Accurate Evolutions of Orbiting Binary Black Holes

We present a detailed analysis of binary black hole evolutions in the last orbit and demonstrate consistent and convergent results for the trajectories of the individual bodies. The gauge choice can significantly affect the overall accuracy of the evolution. It is possible to reconcile certain gauge-dependent discrepancies by examining the convergence limit. We illustrate these results using an initial data set recently evolved by Brügmann et al. [Phys. Rev. Lett. 92, 211101 (2004)]. For our highest resolution and most accurate gauge, we estimate the duration of this data set's last orbit to be approximately 59MADM

Gravitational waves from extreme mass-ratio inspirals in Dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an interesting extension of General Relativity, which finds its way in many different contexts, including string theory, cosmological settings and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasi-circular inspiralling of a small, stellar-mass object into a large non-rotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green's function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LISA, this effect can be used to constrain the coupling parameter effectively.Comment: RevTex4, 18 pages, 7 figures, 1 tabl

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.

Numerical relativity with characteristic evolution, using six angular patches

The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.Comment: 12 pages, 5 figures, submitted to CQG (special NFNR issue

3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints

We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for the associated initial-boundary value problem. The code is first tested with a gauge wave solution, where rather larger amplitudes and for significantly longer times are obtained with respect to other state of the art implementations. Additionally, by minimizing a suitably defined energy for the constraints in terms of free constraint-functions in the formulation one can dynamically single out preferred values of these functions for the problem at hand. We apply the technique to fully three-dimensional simulations of a stationary black hole spacetime with excision of the singularity, considerably extending the lifetime of the simulations.Comment: 21 pages. To appear in PR

Impact of densitized lapse slicings on evolutions of a wobbling black hole

We present long-term stable and second-order convergent evolutions of an excised wobbling black hole. Our results clearly demonstrate that the use of a densitized lapse function extends the lifetime of simulations dramatically. We also show the improvement in the stability of single static black holes when an algebraic densitized lapse condition is applied. In addition, we introduce a computationally inexpensive approach for tracking the location of the singularity suitable for mildly distorted black holes. The method is based on investigating the fall-off behavior and asymmetry of appropriate grid variables. This simple tracking method allows one to adjust the location of the excision region to follow the coordinate motion of the singularity.Comment: 10 pages, 8 figure

Generic effective source for scalar self-force calculations

A leading approach to the modelling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic time-like geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.Comment: 24 pages, 7 figures, final published versio

Book Reviews

Book reviews by Charles S. Desmond, James F. Thornburg, Edward J. Gray, Walter H. E. Jaeger, and Thomas L. Shaffer

Generic Tracking of Multiple Apparent Horizons with Level Flow

We report the development of the first apparent horizon locator capable of finding multiple apparent horizons in a ``generic'' numerical black hole spacetime. We use a level-flow method which, starting from a single arbitrary initial trial surface, can undergo topology changes as it flows towards disjoint apparent horizons if they are present. The level flow method has two advantages: 1) The solution is independent of changes in the initial guess and 2) The solution can have multiple components. We illustrate our method of locating apparent horizons by tracking horizon components in a short Kerr-Schild binary black hole grazing collision.Comment: 13 pages including figures, submitted to Phys Rev

Are moving punctures equivalent to moving black holes?

When simulating the inspiral and coalescence of a binary black-hole system, special care needs to be taken in handling the singularities. Two main techniques are used in numerical-relativity simulations: A first and more traditional one ``excises'' a spatial neighbourhood of the singularity from the numerical grid on each spacelike hypersurface. A second and more recent one, instead, begins with a ``puncture'' solution and then evolves the full 3-metric, including the singular point. In the continuum limit, excision is justified by the light-cone structure of the Einstein equations and, in practice, can give accurate numerical solutions when suitable discretizations are used. However, because the field variables are non-differentiable at the puncture, there is no proof that the moving-punctures technique is correct, particularly in the discrete case. To investigate this question we use both techniques to evolve a binary system of equal-mass non-spinning black holes. We compare the evolution of two curvature 4-scalars with proper time along the invariantly-defined worldline midway between the two black holes, using Richardson extrapolation to reduce the influence of finite-difference truncation errors. We find that the excision and moving-punctures evolutions produce the same invariants along that worldline, and thus the same spacetimes throughout that worldline's causal past. This provides convincing evidence that moving-punctures are indeed equivalent to moving black holes.Comment: 4 pages, 3 eps color figures; v2 = major revisions to introduction & conclusions based on referee comments, but no change in analysis or result