arXiv subjects

Ulrich Sperhake

Publications and source records attributed to Ulrich Sperhake.

At least 19 recordsLinked to original sources

arXiv2026

The Era of Precision in Computational Models of Gravitational Waves

Einstein's equations of general relativity are one of the most complicated set of equations in all of physics and, for all but idealized physical settings, can only be solved by numerical methods on high-performance computing systems. Generating such solutions is a veritable Odyssey in its own right with adventures across the fields of mathematical theory, physical interpretation and computing challenges. These endeavors came to fruition in the mid 2000s when the two-body problem of general relativity was finally solved. And not too soon, as these results and their follow-up investigations came to play a key role in the Nobel-Prize winning discovery of gravitational waves by LIGO in 2015.

gr-qc↗

arXiv2026

Lessons from binary dynamics of inspiralling equal-mass boson-star mergers

We explore the gravitational-wave phenomenology of equal-mass inspiralling boson-star binaries using numerical relativity simulations. In particular, we characterise the waveform differences between binary boson-star and black-hole systems across (i) the early inspiral, by matching our waveforms to post-Newtonian expressions, (ii) merger, and (iii) late ringdown, by extracting the quasi-normal mode frequencies of the remnants. We find that boson-star binaries exhibit the largest deviations from comparable binary black-hole systems during the late inspiral and merger phases. Remarkably, for a subset of these equal-mass boson-star binaries (with certain phase offsets in the scalar-field profiles) we identify the excitation of subdominant odd $m$-multipoles in the gravitational-wave emission, absent in equal-mass nonspinning black-hole binaries. Despite differences in the phenomenology of binary boson-star and black-hole signals, injections of some boson-star signals into detector noise exhibit degeneracy with current waveform approximants. Building on these results, we demonstrate how inspiral-merger-ringdown consistency tests can overcome these degeneracies.

gr-qc↗

arXiv2026

Black Hole-Boson Star Binaries: Gravitational Wave Signals and Tidal Disruption

We present a detailed, fully nonlinear study of binary systems involving one black hole and one boson star, considering the effects of both a quartic self-interaction and a solitonic potential for the scalar field. First, we show the importance of using initial data for which the boson star is in an equilibrated configuration to obtain accurate gravitational waveforms, and discuss methods to further improve constraint violations in the initial data. We then present a series of head-on collisions, showing that even in this simplified scenario the radiative efficiency varies significantly with the scalar potential chosen. In addition to this, we present a preliminary study of inspiral configurations, showing that an appropriate scalar self-interaction can suppress tidal disruption. We comment throughout on implications for attempts to build model-agnostic waveform template banks for exotic compact objects.

gr-qc↗

arXiv2026

Nonlinear Dynamics in General Relativity

Black holes and gravitational waves are consequences of the nonlinear character of the Einstein equations. Yet, the remarkable properties of General Relativity point to the existence of other effects. Here we uncover new nonlinear facets of gravity. We establish higher harmonic generation, spectral broadening and focusing in the Einstein Klein-Gordon system. In vacuum, we show that scattering of monochromatic waves at quadratic order is weakly sensitive to frequency, at large wavelengths. These aspects can both explain the seemingly smooth behavior of mergers, but also caution us against too simplistic an interpretation of waveforms.

gr-qc↗

arXiv2025

Gravitational scattering of solitonic boson stars: Analytics vs Numerics

We study the scattering of boson-star binaries, taking into account three effects: point-mass gravitational, tidal, and short-range scalar-field interactions. We compare analytic results to the scattering angle extracted from four sequences of numerical-relativity simulations at fixed energy and varying impact parameter. The very good agreement exhibits the attractive (repulsive) effect of in-phase (out-of-phase) binaries, wich dominates at small impact parameters. We thus obtain the first effective-one-body potential, central for the construction of analytic gravitational-wave templates.

gr-qc↗

arXiv2025

Long-term stable nonlinear evolutions of ultracompact black-hole mimickers

We study the stability of ultracompact boson stars admitting light rings combining a perturbative analysis with 3+1 numerical-relativity simulations with and without symmetry assumptions. We observe excellent agreement between all perturbative and numerical results which uniformly support the hypothesis that this family of black-hole mimickers is separated into stable and unstable branches by extremal-mass configurations. This separation includes, in particular, thin-shell boson stars with light rings located on the stable branch which we conclude to represent long-term stable black-hole mimickers.

gr-qc↗

arXiv2024

Hair is complicated: Gravitational waves from stable and unstable boson-star mergers

We explore the gravitational-wave emission from head-on collisions of equal-mass solitonic boson-star binaries from simulations spanning a two-dimensional parameter space, consisting of the central scalar-field amplitude of the stars and the solitonic potential parameter. We report the gravitational-wave energies emitted by boson-star binaries which, due to their combination of moderately high compactness with significant deformability, we often find to be louder by up to an order of magnitude than analogous black-hole collisions. The dependence of the radiated energy on the boson-star parameters exhibits striking needle-sharp features and discontinuous jumps to the value emitted by black-hole binaries. We explain these features in terms of the solitonic potential and the stability properties of the respective individual stars.

gr-qc↗

arXiv2024

Gravitational-Wave Data Analysis with High-Precision Numerical Relativity Simulations of Boson Star mergers

Gravitational-wave signals detected to date are commonly interpreted under the paradigm that they originate from pairs of black holes or neutron stars. Here, we explore the alternative scenario of boson-star signals being present in the data stream. We perform accurate and long ($\sim 20$ orbits) numerical simulations of boson-star binaries and inject the resulting strain into LIGO noise. Our Bayesian inference reveals that some boson-star signals. are degenerate with current approximants, albeit with biased parameters, while others exhibit smoking-gun signatures leaving behind conspicuous residuals.

gr-qc↗

arXiv2023

Boson stars in massless and massive scalar-tensor gravity

We study phenomenological features and stability of boson stars in massless and massive scalar-tensor theory of gravity with Damour-Esposito-Farese coupling. This coupling between the tensor and scalar sectors of the theory leads to a phenomenon called spontaneous scalarization, the onset of which we investigate by numerically computing families of boson-star models using shooting and relaxation algorithms. We systematically explore the effects of the theory's coupling, the mass of the gravitational scalar and the choice of the bosonic potential on the structure of weakly and strongly scalarized solutions. Scalarized boson-star models share many common features with neutron stars in the same scalar-tensor theory of gravity. In particular, scalarization can result in boson stars with significantly larger radii and masses, which tend to be energetically favored over their weakly or non-scalarized counterparts. Overall, we find that boson stars are not quite as susceptible to scalarization as neutron stars.

gr-qc↗

arXiv2023

Stochastic gravitational wave background from supernovae in massive scalar-tensor gravity

In massive scalar-tensor gravity, core-collapse supernovae are strong sources of scalar-polarized gravitational waves. These can be detectable out to large distance. The dispersive nature of the propagation of waves in the massive scalar field mean the gravitational wave signals are long lived and many such signals can overlap to form a stochastic background. Using different models for the population of supernova events in the nearby universe, we compute predictions for the energy-density in the stochastic scalar-polarized gravitational wave background from core-collapse events in massive scalar-tensor gravity for theory parameters that facilitate strong scalarization. The resulting energy density is below the current constraints on a Gaussian stochastic gravitational wave background but large enough to be detectable with the current generation of detectors when they reach design sensitivity, indicating that it will soon be possible to place new constraints on the parameter space of massive scalar-tensor gravity.

gr-qc↗

arXiv2023

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.

gr-qc↗

arXiv2022

Curvature and dynamical spacetimes: can we peer into the quantum regime?

Stationary compact astrophysical objects such as black holes and neutron stars behave as classical systems from the gravitational point of view. Their (observable) curvature is everywhere "small". Here we investigate whether mergers of such objects, or other strongly dynamical spacetimes such as collapsing configurations, may probe the strong-curvature regime of General Relativity. Our results indicate that dynamical black hole spacetimes always result in a modest increase $\sim 3$ in the Kretschmann scalar, relative to the stationary state. Our results show that the Kretschmann scalar can dynamically increase by orders of magnitude, during the gravitational collapse of scalar fields, and that the (normalized) peak curvature does not correspond to that of the critical solution. Nevertheless, without fine tuning of initial data, this increase lies far below that needed to render quantum-gravity corrections important.

gr-qc↗

arXiv2022

The irreducible mass and the horizon area of LIGO's black holes

The mass of a Kerr black hole can be separated into irreducible and rotational components -the former is a lower limit to the energy that cannot be possibly extracted from the event horizon and is related to its area. Here we compute the irreducible masses of the stellar-mass black holes observed by gravitational-wave interferometers LIGO and Virgo. Using single-event data, we present a re-parametrization of the posterior distribution that explicitly highlights the irreducible and rotational contributions to the total energy. We exploit the area law to rank the black-hole mergers observed to date according to their irreversibility, thus providing a guide to selecting events for targeted tests of General Relativity. Using population fits, we compute the rate by which the total area of black-hole horizons increases due to the observable mergers.

gr-qc↗

arXiv2022

The Gravitational Afterglow of Boson Stars

In this work we study the long-lived post-merger gravitational wave signature of a boson-star binary coalescence. We use full numerical relativity to simulate the post-merger and track the gravitational afterglow over an extended period of time. We implement recent innovations for the binary initial data, which significantly reduce spurious initial excitations of the scalar field profiles, as well as a measure for the angular momentum that allows us to track the total momentum of the spatial volume, including the curvature contribution. Crucially, we find the afterglow to last much longer than the spin-down timescale. This prolonged gravitational wave afterglow provides a characteristic signal that may distinguish it from other astrophysical sources.

gr-qc↗

arXiv2022

Lessons for adaptive mesh refinement in numerical relativity

We demonstrate the flexibility and utility of the Berger-Rigoutsos Adaptive Mesh Refinement (AMR) algorithm used in the open-source numerical relativity code GRChombo for generating gravitational waveforms from binary black-hole inspirals, and for studying other problems involving non-trivial matter configurations. We show that GRChombo can produce high quality binary black-hole waveforms through a code comparison with the established numerical relativity code Lean. We also discuss some of the technical challenges involved in making use of full AMR (as opposed to, e.g. moving box mesh refinement), including the numerical effects caused by using various refinement criteria when regridding. We suggest several "rules of thumb" for when to use different tagging criteria for simulating a variety of physical phenomena. We demonstrate the use of these different criteria through example evolutions of a scalar field theory. Finally, we also review the current status and general capabilities of GRChombo.

gr-qc↗

arXiv2022

GRChombo: An adaptable numerical relativity code for fundamental physics

GRChombo is an open-source code for performing Numerical Relativity time evolutions, built on top of the publicly available Chombo software for the solution of PDEs. Whilst GRChombo uses standard techniques in NR, it focusses on applications in theoretical physics where adaptability, both in terms of grid structure, and in terms of code modification, are key drivers.

gr-qc↗

arXiv2021

Evidence for violations of Weak Cosmic Censorship in black hole collisions in higher dimensions

We study collisions of boosted rotating black holes in $D=6$ and 7 spacetime dimensions with a non-zero impact parameter. We find that there exists an open set of initial conditions such that the intermediate state of the collision is a black hole with a dumbbell-like horizon which is unstable to a local Gregory-Laflamme-type instability. We are able to provide convincing numerical evidence that the evolution of such an instability leads to a pinch off of the horizon in finite asymptotic time thus forming a naked singularity, as in similar unstable black holes. Since the black holes in the initial state are stable, this is the first genuinely generic evidence for the violation of the Weak Cosmic Censorship Conjecture in higher dimensional asymptotically flat spacetimes.

hep-th↗

arXiv2021

Malaise and remedy of binary boson-star initial data

Through numerical simulations of boson-star head-on collisions, we explore the quality of binary initial data obtained from the superposition of single-star spacetimes. Our results demonstrate that evolutions starting from a plain superposition of individual boosted boson-star spacetimes are vulnerable to significant unphysical artefacts. These difficulties can be overcome with a simple modification of the initial data suggested in [PRD 99 (2018) 044046] for collisions of oscillatons. While we specifically consider massive complex scalar field boson star models up to a 6th-order-polynomial potential, we argue that this vulnerability is universal and present in other kinds of exotic compact systems and hence needs to be addressed.

gr-qc↗