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L. Lehner

Publications and source records attributed to L. Lehner.

At least 19 recordsLinked to original sources
arXiv2026

Fixing EFT equations with a reservoir model

Effective Field Theories with higher derivatives often yield equations of motion which define ill-posed problems. We present a method for enhancing control on such theories by coupling them to a field living in one extra dimension. The resulting action principle helps to define a well-posed problem introducing a mechanism to control UV behavior. Physically this is achieved by dissipating the energy in the short-wavelength modes into the extra dimension. We examine the resulting dynamics and compare it to alternative proposals for studying such theories in the non-linear regime.

hep-th↗
arXiv2020

Towards fidelity and scalability in non-vacuum mergers

We study the evolution of two fiducial configurations for binary neutron stars using two different general relativistic hydrodynamics(GRHD), distributed adaptive mesh codes. One code, HAD, has for many years been used to study mergers of compact object binaries, while a new code, MHDuet, has been recently developed with the experience gained with the older one as well as several novel features for scalability improvements. As such, we examine the performance of each, placing particular focus on future requirements for the extraction of gravitational wave signatures of non-vacuum binaries.

gr-qc↗
arXiv2015

Effects of the microphysical Equation of State in the mergers of magnetized Neutron Stars With Neutrino Cooling

We study the merger of binary neutron stars using different realistic, microphysical nuclear equations of state, as well as incorporating magnetic field and neutrino cooling effects. In particular, we concentrate on the influence of the equation of state on the gravitational wave signature and also on its role, in combination with cooling and electromagnetic effects, in determining the properties of the hypermassive neutron star resulting from the merger, the production of neutrinos, and the characteristics of ejecta from the system. The ejecta we find are consistent with other recent studies that find soft equations of state produce more ejecta than stiffer equations of state. Moreover, the degree of neutron richness increases for softer equations of state. In light of reported kilonova observations (associated to GRB~130603B and GRB~060614) and the discovery of relatively low abundances of heavy, radioactive elements in deep sea deposits (with respect to possible production via supernovae), we speculate that a soft EoS might be preferred---because of its significant production of sufficiently neutron rich ejecta---if such events are driven by binary neutron star mergers. We also find that realistic magnetic field strengths, obtained with a sub-grid model tuned to capture magnetic amplification via the Kelvin-Helmholtz instability at merger, are generally too weak to affect the gravitational wave signature post-merger within a time scale of $\approx 10$~ms but can have subtle effects on the post-merger dynamics.

gr-qc↗
arXiv2007

Do unbounded bubbles ultimately become fenced inside a black hole?

We examine the dynamical behavior of recently introduced bubbles in asymptotically flat, five-dimensional spacetimes. Using numerical methods, we find that even bubbles that initially start expanding eventually collapse to a Schwarzschild-Tangherlini black hole.

hep-th↗
arXiv2007

Orbital Dynamics of Binary Boson Star Systems

We extend our previous studies of head-on collisions of boson stars by considering orbiting binary boson stars. We concentrate on equal mass binaries and study the dynamical behavior of boson/boson and boson/antiboson pairs. We examine the gravitational wave output of these binaries and compare with other compact binaries. Such a comparison lets us probe the apparent simplicity observed in gravitational waves produced by black hole binary systems. In our system of interest however, there is an additional internal freedom which plays a significant role in the system's dynamics, namely the phase of each star. Our evolutions show rather simple behavior at early times, but large differences occur at late times for the various initial configurations.

gr-qc↗
arXiv2006

Head-on collisions of boson stars

We study head-on collisions of boson stars in three dimensions. We consider evolutions of two boson stars which may differ in their phase or have opposite frequencies but are otherwise identical. Our studies show that these phase differences result in different late time behavior and gravitational wave output.

gr-qc↗
arXiv2005

Gravitational Instability of a Kink

We study the equilibria of a self-gravitating scalar field in the region outside a reflecting barrier. By introducing a potential difference between the barrier and infinity, we create a kink which cannot decay to a zero energy state. In the realm of small amplitude, the kink decays to a known static solution of the Einstein-Klein-Gordon equation. However, for larger kinks the static equilibria are degenerate, forming a system with two energy levels. The upper level is unstable and, under small perturbations, decays to the lower energy stable equilibrium. Under large perturbations, the unstable upper level undergoes collapse to a black hole. The equilibrium of the system provides a remarkably simple and beautiful illustration of a turning point instability.

gr-qc↗
arXiv2004

The 3-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein--Klein--Gordon system is calibrated to be second order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the $\ell=2$ quasinormal mode.

gr-qc↗
arXiv2004

A numerical examination of an evolving black string horizon

We use the numerical solution describing the evolution of a perturbed black string presented in Choptuik et al. (2003) to elucidate the intrinsic behavior of the horizon. It is found that by the end of the simulation, the affine parameter on the horizon has become very large and the expansion and shear of the horizon in turn very small. This suggests the possibility that the horizon might pinch off in infinite affine parameter.

gr-qc↗
arXiv2003

Towards the Final Fate of an Unstable Black String

Black strings, one class of higher dimensional analogues of black holes, were shown to be unstable to long wavelength perturbations by Gregory and Laflamme in 1992, via a linear analysis. We revisit the problem through numerical solution of the full equations of motion, and focus on trying to determine the end-state of a perturbed, unstable black string. Our preliminary results show that such a spacetime tends towards a solution resembling a sequence of spherical black holes connected by thin black strings, at least at intermediate times. However, our code fails then, primarily due to large gradients that develop in metric functions, as the coordinate system we use is not well adapted to the nature of the unfolding solution. We are thus unable to determine how close the solution we see is to the final end-state, though we do observe rich dynamical behavior of the system in the intermediate stages.

gr-qc↗
arXiv2000

Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with $l_1$ and $l_\infty$ norms of violation of the constraint equations falling below those of the truncation error (residual error due to discretization) present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of $h=M/4$, and an "attenuated" superposition yields data usable to resolutions at least as fine as $h=M/8$. In addition, the attenuated approximate data may be more tractable in a full (computational) exact solution to the initial value problem.

gr-qc↗
arXiv1999

The incorporation of matter into characteristic numerical relativity

A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The extended code has been written and validated in a number of cases. It is stable and capable of contributing towards an understanding of a number of problems in black hole astrophysics.

gr-qc↗
arXiv1998

Cauchy-characteristic matching

This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading approaches to computational gravitation, carving up spacetime via Cauchy hypersurfaces within a central worldtube, and using characteristic hypersurfaces in its exterior to connect this region with null infinity and study gravitational radiation. It has worked well in simplified test problems, and is currently being used to build computer codes to simulate black hole collisions in 3-D.

gr-qc↗
arXiv1997

Boosted three-dimensional black-hole evolutions with singularity excision

Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of duration ~60M.

gr-qc↗
arXiv1997

Moving Black Holes in 3D

We model a radiating, moving black hole in terms of a worldtube-nullcone boundary value problem. We evolve this data in the region interior to the worldtube but exterior to a trapped surface by means of a characteristic evolution based upon a family of ingoing null hypersurfaces. Data on the worldtube is induced from a Schwarzschild spacetime but the worldtube is allowed to move relative to the static Schwarzschild trajectories. When the worldtube is stationary (static or rotating in place), a distorted black hole inside it evolves to equilibrium with the Schwarzschild boundary. A boost of the worldtube with respect to the Schwarzschild black hole does not affect these results. The code also stably tracks an unlimited number of orbits when the worldtube wobbles periodically. The work establishes that characteristic evolution can evolve a spacetime with a distorted black hole moving on a 3-dimensional grid with the controlled accuracy and long term stability necessary to investigate new facets of black hole physics.

gr-qc↗
arXiv1997

Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code.

gr-qc↗
arXiv1997

Cauchy-characteristic extraction in numerical relativity

We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube $Γ$ and on characteristic data on an outgoing null cone emanating from an initial cross-section of $Γ$. We present the details of a 3-dimensional computational algorithm which evolves this initial data on a numerical grid, which is compactified to include future null infinity as finite grid points. A code implementing this algorithm is calibrated in the quasispherical regime. We consider the application of this procedure to the extraction of waveforms at infinity from an interior Cauchy evolution, which provides the boundary data on $Γ$. This is a first step towards Cauchy-characteristic matching in which the data flow at the boundary $Γ$ is two-way, with the Cauchy and characteristic computations providing exact boundary values for each other. We describe strategies for implementing matching and show that for small target error it is much more computationally efficient than alternative methods.

gr-qc↗