Helvi Witek

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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 time scale 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 time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d ≥ 6.

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 binarys total mass is ~100–200M⊙, 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.

Superradiant instabilities in astrophysical systems

Light bosonic degrees of freedom have become a serious candidate for dark matter, which seems to pervade our entire Universe. 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 colorful examples of superradiance and nonlinear bosenovalike 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. The evolution of generic initial data has a very rich structure, depending on the mass of the field and of the black hole. Quasinormal ringdown or exponential decay followed by a power-law tail at very late times is a generic feature of massless fields at intermediate times. Massive fields generically show a transition to power-law tails early on. 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 quasibound states, the generic outcome is an amplitude modulated sinusoidal, or beating, signal, whose envelope is well described by the two lowest overtones. 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. A fine-tuning of the initial data allows one to see the evolution of the nearly pure bound state mode that turns unstable for sufficiently large black hole (BH) rotation. For the first time we explore massive vector fields in a generic black hole background that are difficult, if not impossible, to separate in the Kerr background. Our results show that spinning BHs are generically strongly unstable against massive vector fields.

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.

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

Higher dimensional black holes play an exciting role in fundamental physics, such as high energy physics. In this paper, we use the formalism and numerical code reported in [1] 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 ± 0.006)% of the center 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.

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 modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to 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≥5, or SO(D-3) for D≥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 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 nonspinning 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.

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 spacetime 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. 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.

Black holes and fundamental fields in numerical relativity: Initial data construction and evolution of bound states

Fundamental fields are a natural outcome in cosmology and particle physics and might therefore serve as a proxy for more complex interactions. The equivalence principle implies that all forms of matter gravitate, and one therefore expects relevant, universal imprints of new physics in strong field gravity, such as that encountered close to black holes. Fundamental fields in the vicinities of supermassive black holes give rise to extremely long-lived, or even unstable, configurations which slowly extract angular momentum from the black hole or simply evolve non-linearly over long timescales, with important implications for particle physics and gravitational-wave physics. Here, we perform a fully non-linear study of scalar-field condensates around rotating black holes. We provide novel ways to specify initial data for the Einstein-Klein-Gordon system, with potential applications in a variety of scenarios. Our numerical results confirm the existence of long-lived bar-modes which act as lighthouses for gravitational wave emission: the scalar field condenses outside the black hole geometry and acts as a constant frequency gravitational-wave source for very long timescales. This effect could turn out to be a potential signature of beyond standard model physics and also a promising source of gravitational waves for future gravitational wave detectors.

Black holes in a box: Toward the numerical evolution of black holes in AdS space-times

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 nonglobally hyperbolic space-times and the Cauchy problem may only be well defined if the initial data are supplemented by boundary conditions at the timelike 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 mirrorlike 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 observed only in the first interaction. We discuss the possible role of superradiant scattering for this result. Unlike the studies with outgoing boundary conditions, both of the Newman-Penrose scalars Ψ4 and Ψ0 are nontrivial in our setup, and we show that the numerical data verifies the expected relations between them.