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Luis Lehner

Publications and source records attributed to Luis Lehner.

144 records · Page 8Linked to original sources
arXiv2004

Adaptive Mesh Refinement for Characteristic Codes

The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference discretizations of wave-like equations using characteristic coordinates. We demonstrate the algorithm by constructing a code implementing the Einstein-Klein-Gordon system of equations in spherical symmetry. We discuss how the algorithm can trivially be generalized to higher dimensional systems, and suggest a method that can be used to parallelize a characteristic code.

gr-qc↗
arXiv2004

The discrete energy method in numerical relativity: Towards long-term stability

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or ``artificial instabilities,'' contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth.

gr-qc↗
arXiv2003

A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole

We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a non-zero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a rigid body whose center follows a geodesic. The necessary theoretical framework is developed and then implemented in a computer code that uses the null-cone, or characteristic, formulation of numerical relativity. The performance of the code is illustrated in test runs, including a complete orbit (near r=9M) of a Schwarzschild black hole.

gr-qc↗
arXiv2003

No naked singularities in homogeneous, spherically symmetric bubble spacetimes?

We study the evolution of bubble spacetimes in vacuum and electrovac scenarios by numerical means. We find strong evidence against the formation of naked singularities in (i) scenarios with negative masses displaying initially collapsing conditions and (ii) scenarios with negative masses displaying initially expanding conditions, previously reported to give rise to such singularities. Additionally, we show that the presence of strong gauge fields implies that an initially collapsing bubble bounces back and expands. By fine-tuning the strength of the gauge field we find that the solution approaches a static bubble solution.

hep-th↗
arXiv2003

Mode coupling in the nonlinear response of black holes

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.

gr-qc↗
arXiv2002

Gravitational Waves from a Fissioning White Hole

We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.

gr-qc↗
arXiv2002

Energy and angular momentum radiated for non head-on binary black hole collisions

We investigate the possible total radiated energy produced by a binary black hole system containing non-vanishing total angular momentum. For the scenearios considered we find that the total radiated energy does not exceed 1%. Additionally we explore the gravitational radiation field and the variation of angular momentum in the process.

gr-qc↗
arXiv2002

Numerical Relativity: Status and Prospects

We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important messages so far hidden in the theory. Despite the problems still found in present applications, significant progress is being achieved in a number of areas where simulations are on the verge of providing useful physical information. This article reviews recent progress made in the field, paying particular attention to black hole spacetimes and discuss open problems and prospects for the future.

gr-qc↗
arXiv2001

Constraint-preserving boundary conditions in numerical relativity

This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally coupled scalar field, within the Einstein-Christoffel symmetric hyperbolic formulation of Einstein's equations. By exploiting the characteristic propagation of the main variables and constraints, we are able to single out the only free modes at the outer boundary for these problems. In the vacuum case a single free modes exists which corresponds to a gauge freedom, while in the matter case an extra mode exists which is associated with the scalar field. We make use of the fact that the EC formulation has no superluminal characteristic speeds to excise the singularity. We present a second-order, finite difference discretization to treat these scenarios, where we implement these constraint-preserving boundary conditions, and are able to evolve the system for essentially unlimited times. As a test of the robustness of our approach, we allow large pulses of gauge and scalar field enter the domain through the outer boundary. We reproduce expected results, such as trivial (in the physical sense) evolution in the vacuum case (even in gauge- dynamical simulations), and the tail decay for the scalar field.

gr-qc↗
arXiv2001

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.

gr-qc↗
arXiv2000

Grazing Collisions of Black Holes via the Excision of Singularities

We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes $m$ are separated a distance $\approx10m$ and with impact parameter $\approx2m$. Initial data are based on superposed, boosted (velocity $\approx0.5c$) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to $t \approx 35m$ are obtained in which two initially separate apparent horizons are present for $t\approx3.8m$. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities.

gr-qc↗
arXiv2000

Notes on causal differencing in ADM/CADM formulations: a 1D comparison

Causal differencing has shown to be one of the promising and successful approaches towards excising curvature singularities from numerical simulations of black hole spacetimes. So far it has only been actively implemented in the ADM and Einstein-Bianchi 3+1 formulations of the Einstein equations. Recently, an approach closely related to the ADM one, commonly referred to as as ``conformal ADM'' (CADM) has shown excellent results when modeling waves on flat spacetimes and black hole spacetimes where singularity avoiding slices are used to deal with the singularity. In these cases, the use of CADM has yielded longer evolutions and better outer boundary dependence than those obtained with the ADM one. If this success translates to the case where excision is implemented, then the CADM formulation will likely be a prime candidate for modeling generic black hole spacetimes. In the present work we investigate the applicability of causal differencing to CADM, presenting the equations in a convenient way for such a goal and compare its application with the ADM approach in 1D.

gr-qc↗
arXiv1999

Matching characteristic codes: exploiting two directions

Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null infinity and the interior region simultaneously (assuming the foliation is free of caustics and crossovers). We discuss how this combination can be performed and illustrate its behavior in the Einstein-Klein-Gordon field in 1D.

gr-qc↗
arXiv1999

Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence

We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.

gr-qc↗
arXiv1998

A dissipative algorithm for wave-like equations in the characteristic formulation

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the highly nonlinear regime where previous methods have failed to give a stable evolution in three dimensions. The algorithm presented in this work is directly applicable to hyperbolic systems proper of Electromagnetism, Yang-Mills and General Relativity theories. We carry out an analysis of the stability of the algorithm and test its properties with linear waves propagating on a Minkowski background and the scattering off a Scwharszchild black hole in General Relativity.

gr-qc↗
arXiv1997

High-powered Gravitational News

We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard $N_{+}$ and $N_{\times}$ polarization components. The resulting code is stable and second-order convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about $10^{13}M_{\odot}/sec$.

gr-qc↗