Numerical simulations of single and binary black holes in scalar-tensor theories: circumventing the no-hair theorem

Scalar-tensor theories are a compelling alternative to general relativity and one of the most accepted extensions of Einstein's theory. Black holes in these theories have no hair, but could grow "wigs" supported by time-dependent boundary conditions or spatial gradients. Time-dependent or spatially varying fields lead in general to nontrivial black hole dynamics, with potentially interesting experimental consequences. We carry out a numerical investigation of the dynamics of single and binary black holes in the presence of scalar fields. In particular we study gravitational and scalar radiation from black-hole binaries in a constant scalar-field gradient, and we compare our numerical findings to analytical models. In the single black hole case we find that, after a short transient, the scalar field relaxes to static configurations, in agreement with perturbative calculations. Furthermore we predict analytically (and verify numerically) that accelerated black holes in a scalar-field gradient emit scalar radiation. For a quasicircular black-hole binary, our analytical and numerical calculations show that the dominant component of the scalar radiation is emitted at twice the binary's orbital frequency.Comment: 21 pages, 6 figures, matches version accepted in Physical Review

Head-On collisions of different initial data

We discuss possible origins for discrepancies observed in the radiated energies in head-on collisions of non-spinning binaries starting from Brill-Lindquist and superposed Kerr-Schild data. For this purpose, we discuss the impact of different choices of gauge parameters and a small initial boost of the black holes.Comment: Proceedings of the Eleventh Marcel Grossmann Meeting; 3 pages (limit

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

NR/HEP: roadmap for the future

Physic in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high-energy physics (HEP). 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 HEP processes such as 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 a roadmap for the next years

Binary black-hole evolutions of excision and puncture data

We present a new numerical code developed for the evolution of binary black-hole spacetimes using different initial data and evolution techniques. The code is demonstrated to produce state-of-the-art simulations of orbiting and inspiralling black-hole binaries with convergent waveforms. We also present the first detailed study of the dependence of gravitational waveforms resulting from three-dimensional evolutions of different types of initial data. For this purpose we compare the waveforms generated by head-on collisions of superposed Kerr-Schild, Misner and Brill-Lindquist data over a wide range of initial separations.Comment: 21 pages, 13 figures, final version accepted for publication in PR

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 \Psi_4 and \Psi_0 are non-trivial in our setup, and we show that the numerical data verifies the expected relations between them.Comment: REvTex4, 17 pages, 12 Figs. v2: Minor improvements. Published version. Animation of a black hole binary in a box can be found at http://blackholes.ist.utl.pt

Mining information from binary black hole mergers: a comparison of estimation methods for complex exponentials in noise

The ringdown phase following a binary black hole merger is usually assumed to be well described by a linear superposition of complex exponentials (quasinormal modes). In the strong-field conditions typical of a binary black hole merger, non-linear effects may produce mode coupling. Artificial mode coupling can also be induced by the black hole's rotation, if the radiation field is expanded in terms of spin-weighted spherical (rather than spheroidal) harmonics. Observing deviations from linear black hole perturbation theory requires optimal fitting techniques to extract ringdown parameters from numerical waveforms, which are inevitably affected by errors. So far, non-linear least-squares fitting methods have been used as the standard workhorse to extract frequencies from ringdown waveforms. These methods are known not to be optimal for estimating parameters of complex exponentials. Furthermore, different fitting methods have different performance in the presence of noise. The main purpose of this paper is to introduce the gravitational wave community to modern variations of a linear parameter estimation technique first devised in 1795 by Prony: the Kumaresan-Tufts and matrix pencil methods. Using "test" damped sinusoidal signals in Gaussian white noise we illustrate the advantages of these methods, showing that they have variance and bias at least comparable to standard non-linear least-squares techniques. Then we compare the performance of different methods on unequal-mass binary black hole merger waveforms. The methods we discuss should be useful both theoretically (to monitor errors and search for non-linearities in numerical relativity simulations) and experimentally (for parameter estimation from ringdown signals after a gravitational wave detection).Comment: 20 pages, 7 figures, minor changes to match version in press in PR

Zoom-Whirl Orbits in Black Hole Binaries

Zoom-whirl behavior has the reputation of being a rare phenomenon. The concern has been that gravitational radiation would drain angular momentum so rapidly that generic orbits would circularize before zoom-whirl behavior could play out, and only rare highly tuned orbits would retain their imprint. Using full numerical relativity, we catch zoom-whirl behavior despite dissipation. The larger the mass ratio, the longer the pair can spend in orbit before merging and therefore the more zooms and whirls seen. Larger spins also enhance zoom-whirliness. An important implication is that these eccentric orbits can merge during a whirl phase, before enough angular momentum has been lost to truly circularize the orbit. Waveforms will be modulated by the harmonics of zoom-whirls, showing quiet phases during zooms and louder glitches during whirls.Comment: Replaced with published versio

Where do moving punctures go?

Currently the most popular method to evolve black-hole binaries is the ``moving puncture'' method. It has recently been shown that when puncture initial data for a Schwarzschild black hole are evolved using this method, the numerical slices quickly lose contact with the second asymptotically flat end, and end instead on a cylinder of finite Schwarzschild coordinate radius. These slices are stationary, meaning that their geometry does not evolve further. We will describe these results in the context of maximal slices, and present time-independent puncture-like data for the Schwarzschild spacetime.Comment: Proceedings for 29th Spanish Relativity Meeting. Added more details about the time-independent solution, with reference to the analytic result of Baumgarte and Naculic

Collisions of charged black holes

We perform fully nonlinear numerical simulations of charged-black-hole collisions, described by the Einstein-Maxwell equations, and contrast the results against analytic expectations. We focus on head-on collisions of nonspinning black holes, starting from rest and with the same charge-to-mass ratio, Q/M. The addition of charge to black holes introduces a new interesting channel of radiation and dynamics, most of which seem to be captured by Newtonian dynamics and flat-space intuition. The waveforms can be qualitatively described in terms of three stages: (i) an infall phase prior to the formation of a common apparent horizon; (ii) a nonlinear merger phase that corresponds to a peak in gravitational and electromagnetic energy; (iii) the ringdown marked by an oscillatory pattern with exponentially decaying amplitude and characteristic frequencies that are in good agreement with perturbative predictions. We observe that the amount of gravitational-wave energy generated throughout the collision decreases by about 3 orders of magnitude as the charge-to-mass ratio Q/M is increased from 0 to 0.98. We interpret this decrease as a consequence of the smaller accelerations present for larger values of the charge. In contrast, the ratio of energy carried by electromagnetic to gravitational radiation increases, reaching about 22% for the maximum Q/M ratio explored, which is in good agreement with analytic predictions