also on impact parameter. We also find that these mergers can produce accretion disks of up to a tenth of a solar mass and unbound ejected material of up to a few percent of a solar mass. We comment on the gravitational radiation and electromagnetic transients that these sources may produce.
  08/2012;
• Article: Conformal Thin-Sandwich Solver for Generic Initial Data

  William E. East, Fethi M. Ramazanoğlu, Frans Pretorius
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  ABSTRACT: We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for determining free data based on superposition, as well as a way to handle black hole singularities without excision. We numerically solve the constraint equations using a multigrid algorithm with mesh refinement. We demonstrate the efficacy of the method with initial data solutions for several applications: a quasicircular binary black hole merger, a dynamical capture black hole-neutron star merger, and an ultrarelativistic collision.
  08/2012;
• Article: Hydrodynamics in full general relativity with conservative adaptive mesh refinement

  William E. East, Frans Pretorius, Branson C. Stephens
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  ABSTRACT: There is great interest in numerical relativity simulations involving matter due to the likelihood that binary compact objects involving neutron stars will be detected by gravitational wave observatories in the coming years, as well as to the possibility that binary compact object mergers could explain short-duration gamma-ray bursts. We present a code designed for simulations of hydrodynamics coupled to the Einstein field equations targeted toward such applications. This code has recently been used to study eccentric mergers of black hole-neutron star binaries. We evolve the fluid conservatively using high-resolution shock-capturing methods, while the field equations are solved in the generalized-harmonic formulation with finite differences. In order to resolve the various scales that may arise, we use adaptive mesh refinement (AMR) with grid hierarchies based on truncation error estimates. A noteworthy feature of this code is the implementation of the flux correction algorithm of Berger and Colella to ensure that the conservative nature of fluid advection is respected across AMR boundaries. We present various tests to compare the performance of different limiters and flux calculation methods, as well as to demonstrate the utility of AMR flux corrections.
  Phys. Rev. D. 06/2012; 85(12).
• Source

  Available from: ArXiv

  Article: Hydrodynamics in full general relativity with conservative AMR

  William E. East, Frans Pretorius, Branson C. Stephens
  [show abstract] [hide abstract]
  ABSTRACT: There is great interest in numerical relativity simulations involving matter due to the likelihood that binary compact objects involving neutron stars will be detected by gravitational wave observatories in the coming years, as well as to the possibility that binary compact object mergers could explain short-duration gamma-ray bursts. We present a code designed for simulations of hydrodynamics coupled to the Einstein field equations targeted toward such applications. This code has recently been used to study eccentric mergers of black hole-neutron star binaries. We evolve the fluid conservatively using high-resolution shock-capturing methods, while the field equations are solved in the generalized-harmonic formulation with finite differences. In order to resolve the various scales that may arise, we use adaptive mesh refinement (AMR) with grid hierarchies based on truncation error estimates. A noteworthy feature of this code is the implementation of the flux correction algorithm of Berger and Colella to ensure that the conservative nature of fluid advection is respected across AMR boundaries. We present various tests to compare the performance of different limiters and flux calculation methods, as well as to demonstrate the utility of AMR flux corrections.
  12/2011;
• Source

  Available from: ArXiv

  Article: Eccentric black hole-neutron star mergers: effects of black hole spin and equation of state

  William E. East, Frans Pretorius, Branson C. Stephens
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  ABSTRACT: There is a high level of interest in black hole-neutron star binaries, not only because their mergers may be detected by gravitational wave observatories in the coming years, but also because of the possibility that they could explain a class of short duration gamma-ray bursts. We study black hole-neutron star mergers that occur with high eccentricity as may arise from dynamical capture in dense stellar regions such as nuclear or globular clusters. We perform general relativistic simulations of binaries with a range of impact parameters, three different initial black hole spins (zero, aligned and anti-aligned with the orbital angular momentum), and neutron stars with three different equations of state. We find a rich diversity across these parameters in the resulting gravitational wave signals and matter dynamics, which should also be reflected in the consequent electromagnetic emission. Before tidal disruption, the gravitational wave emission is significantly larger than perturbative predictions suggest for periapsis distances close to effective innermost stable separations, exhibiting features reflecting the zoom-whirl dynamics of the orbit there. Guided by the simulations, we develop a simple model for the change in orbital parameters of the binary during close encounters. Depending upon the initial parameters of the system, we find that mass transfer during non-merging close encounters can range from essentially zero to a sizable fraction of the initial neutron star mass. The same holds for the amount of material outside the black hole post-merger, and in some cases roughly half of this material is estimated to be unbound. We also see that non-merging close encounters generically excite large oscillations in the neutron star that are qualitatively consistent with f-modes.
  11/2011;
• Source

  Available from: ArXiv

  Article: Eccentric Black Hole-Neutron Star Mergers

  Branson C. Stephens, William E. East, Frans Pretorius
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  ABSTRACT: Within the next few years gravitational waves (GWs) from merging black holes (BHs) and neutron stars (NSs) may be directly detected, making a thorough theoretical understanding of these systems a high priority. As an additional motivation, these systems may represent a subset of short-duration gamma-ray burst (sGRB) progenitors. BH-NS mergers are expected to result from primordial, quasi-circular inspiral as well as dynamically formed capture binaries. The latter channel allows mergers with high eccentricity, resulting in a richer variety of outcomes. We perform general relativistic simulations of BH-NS interactions with a range of impact parameters, and find significant variation in the properties of these events that have potentially observable consequences, namely the GW signature, remnant accretion disk mass, and amount of unbound material.
  05/2011;