# Research of the Numerical-Relativity group

Black holes are the most extreme objects predicted by Einstein’s relativity, enveloped in an event horizon and producing large distortions in the surrounding spacetime. These distortions are of particular current interest, because in dynamical situations (such as oscillating or orbiting black holes) they result in propagating gravitational waves. Inspiralling black holes are the strongest potential signal source of gravitational waves to be detected by ground-based interferometers, such as LIGO, GEO600 and Virgo. It is important to have accurate models of such inspirals for both the detection, and also the understanding, of the signals from these detectors.

## Black-Hole Physics

Our work is focussed on understanding the dynamics of black holes through computer simulation of binary inspirals. This involves studying horizon dynamics and extracting gravitational wave information from physically realistic models.

**Calculation of gravitational waveforms:**In order to detect gravitational waves and characterise their sources, accurate theoretical models are required. We use the Llama and Whisky codes to produce highly accurate waveforms which can then be used to generate waveform*templates*for various sources, against which experimental data will be compared. The AEI participates in the NINJA project, which aims to test the effects of including numerical relativity waveforms in experimental data analysis pipelines, and the NR-AR project, which aims to perform highly accurate comparisons with analytical models for the purpose of template generation.**Nonlinear black-hole physics:**Recent work in Numerical Relativity has been focused on the generation of gravitational waves, but black holes are fascinating objects in their own right. When two generic black holes inspiral and merge, the anisotropic emission of linear momentum carried by the waves causes a “kick” to the final black hole that is produced. We study this because it is important astrophysically for understanding the ejection of supermassive black holes from galaxies in galaxy mergers. We are also studying the properties of the black hole horizons, the surfaces beyond which nothing, not even light, can escape, as well as the nonlinear dynamics of the geometry of a binary black hole spacetime.**Formulation of the Einstein equations:**There are many different ways to write Einstein’s equation as a time-evolution partial differential equations. Each of these*formulations*has different mathematical properties, and some are more amenable to numerical solution than others. We are interested in choosing the best formulation for a given problem, and are studying the effects of using different formulations on the evolution of binary black hole spacetimes.**EMRIs and IMRIs**: While the full Einstein equations are required for solving comparable mass binary black hole systems, for extreme mass ratios, e.g. 1:100000, this is not computationally feasible. Instead, these systems are approached using*perturbation theory*, where the approximation that the mass ratio is small is used. The smaller mass is treated as a point particle and the Einstein equations are linearized about the background of the larger mass. However, the point particle approximation results in a perturbation which must be regularized before it can give meaningful results. We study methods for computing such regularized perturbations with the goal of accurately modeling EMRIs.**EM counterparts to SMBHs mergers**: When supermassive black holes merge in the presence of gas and magnetic fields, they emit not only gravitational waves, but also traditional electromagnetic radiation, for example X-rays. These*electromagnetic counterparts*to gravitational wave signals might be useful for more accurately determining the sky location of a gravitational wave source. We study the relation of the EM radiation to the black hole motion and the gravitational waves for various magnetic field configurations.**Approximation methods:**Although a lot of our work is done via numerical simulations, we try and resort to them only if strictly necessary. Whenever, possible, in fact, we use approximation techniques such as the post-Newtonian expansion or the effective-one-body (EOB) approach, to model the gravitational-wave signal produced by the binaries we evolve with the simulations. We also try to be creative when it comes to “toy models” or phenomenological descriptions. These allow us to obtain a very good description of the problem at hand with only modest resources and to also gain insight on the numerical results.

## Neutron-Star Physics: Relativistic Hydrodynamics and Magnetohydrodynamics

The aim of our (magneto)hydrodynamics projects is to study the nonlinear dynamics of astrophysical matter under general relativistic conditions. We particularly focus on neutron stars (NSs), both isolated and in binaries. To this end we have developed a fully three dimensional numerical code for carrying out simulations of general relativistic hydrodynamics. For details see the Whisky code.

**NS-NS binaries:**Binary neutron stars are among the most promising sources of gravitational waves and are leading candidates as short-hard gamma-ray burst progenitors. The numerical investigation of their coalescence and merger within the framework of General Relativity is thus fundamental. Over the years, we have performed fully general-relativistic simulations of these systems, for various mass ratios and for both unmagnetized and magnetized neutron stars, reaching high accuracy standards. In doing this, major contributions to the development of the Whisky code were made. Particular attention has been put into the investigation of the rich late-time dynamics, the outcome of which includes the possible formation of tori and accretion disks, prompt collapse to a BH, and the chance of having the formation of hypermassive NS transients.**BH-NS binaries:**These binaries share with BH-BH and NS-NS binaries the importance of being leading gravitational wave source candidates; they have also been indicated, along with binary neutron stars, as possible progenitors of a part of the short-hard gamma-ray bursts we observe. The major challenge with this type of binary is dealing simultaneously with the difficulties related to the BH and to the NS. Recently, the Numerical Relativity group has been investigating these systems in two directions: by performing accurate, general relativistic simulations of their merger, focusing especially on the effects of having a magnetized NS, and by elaborating semi-analytical models in order to predict the dependance on the binary physical parameters of poorly constrained key features of the outcome of its merger, such as the mass of the torus that may possibly form.**Isolated neutron stars:**During its life, it is likely that every neutron star undergoes an oscillatory phase: neutron star oscillations may be excited, for example, as matter is accreted from a companion, after a core collapse, during a starquake induced by the spin-down of the star or by a large phase transition, as transients during a gravitational collapse. The rich phenomenology associated with these oscillations includes, among the others, hydrodynamical instabilities, secular instabilities, gravitational wave emission, and critical phenomena, topics on which we have been extensively working, within the framework of general-relativistic simulations. We have also been addressing the stability of magnetars (young, isolated neutron stars with very strong magnetic fields), which are believed to be behind the observed soft gamma repeaters and anomalous X-ray pulsars.**Accretion-disc physics:**The time-varying behaviour of accretion flows is responsible for a large amount of observational evidence from compact objects, either black holes or neutron stars. This topic has attracted a lot of interest in the last few years, in connection with several fundamental physical effects taking place in accretion discs, such as the development of the magneto-rotational instability, the transport of angular momentum through magnetic turbulence, the time evolution of magnetohydrodynamic warps or the excitation of various kinds of oscillation modes and waves. Recently, we have investigated the response of a non-Keplerian circumbinary discs that responds to the loss of mass and to the recoil velocity of the black hole produced after the merger of two supermassive black holes.**Radiative transfer and microphysics:**A correct and complete physical description of a neutron star is necessary to make accurate predictions of gravitational waveforms and to connect the emitted gravitational radiation to the physics behind it. Such a description would have to include not only the gravitational behaviour of the star, but also all aspects of its microphysics. Given the extreme densities in neutron stars and the many timescales involved, this is a very complicated theoretical and numerical problem, which is yet unresolved. It touches various fields of physics, such as electroweak interactions, thermodynamics, quantum chromodynamics. Our research is currently focused on neutrino emission and radiative transfer, which play a very important role in the gamma-ray burst fireball model.