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Non-linear numerical schemes in general relativity
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Anomalies in the gravitational recoil of eccentric black-hole mergers with unequal mass ratios
The radiation of linear momentum imparts a recoil (or "kick") to the center of mass of a merging black-hole binary system. Recent numerical relativity calculations have shown that eccentricity can lead to an approximate 25% increase in recoil velocities for equal-mass, spinning binaries with spins lying in the orbital plane ("superkick" configurations) [U. Sperhake et al. Phys. Rev. D 101, 024044 (2020)]. Here we investigate the impact of nonzero eccentricity on the kick magnitude and gravitational-wave emission of nonspinning, unequal-mass black hole binaries. We confirm that nonzero eccentricities at merger can lead to kicks which are larger by up to similar to 25% relative to the quasicircular case. We also find that the kick velocity v has an oscillatory dependence on eccentricity, which we interpret as a consequence of changes in the angle between the infall direction at merger and the apoapsis (or periapsis) direction
PREFACE — NR/HEP2: Spring School on Numerical Relativity and High Energy Physics
Preface to the special issue on Numerical Relativity and High Energy Physics (NR/HEP2 Spring School
Numerical simulations of single and binary black holes in scalar-tensor theories: Circumventing the no-hair theorem
Scalar-tensor theories are a compelling alternative to general relativity and one of the most accepted extensions of Einstein's theory. Black holes in these theories have no hair, but could grow "wigs" supported by time-dependent boundary conditions or spatial gradients. Time-dependent or spatially varying fields lead in general to nontrivial black hole dynamics, with potentially interesting experimental consequences. We carry out a numerical investigation of the dynamics of single and binary black holes in the presence of scalar fields. In particular we study gravitational and scalar radiation from black-hole binaries in a constant scalar-field gradient, and we compare our numerical findings to analytical models. In the single black hole case we find that, after a short transient, the scalar field relaxes to static configurations, in agreement with perturbative calculations. Furthermore we predict analytically (and verify numerically) that accelerated black holes in a scalar-field gradient emit scalar radiation. For a quasicircular black-hole binary, our analytical and numerical calculations show that the dominant component of the scalar radiation is emitted at twice the binary's orbital frequency
Nonlinear radial oscillations of neutron stars
The effects of nonlinear oscillations in compact stars are attracting considerable current interest. In order to study such phenomena in the framework of fully nonlinear general relativity, highly accurate numerical studies are required. A numerical scheme specifically tailored for such a study is based on formulating the time evolution in terms of deviations from a stationary equilibrium configuration. Using this technique, we investigate over a wide range of amplitudes nonlinear effects in the evolution of radial oscillations of neutron stars. In particular, we discuss mode coupling due to nonlinear interaction, the occurrence of resonance phenomena, shock formation near the stellar surface as well as the capacity of nonlinearities to stabilize perturbatively unstable neutron star models
Dynamics of black holes in de Sitter spacetimes
Nonlinear dynamics in cosmological backgrounds has the potential to teach us immensely about our Universe, and also to serve as prototype for nonlinear processes in generic curved spacetimes. Here we report on dynamical evolutions of black holes in asymptotically de Sitter spacetimes. We focus on the head-on collision of equal mass binaries and for the first time compare analytical and perturbative methods with full blown nonlinear simulations. Our results include an accurate determination of the merger/scatter transition (consequence of an expanding background) for small mass binaries and a test of the cosmic censorship conjecture, for large mass binaries. We observe that, even starting from small separations, black holes in large mass binaries eventually lose causal contact, in agreement with the conjecture
Higher-dimensional puncture initial data
We calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of D-dimensional vacuum gravity. The data are generated by a modification of the pseudospectral code presented in [M. Ansorg, B. Bruegmann, and W. Tichy, Phys. Rev. D 70, 064011 (2004).] and made available as the TWOPUNCTURES thorn inside the CACTUS computational toolkit. As examples, we exhibit convergence plots, the violation of the Hamiltonian constraint as well as the initial data for D = 4, 5, 6, 7. These initial data are the starting point to perform high-energy collisions of black holes in D dimensions
Simulations of black holes in compactified spacetimes
From the gauge/gravity duality to braneworld scenarios, black holes in compactified spacetimes play an important role in fundamental physics. Our current understanding of black hole solutions and their dynamics in such spacetimes is rather poor because analytical tools are capable of handling a limited class of idealized scenarios, only. Breakthroughs in numerical relativity in recent years, however, have opened up the study of such spacetimes to a computational treatment which facilitates accurate studies of a wider class of configurations. We here report on recent efforts of our group to perform numerical simulations of black holes in cylindrical spacetimes
Tensor-multi-scalar theories: relativistic stars and 3 + 1 decomposition
Gravitational theories with multiple scalar fields coupled to the metric and each other—a natural extension of the well studied single-scalar-tensor theories—are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the N-tuple of scalar fields takes values in a coordinate patch of an N-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In preparation for numerical relativity simulations, we also write down the 3 + 1 decomposition of the field equations for generic tensor-multi-scalar theories
Unequal-mass boson-star binaries: Initial data and merger dynamics
We present a generalization of the curative initial data construction derived
for equal-mass compact binaries in Helfer {\it et al} (2019 Phys. Rev. D 99
044046; 2022 Class. Quantum Grav. 39 074001) to arbitrary mass ratios. We
demonstrate how these improved initial data avoid substantial spurious
artifacts in the collision dynamics of unequal-mass boson-star binaries in the
same way as has previously been achieved with the simpler method restricted to
the equal-mass case. We employ the improved initial data to explore in detail
the impact of phase offsets in the coalescence of equal- and unequal-mass boson
star binaries.Comment: 37 pages, 12 figures, to match published version in CQ
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