arXiv subjects

Frans Pretorius

Publications and source records attributed to Frans Pretorius.

At least 73 records · Page 4Linked to original sources

arXiv2013

Ultrarelativistic black hole formation

We study the ultrarelativistic head-on collision of equal mass particles, modeled as self-gravitating fluid spheres, by numerically solving the coupled Einstein-hydrodynamic equations. We focus on cases well within the kinetic energy dominated regime, where between 88-92% ($γ=8$ to 12) of the initial net energy of the spacetime resides in the translation kinetic energy of the particles. We find that for sufficiently large boosts, black hole formation occurs. Moreover, near yet above the threshold of black hole formation, the collision initially leads to the formation of two distinct apparent horizons that subsequently merge. We argue that this can be understood in terms of a focusing effect, where one boosted particle acts as a gravitational lens on the other and vice versa, and that this is further responsible for the threshold being lower (by a factor of a few) compared to simple hoop conjecture estimates. Cases slightly below threshold result in complete disruption of the model particles. The gravitational radiation emitted when black holes form reaches luminosities of 0.014 $c^5/G$, carrying $16\pm2%$ of the total energy.

gr-qc↗

arXiv2013

Observing complete gravitational wave signals from dynamical capture binaries

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.

gr-qc↗

arXiv2013

Gravitational waves and stalled satellites from massive galaxy mergers at z <= 1

We present a model for merger-driven evolution of the mass function for massive galaxies and their central supermassive black holes at late times. We discuss the current observational evidence in favor of merger-driven massive galaxy evolution during this epoch, and demonstrate that the observed evolution of the mass function can be reproduced by evolving an initial mass function under the assumption of negligible star formation. We calculate the stochastic gravitational wave signal from the resulting black-hole binary mergers in the low redshift universe (z <= 1) implied by this model, and find that this population has a signal-to-noise ratio as much as ~5x larger than previous estimates for pulsar timing arrays, with an expectation value for the characteristic strain h_c (f=1 yr^{-1}) = 4.1 x 10^{-15} that may already be in tension with observational constraints, and a {2-sigma, 3-sigma} lower limit within this model of h_c (f=1 yr^{-1}) = {1.1 x 10^{-15}, 6.8 x 10^{-16}}. The strength of this signal is sufficient to make it detectable with high probability under conservative assumptions within the next several years, if the principle assumption of merger-driven galaxy evolution since z = 1 holds true. For cases where a galaxy merger fails to lead to a black hole merger, we estimate the probability for a given number of satellite unmerged black holes to remain within a massive host galaxy, and interpret the result in light of ULX observations. In particular, we find that the brightest cluster galaxies should have 1-2 such sources with luminosities above 10^{39} erg/s, which is consistent with the statistics of observed ULXs.

astro-ph.CO↗

arXiv2013

Eccentric binary neutron star mergers

Neutron star binaries offer a rich phenomenology in terms of gravitational waves and merger remnants. However, most general relativistic studies have been performed for nearly circular binaries, with the exception of head-on collisions. We present the first numerical relativity investigation of mergers of eccentric equal-mass neutron-star binaries that probes the regime between head-on and circular. In addition to gravitational waves generated by the orbital motion, we find that the signal also contains a strong component due to stellar oscillations (f-modes) induced by tidal forces, extending a classical result for Newtonian binaries. The merger can lead to rather massive disks on the order of 10% of the total initial mass.

gr-qc↗

arXiv2012

The imminent detection of gravitational waves from massive black-hole binaries with pulsar timing arrays

Recent observations of massive galaxies indicate that they double in mass and quintuple in size between redshift z = 1 and the present, despite undergoing very little star formation, suggesting that galaxy mergers drive the evolution. Since these galaxies will contain supermassive black holes, this suggests a larger black hole merger rate, and therefore a larger gravitational-wave signal, than previously expected. We calculate the merger-driven evolution of the mass function, and find that merger rates are 10 to 30 times higher and gravitational waves are 3 to 5 times stronger than previously estimated, so that the gravitational-wave signal may already be detectable with existing data from pulsar timing arrays. We also provide an explanation for the disagreement with past estimates that were based on dark matter halo simulations.

astro-ph.CO↗

arXiv2012

Conformal Thin-Sandwich Solver for Generic Initial Data

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.

gr-qc↗

arXiv2012

Dynamical Capture Binary Neutron Star Mergers

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.

astro-ph.HE↗

arXiv2012

Hydrodynamics in full general relativity with conservative AMR

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.

gr-qc↗

arXiv2012

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

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.

astro-ph.HE↗

arXiv2012

Simulation of Asymptotically AdS5 Spacetimes with a Generalized Harmonic Evolution Scheme

Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be described by the (t,r,χ,θ,ϕ) spherical coordinates adapted to the R{\times}S3 boundary. We focus on solutions that preserve an SO(3) symmetry that acts to rotate the 2-spheres parametrized by θ,ϕ. In the boundary conformal field theory (CFT), the way in which this symmetry manifests itself hinges on the way we choose to embed Minkowski space in R{\times}S3. We present results from an ongoing study of prompt black hole formation via scalar field collapse, and explore the subsequent quasi-normal ringdown. Beginning with initial data characterized by highly distorted apparent horizon geometries, the metrics quickly evolve, via quasi-normal ringdown, to equilibrium static black hole solutions at late times. The lowest angular number quasi-normal modes are consistent with the linear modes previously found in perturbative studies, whereas the higher angular modes are a combination of linear modes and of harmonics arising from non-linear mode-coupling. We extract the stress energy tensor of the dual CFT on the boundary, and find that despite being highly inhomogeneous initially, it nevertheless evolves from the outset in a manner that is consistent with a thermalized N=4 SYM fluid. As a first step towards closer contact with relativistic heavy ion collision physics, we map this solution to a Minkowski piece of the R{\times}S3 boundary, and obtain a corresponding fluid flow in Minkowski space.

hep-th↗

arXiv2012

Detectable seismic consequences of the interaction of a primordial black hole with Earth

Galaxies observed today are likely to have evolved from density perturbations in the early universe. Perturbations that exceeded some critical threshold are conjectured to have undergone gravitational collapse to form primordial black holes (PBHs) at a range of masses. Such PBHs serve as candidates for cold dark matter and their detection would shed light on conditions in the early universe. Here we propose a mechanism to search for transits of PBHs through/nearby Earth by studying the associated seismic waves. Using a spectral-element method, we simulate and visualize this seismic wave field in Earth's interior. We predict the emergence of two unique signatures, namely, a wave that would arrive almost simultaneously everywhere on Earth's free surface and the excitation of unusual spheroidal modes with a characteristic frequency-spacing in free oscillation spectra. These qualitative characteristics are unaffected by the speed or proximity of the PBH trajectory. The seismic energy deposited by a proximal ${M^{PBH} = 10^{15}}$ g PBH is comparable to a magnitude $M_w=4$ earthquake. The non-seismic collateral damage due to the actual impact of such small PBHs with Earth would be negligible. Unfortunately, the expected collision rate is very low even if PBHs constituted all of dark matter, at ${\sim 10^{-7} {yr}^{-1}}$, and since the rate scales as ${1/M^{PBH}}$, fortunately encounters with larger, Earth-threatening PBHs are exceedingly unlikely. However, the rate at which non-colliding close encounters of PBHs could be detected by seismic activity alone is roughly two orders of magnitude larger --- that is once every hundred thousand years --- than the direct collision rate.

astro-ph.CO↗

arXiv2012

NR/HEP: roadmap for the future

Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong field astrophysical processes, could prove extremely useful to understand high-energy physics processes like trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with guidelines for the next years. This writeup is a summary of the "NR/HEP Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011.

hep-th↗

arXiv2011

Gravitational Wave Tests of General Relativity with the Parameterized Post-Einsteinian Framework

Gravitational wave astronomy has tremendous potential for studying extreme astrophysical phenomena and exploring fundamental physics. The waves produced by binary black hole mergers will provide a pristine environment in which to study strong field, dynamical gravity. Extracting detailed information about these systems requires accurate theoretical models of the gravitational wave signals. If gravity is not described by General Relativity, analyses that are based on waveforms derived from Einstein's field equations could result in parameter biases and a loss of detection efficiency. A new class of "parameterized post-Einsteinian" (ppE) waveforms has been proposed to cover this eventuality. Here we apply the ppE approach to simulated data from a network of advanced ground based interferometers (aLIGO/aVirgo) and from a future spaced based interferometer (LISA). Bayesian inference and model selection are used to investigate parameter biases, and to determine the level at which departures from general relativity can be detected. We find that in some cases the parameter biases from assuming the wrong theory can be severe. We also find that gravitational wave observations will beat the existing bounds on deviations from general relativity derived from the orbital decay of binary pulsars by a large margin across a wide swath of parameter space.

gr-qc↗

arXiv2011

Eccentric Black Hole-Neutron Star Mergers

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.

astro-ph.HE↗

arXiv2011

Final State of Gregory-Laflamme Instability

We describe the behavior of a perturbed 5-dimensional black string subject to the Gregory-Laflamme instability. We show that the horizon evolves in a self-similar manner, where at any moment in the late-time development of the instability the horizon can be described as a sequence of 3-dimensional spherical black holes of varying size, joined by black string segments of similar radius. As with the initial black string, each local string segment is itself unstable, and this fuels the self-similar cascade to (classically) arbitrarily small scales; in the process the horizon develops a fractal structure. In finite asymptotic time, the remaining string segments shrink to zero-size, yielding a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship. We further discuss how this behavior is related to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability, and estimate the fractal dimension of the horizon prior to formation of the naked singularity.

gr-qc↗

arXiv2011

Surprises in the Evaporation of 2-Dimensional Black Holes

Quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes is analyzed in the mean field approximation. This semi-classical theory incorporates back reaction. Detailed analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties (which are distinct from the features observed in the simplified, exactly soluble models). Although the literature on CGHS black holes is quite rich, these features had escaped previous analyses, in part because of lack of required numerical precision, and in part because certain properties and symmetries of the model were not fully recognized. Finally, our results provide support for the full quantum gravity scenario recently developed by Ashtekar, Taveras and Varadarajan.

gr-qc↗

arXiv2011

A Dynamical Systems Approach to Schwarzschild Null Geodesics

The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum Lc corresponds to the unstable circular orbit at r=3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r=0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the limit as L goes to infinity, as described in Schwarzschild coordinates, these geodesics begin at r=0, flow along t=constant lines, turn around at r=2M, then continue to r=0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.

gr-qc↗

arXiv2011

Evaporation of 2-Dimensional Black Holes

We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes within the mean-field approximation. This semi-classical theory incorporates back reaction. Our analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. One of the anticipated properties we confirm is that the semi-classical space-time is asymptotically flat at right future null infinity, $\spr$, yet incomplete in the sense that null observers reach a future Cauchy horizon in finite affine time. Unexpected behavior includes that the Bondi mass traditionally used in the literature can become negative even when the area of the horizon is macroscopic; an improved Bondi mass remains positive until the end of semi-classical evaporation, yet the final value can be arbitrarily large relative to the Planck mass; and the flux of the quantum radiation at $\spr$ is non-thermal even when the horizon area is large compared to the Planck scale. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties. Although the literature on CGHS black holes is quite rich, these features had escaped previous analyses, in part because of lack of required numerical precision, and in part due to misinterpretation of certain properties and symmetries of the model. Finally, our results provide support for the full quantum scenario recently developed by Ashtekar, Taveras and Varadarajan, and also offer a number of interesting problems to the mathematical relativity and geometric analysis communities.

gr-qc↗