Alex Vañó-Viñuales

The formation of black holes by the gravitational collapse of stars is known to spontaneously excite particle pairs out of the quantum vacuum. For the canonical vacuum state at past null infinity, the expected number of particles received at future null infinity can be obtained in full closed form at sufficiently late times. However, for intermediate times, or for more complicated astrophysical processes (e.g. binary black hole mergers), the problem is technically challenging and has not yet been resolved. We develop here a numerical approach to study scattering problems of massless quantum fields in asymptotically flat spacetimes, based on the hyperboloidal slice method used in numerical relativity and perturbation theory. This promising approach can reach both past and future null infinities, and therefore it has the potential to address the Hawking scattering problem more rigorously than evolution on the usual Cauchy slices. In this first work, we test this approach with some dynamical toy models in Minkowski using effective potentials that mimic the effects of gravity, and compute the spectrum of particles received at future null infinity. We finally discuss future prospects for applying this framework in more relevant gravitational scenarios.

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

The focus of this work is on the construction of initial data including a neutron star on a hyperboloidal slice. As simplest scenario for this first step, spherical symmetry is considered together with a polytropic-like equation of state for the neutron star. Constraint-satisfying hyperboloidal initial data are obtained for a single neutron star and for a combination of neutron star with a black hole in its center. To the author’s best knowledge this is the first time that full hyperboloidal slices of a neutron star spacetime are constructed. The obtained initial data are suitable for evolutions of the Einstein and relativistic hydrodynamic equations on hyperboloidal slices.

Editorial introducing the GRG Topical Collection "Hyperboloidal foliations in the era of gravitational-wave astronomy," on hyperboloidal slices. The collection includes contributions spanning black-hole perturbations, asymptotic geometry, initial-data, and high-accuracy numerical methods relevant to gravitational-wave modeling. The collection grew out of the 2023 "Infinity on a Gridshell" workshop in Copenhagen.

We present simulations of the Einstein–Maxwell–Klein–Gordon system on compactified hyperboloidal slices. To the best of our knowledge, these are the first hyperboloidal evolutions of this system that employ a common formulation like BSSN/Z4. Hyperboloidal slices smoothly reach future null infinity, the only location in spacetime where radiation (such as gravitational waves) is unambiguously defined. We are thus able to reach null infinity and extract signals there. We showcase the capabilities of our implementation in spherical symmetry with the evolution of a charged scalar field perturbing a regular spacetime and near an electrically charged black hole. We also present the collapse of a charged scalar field into a Reissner–Nördstrom black hole. Here we show sample evolutions and validation tests for these setups.

Numerical evolutions of a system of equations close to null infinity in the geometric background of the inversion-Minkowski spacetime are performed. The evolved equations correspond to the linearisation of a second order metric formulation of the conformal Einstein field equations (CEFEs). These linear equations were first presented in [1] and the main purpose of this paper is to illustrate, through numerical evolutions, the scri-fixing technique via gauge source functions introduced [1] for the linearised CEFEs. A comparison of evolutions using scri-fixing gauge sources and trivial gauge source function in spherical and axial symmetry is presented.