arXiv subjects

Helvi Witek

Publications and source records attributed to Helvi Witek.

50 records · Page 3Linked to original sources

arXiv2013

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

gr-qc↗

arXiv2013

Lecture Notes: Numerical Relativity in higher dimensional spacetimes

Black holes are among the most exciting phenomena predicted by General Relativity and play a key role in fundamental physics. Many interesting phenomena involve dynamical black hole configurations in the high curvature regime of gravity. In these lecture notes I will summarise the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic $D$-dimensional spacetimes.

gr-qc↗

arXiv2013

Black hole dynamics in generic spacetimes

The dynamics of black hole spacetimes play a crucial role in astrophysics, high energy physics and fundamental physics. In this thesis I have investigated the dynamics of black holes in generic spacetimes by extending established numerical relativity methods to higher dimensional or non-asymptotically flat spacetimes. Additionally, I have explored BH spacetimes perturbed my massive scalar fields. By developing and further improving NR techniques I have been able to push our knowledge to new grounds.

gr-qc↗

arXiv2013

Superradiant instabilities in astrophysical systems

Light bosonic degrees of freedom have become a serious candidate for dark matter. The evolution of these fields around curved spacetimes is poorly understood but is expected to display interesting effects. In particular, the interaction of light bosonic fields with supermassive black holes, key players in most galaxies, could provide colourful examples of superradiance and nonlinear bosenova-like collapse. In turn, the observation of spinning black holes is expected to impose stringent bounds on the mass of putative massive bosonic fields in our universe. Our purpose here is to present a comprehensive study of the evolution of linearized massive scalar and vector fields in the vicinities of rotating black holes. For a certain boson field mass range, the field can become trapped in a potential barrier outside the horizon and transition to a bound state. Because there are a number of such quasi-bound states, the generic outcome is an amplitude modulated sinusoidal, or beating, signal. We believe that the appearance of such beatings has gone unnoticed in the past, and in fact mistaken for exponential growth. The amplitude modulation of the signal depends strongly on the relative excitation of the overtones, which in turn is strongly tied to the bound-state geography. For the first time we explore massive vector fields in generic BH background which are hard, if not impossible, to separate in the Kerr background. Our results show that spinning BHs are generically strongly unstable against massive vector fields.

gr-qc↗

arXiv2012

Dynamics of black holes in de Sitter spacetimes

Nonlinear dynamics in cosmological backgrounds has the potential to teach us immensely about our universe, and also to serve as prototype for nonlinear processes in generic curved spacetimes. Here we report on dynamical evolutions of black holes in asymptotically de Sitter spacetimes. We focus on the head-on collision of equal mass binaries and for the first time compare analytical and perturbative methods with full blown nonlinear simulations. Our results include an accurate determination of the merger/scatter transition (consequence of an expanding background) for small mass binaries and a test of the Cosmic Censorship conjecture, for large mass binaries. We observe that, even starting from small separations, black holes in large mass binaries eventually lose causal contact, in agreement with the conjecture.

gr-qc↗

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

Higher-dimensional puncture initial data

We calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of D dimensional vacuum gravity. The data are generated by a modification of the pseudo-spectral code presented in arXiv:gr-qc/0404056 and made available as the TwoPunctures thorn inside the Cactus computational toolkit. As examples, we exhibit convergence plots, the violation of the Hamiltonian constraint as well as the initial data for D=4,5,6,7. These initial data are the starting point to perform high energy collisions of black holes in D dimensions.

gr-qc↗

arXiv2011

Stability of the puncture method with a generalized BSSN formulation

The puncture method for dealing with black holes in the numerical simulation of vacuum spacetimes is remarkably successful when combined with the BSSN formulation of the Einstein equations. We examine a generalized class of formulations modeled along the lines of the Laguna-Shoemaker system, including BSSN as a special case. The formulation is a two parameter generalization of the choice of variables used in standard BSSN evolutions. Numerical stability of the standard finite difference methods is proven for the formulation in the linear regime around flat space, a special case of which is the numerical stability of BSSN. Numerical evolutions are presented and compared with a standard BSSN implementation. We find that a significant portion of the parameter space leads to stable evolutions and that standard BSSN is located near the edge of the stability region. Non-standard parameter choices typically result in smoother behaviour of the evolution variables close to the puncture and thus hold promise for improved accuracy in, e.g., long-term BH binary inspirals, and for overcoming (numerical) stability problems still encountered in some types of black-hole simulations, e.g., in $D \ge 6$ dimensions.

gr-qc↗

arXiv2011

Extreme black hole simulations: collisions of unequal mass black holes and the point particle limit

Numerical relativity has seen incredible progress in the last years, and is being applied with success to a variety of physical phenomena, from gravitational-wave research and relativistic astrophysics to cosmology and high-energy physics. Here we probe the limits of current numerical setups, by studying collisions of unequal mass, non-rotating black holes of mass-ratios up to 1:100 and making contact with a classical calculation in General Relativity: the infall of a point-like particle into a massive black hole. Our results agree well with the predictions coming from linearized calculations of the infall of point-like particles into non-rotating black holes. In particular, in the limit that one hole is much smaller than the other, and the infall starts from an infinite initial separation, we recover the point-particle limit. Thus, numerical relativity is able to bridge the gap between fully non-linear dynamics and linearized approximations, which may have important applications. Finally, we also comment on the "spurious" radiation content in the initial data and the linearized predictions.

gr-qc↗

arXiv2011

Head-on collisions of unequal mass black holes in D=5 dimensions

We study head-on collisions of unequal mass black hole binaries in D=5 space-time dimensions, with mass ratios between 1:1 and 1:4. Information about gravitational radiation is extracted by using the Kodama-Ishibashi gauge-invariant formalism and details of the apparent horizon of the final black hole. For the first time, we present waveforms, total integrated energy and momentum for this process. Our results show surprisingly good agreement, within 5% or less, with those extrapolated from linearized, point-particle calculations. Our results also show that consistency with the area theorem bound requires that the same process in a large number of spacetime dimensions must display new features.

gr-qc↗

arXiv2010

Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction

Black objects in higher dimensional space-times have a remarkably richer structure than their four dimensional counterparts. They appear in a variety of configurations (e.g. black holes, black branes, black rings, black Saturns), and display complex stability phase diagrams. They might also play a key role in high energy physics: for energies above the fundamental Planck scale, gravity is the dominant interaction which, together with the hoop-conjecture, implies that the trans-Planckian scattering of point particles should be well described by black hole scattering. Higher dimensional scenarios with a fundamental Planck scale of the order of TeV predict, therefore, black hole production at the LHC, as well as in future colliders with yet higher energies. In this setting, accurate predictions for the production cross-section and energy loss (through gravitational radiation) in the formation of black holes in parton-parton collisions is crucial for accurate phenomenological modelling in Monte Carlo event generators. In this paper, we use the formalism and numerical code reported in arXiv:1001.2302 to study the head-on collision of two black holes. For this purpose we provide a detailed treatment of gravitational wave extraction in generic D-dimensional space-times, which uses the Kodama-Ishibashi formalism. For the first time, we present the results of numerical simulations of the head-on collision in five space-time dimensions, together with the relevant physical quantities. We show that the total radiated energy, when two black holes collide from rest at infinity, is approximately (0.089\pm 0.006)% of the centre of mass energy, slightly larger than the 0.055% obtained in the four dimensional case, and that the ringdown signal at late time is in very good agreement with perturbative calculations.

gr-qc↗

arXiv2010

Black holes in a box: towards the numerical evolution of black holes in AdS

The evolution of black holes in "confining boxes" is interesting for a number of reasons, particularly because it mimics the global structure of Anti-de Sitter geometries. These are non-globally hyperbolic space-times and the Cauchy problem may only be well defined if the initial data is supplemented by boundary conditions at the time-like conformal boundary. Here, we explore the active role that boundary conditions play in the evolution of a bulk black hole system, by imprisoning a black hole binary in a box with mirror-like boundary conditions. We are able to follow the post-merger dynamics for up to two reflections off the boundary of the gravitational radiation produced in the merger. We estimate that about 15% of the radiation energy is absorbed by the black hole per interaction, whereas transfer of angular momentum from the radiation to the black hole is only observed in the first interaction. We discuss the possible role of superradiant scattering for this result. Unlike the studies with outgoing boundary conditions, both the Newman-Penrose scalars Ψ_4 and Ψ_0 are non-trivial in our setup, and we show that the numerical data verifies the expected relations between them.

hep-th↗

arXiv2010

Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests

The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV gravity scenarios, analysis of the stability of exact solutions and tests of Cosmic Censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D\ge 5, or SO(D-3) for D\ge 6. Performing a dimensional reduction on a (D-4)-sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata and Nakamura (BSSN) formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the LEAN code and perform a variety of simulations of non-spinning black hole space-times. Specifically, we present a modified moving puncture gauge which facilitates long term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5,6.

gr-qc↗

arXiv2009

Geodesic stability, Lyapunov exponents and quasinormal modes

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability timescale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black hole background are unstable, and (ii) the instability timescale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d > 5.

hep-th↗