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Carlos O. Lousto

Publications and source records attributed to Carlos O. Lousto.

At least 109 records · Page 6Linked to original sources
arXiv2006

Relativistic three-body effects in black hole coalescence

Three-body interactions are expected to be common in globular clusters and in galactic cores hosting supermassive black holes. Here we consider an equal-mass binary-black-hole system in the presence of a third black hole. Using numerically generated binary-black-hole initial-data sets, and first- and second-order post-Newtonian (1PN and 2PN) techniques, we find that the presence of the third black hole has non-negligible relativistic effects on the location of the innermost stable circular orbit (ISCO), and that these effects arise at 2PN order. In particular, we study the more astrophysically realistic situation of a stellar-mass black-hole binary in orbit about a third supermassive black hole. In general, the proximity of the massive black hole has stabilizing effects on the orbiting binary, leading to an increase in merger time and a decrease of the terminal orbital frequency, and an amplification of the gravitational radiation emitted from the binary system by up to 6 percent.

astro-ph↗
arXiv2006

A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit

We obtain a fourth order accurate numerical algorithm to integrate the Zerilli and Regge-Wheeler wave equations, describing perturbations of nonrotating black holes, with source terms due to an orbiting particle. Those source terms contain the Dirac's delta and its first derivative. We also re-derive the source of the Zerilli and Regge-Wheeler equations for more convenient definitions of the waveforms, that allow direct metric reconstruction (in the Regge-Wheeler gauge).

gr-qc↗
arXiv2006

The Lazarus Project. II. Spacelike extraction with the quasi-Kinnersley tetrad

The Lazarus project was designed to make the most of limited 3D binary black-hole simulations, through the identification of perturbations at late times, and subsequent evolution of the Weyl scalar $Ψ_4$ via the Teukolsky formulation. Here we report on new developments, employing the concept of the ``quasi-Kinnersley'' (transverse) frame, valid in the full nonlinear regime, to analyze late-time numerical spacetimes that should differ only slightly from Kerr. This allows us to extract the essential information about the background Kerr solution, and through this, to identify the radiation present. We explicitly test this procedure with full numerical evolutions of Bowen-York data for single spinning black holes, head-on and orbiting black holes near the ISCO regime. These techniques can be compared with previous Lazarus results, providing a measure of the numerical-tetrad errors intrinsic to the method, and give as a by-product a more robust wave extraction method for numerical relativity.

gr-qc↗
arXiv2005

Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation

We reformulate the theory of Schwarzschild black hole perturbations in terms of the metric perturbation in the Lorenz gauge. In this formulation, each tensor-harmonic mode of the perturbation is constructed algebraically from 10 scalar functions, satisfying a set of 10 wavelike equations, which are decoupled at their principal parts. We solve these equations using numerical evolution in the time domain, for the case of a pointlike test particle set in a circular geodesic orbit around the black hole. Our code uses characteristic coordinates, and incorporates a constraint damping scheme. The axially-symmetric, odd-parity modes of the perturbation are obtained analytically. The approach developed here is especially advantageous in applications requiring knowledge of the local metric perturbation near a point particle; in particular, it offers a useful framework for calculations of the gravitational self force.

gr-qc↗
arXiv2005

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature II: The Regge-Wheeler gauge

Perturbation theory of rotating black holes is described in terms of the Weyl scalars $ψ_4$ and $ψ_0$; each satisfying the Teukolsky's complex master wave equation with spin $s=\mp2$, and respectively representing outgoing and ingoing radiation. We explicitly construct the metric perturbations out of these Weyl scalars in the Regge-Wheeler gauge in the nonrotating limit. We propose a generalization of the Regge-Wheeler gauge for Kerr background in the Newman-Penrose language, and discuss the approach for building up the perturbed spacetime of a rotating black hole. We also provide both-way relationships between waveforms defined in the metric and curvature approaches in the time domain, also known as the (inverse-) Chandrasekhar transformations, generalized to include matter.

gr-qc↗
arXiv2004

Numerical integration of the Teukolsky Equation in the time domain

We present a fourth order convergent (2+1) numerical code to solve the Teukolsky equation in the time domain. Our approach is to rewrite the Teukolsky equation as a system of first order differential equations. In this way we get a system that has the form of an advection equation. This is used in combination with a series expansion of the solution in powers of time. To obtain a fourth order scheme we kept terms up to fourth derivative in time and use the advection-like system of differential equations to substitute the temporal derivatives by spatial derivatives. A local stability study leads to a Courant factor of 1.5 for the nonrotating case. This scheme is used to evolve gravitational perturbations in Schwarzschild and Kerr backgrounds. Our numerical method proved to be fourth order convergent in r* and theta directions. The correct power-law tail, ~1/t^{2\ell+3}, for general initial data, and ~1/t^{2\ell+4}, for time symmetric data, was found in the simulations where the duration in time of the tail phase was long enough. We verified that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, the quasinormal modes frequencies provided a test to determine the validity of our code.

gr-qc↗
arXiv2002

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $ψ_4$ and $ψ_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $Ψ$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $ψ_4$ and $ψ_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.

gr-qc↗
arXiv2001

Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes

Here we present the results of applying the generalized Riemann zeta-function regularization method to the gravitational radiation reaction problem. We analyze in detail the headon collision of two nonspinning black holes with extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.

gr-qc↗
arXiv1998

The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case

Gravitational perturbations about a Kerr black hole in the Newman-Penrose formalism are concisely described by the Teukolsky equation. New numerical methods for studying the evolution of such perturbations require not only the construction of appropriate initial data to describe the collision of two orbiting black holes, but also to know how such new data must be imposed into the Teukolsky equation. In this paper we show how Cauchy data can be incorporated explicitly into the Teukolsky equation for non-rotating black holes. The Teukolsky function $% Ψ$ and its first time derivative $\partial_t Ψ$ can be written in terms of only the 3-geometry and the extrinsic curvature in a gauge invariant way. Taking a Laplace transform of the Teukolsky equation incorporates initial data as a source term. We show that for astrophysical data the straightforward Green function method leads to divergent integrals that can be regularized like for the case of a source generated by a particle coming from infinity.

gr-qc↗
arXiv1998

The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations

We revisit the question of the imposition of initial data representing astrophysical gravitational perturbations of black holes. We study their dynamics for the case of nonrotating black holes by numerically evolving the Teukolsky equation in the time domain. In order to express the Teukolsky function Psi explicitly in terms of hypersurface quantities, we relate it to the Moncrief waveform phi_M through a Chandrasekhar transformation in the case of a nonrotating black hole. This relation between Psi and phi_M holds for any constant time hypersurface and allows us to compare the computation of the evolution of Schwarzschild perturbations by the Teukolsky and by the Zerilli and Regge-Wheeler equations. We explicitly perform this comparison for the Misner initial data in the close limit approach. We evolve numerically both, the Teukolsky (with the recent code of Ref. [1]) and the Zerilli equations, finding complete agreement in resulting waveforms within numerical error. The consistency of these results further supports the correctness of the numerical code for evolving the Teukolsky equation as well as the analytic expressions for Psi in terms only of the three-metric and the extrinsic curvature.

gr-qc↗
arXiv1998

The imposition of Cauchy data to the Teukolsky equation III: The rotating case

We solve the problem of expressing the Weyl scalars $ψ$ that describe gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do so we use geometrical identities (like the Gauss-Codazzi relations) as well as Einstein equations. We are able to explicitly express $ψ$ and $\partial _tψ$ as functions only of the extrinsic curvature and the three-metric (and geometrical objects built out of it) of a generic spacelike slice of the spacetime. These results provide the link between initial data and $ψ$ to be evolved by the Teukolsky equation, and can be used to compute the gravitational radiation generated by two orbiting black holes in the close limit approximation. They can also be used to extract waveforms from spacetimes completely generated by numerical methods.

gr-qc↗
arXiv1997

Improved initial data for black hole collisions

Numerical relativity codes now being developed will evolve initial data representing colliding black holes at a relatively late stage in the collision. The choice of initial data used for code development has been made on the basis of mathematical definitiveness and usefulness for computational implementation. By using the ``particle limit'' (the limit of an extreme ratio of masses of colliding holes) we recently showed that the standard choice is not a good representation of astrophysically generated initial data. Here we show that, for the particle limit, there is a very simple alternative choice that appears to give excellent results. That choice, ``convective'' initial data is, roughly speaking, equivalent to the start of a time sequence of parameterized solutions of the Hamiltonian constraint; for a particle in circular orbit, it is the initial data of the steady state solution on any hypersurface. The implementation of related schemes for equal mass holes is discussed.

gr-qc↗
arXiv1997

Regularization of the Teukolsky Equation for Rotating Black Holes

We show that the radial Teukolsky equation (in the frequency domain) with sources that extend to infinity has well-behaved solutions. To prove that, we follow Poisson approach to regularize the non-rotating hole, and extend it to the rotating case. To do so we use the Chandrasekhar transformation among the Teukolsky and Regge-Wheeler-like equations, and express the integrals over the source in terms of solutions to the homogeneous Regge-Wheeler-like equation, to finally regularize the resulting integral. We then discuss the applicability of these results.

gr-qc↗
arXiv1997

An exact self-consistent gravitational shock wave in semiclassical gravity

We find a self-consistent pp-gravitational shock wave solution to the semiclassical Einstein equations resulting from the $1/N$ approach to the effective action. We model the renormalized matter stress-energy-momentum tensor by $N$ massless scalar fields in the Minkowski vacuum plus a classical particle. We show that quantum effects generate a milder singularity at the position of the particle than the classical solution, but the singularity does not disappear. At large distances from the particle, the quantum correction decreases slowly, as $1/ρ^2$ ($ρ$ being the distance to the particle in the shock wave plane). We argue that this large distance correction is a necessary consequence of quantum gravity.

gr-qc↗
arXiv1997

Understanding initial data for black hole collisions

Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying prescriptions, such as conformal flatness of the 3-geometry and longitudinality of the extrinsic curvature. In the case of head on collisions of equal mass holes, there is evidence that such prescriptions work reasonably well, but it is not clear why, or whether this success is more generally valid. Here we study these questions by considering the ``particle limit'' for head on collisions of nonspinning holes. Einstein's equations are linearized in the mass of the small hole, and described by a single gauge invariant spacetime function psi, for each multipole. The resulting equations have been solved by numerical evolution for collisions starting from various initial separations, and the evolution is studied on a sequence of hypersurfaces. In particular, we extract hypersurface data, that is psi and its time derivative, on surfaces of constant background Schwarzschild time. These evolved data can then be compared with ``prescribed'' data, evolved data can be replaced by prescribed data on any hypersurface, and evolved further forward in time, a gauge invariant measure of deviation from conformal flatness can be evaluated, etc. The main findings of this study are: (i) For holes of unequal mass the use of prescribed data on late hypersurfaces is not successful. (ii) The failure is likely due to the inability of the prescribed data to represent the near field of the smaller hole. (iii) The discrepancy in the extrinsic curvature is more important than in the 3-geometry. (iv) The use of the more general conformally flat longitudinal data does not notably improve this picture.

gr-qc↗
arXiv1997

Infall of a particle into a black hole as a model for gravitational radiation from the galactic center

I present here the results of the study of the gravitational radiation generated by the infall (from rest at radius $r_0$) of a point particle of mass $m_0$ into a Schwarzschild black hole of mass $M$. We use Laplace's transform methods and find that the spectra of radiation for $\sim5M<r_0<\infty$ presents a series of evenly spaced bumps. The total radiated energy is not monotonically decreasing with $r_0$, but presents a joroba (hunch-back) at around $r_0\approx4.5M$. I finally discuss the detectability of the gravitational radiation coming from the black hole in the center of our galaxy.

gr-qc↗
arXiv1996

Head-on collisions of black holes: the particle limit

We compute gravitational radiation waveforms, spectra and energies for a point particle of mass $m_0$ falling from rest at radius $r_0$ into a Schwarzschild hole of mass $M$. This radiation is found to lowest order in $(m_0/M)$ with the use of a Laplace transform. In contrast with numerical relativity results for head-on collisions of equal-mass holes, the radiated energy is found not to be a monotonically increasing function of initial separation; there is a local radiated-energy maximum at $r_0\approx4.5M$. The present results, along with results for infall from infinity, provide a complete catalog of waveforms and spectra for particle infall. We give a representative sample from that catalog and an interesting observation: Unlike the simple spectra for other head-on collisions (either of particle and hole, or of equal mass holes) the spectra for $\infty>r_0>\sim5M$ show a series of evenly spaced bumps. A simple explanation is given for this. Lastly, our energy vs. $r_0$ results are compared with approximation methods used elsewhere, for small and for large initial separation.

gr-qc↗