Abstracts

MONDAY

Sascha Husa - The interplay of Gravitational Waves Observations and Numerical Relativity

The prospects of gravitational wave observations have been a key driver for the development of numerical relativity, and numerical relativity results form an integral part of all the waveform models that are used to decode the gravitational wave signals that have been observed. In this talk I will review the way in which numerical relativity is used in waveform modeling, and the open challenges on the way to next generation gravitational wave detectors.

Miguel Zilhao - Introduction to Numerical Relativity

We give an introduction to Numerical Relativity, including a brief historical perspective, major milestones, different formalisms, and corresponding applications.

Bruno Giacomazzo - Introduction to MHD

I will briefly describe the importance of relativistic MHD simulations in high-energy astrophysics and provide a short introduction to the equations that need to be solved when dealing with relativistic magnetized fluids

Ian Hawke - Numerical methods in GR

The "best" numerical methods depend on the model being simulated, the accuracy needed, and the resources available. This talk will survey the methods currently used across the field, particularly those available through the Einstein toolkit. The links for the next generation of simulations between numerical methods, models of the matter and spacetime, and near-future computing hardware will also be explored.

Steve Brandt/ Roland Haas/ Peter Diener - An Introduction to the Einstein Toolkit

This course covers the basics of the Einstein Toolkit:

1. A brief history;

2. what the Einstein Toolkit is and can do;

3, How to install the ET (including prerequisites);

4. How to run the ET and create a rudimentary plot of some of the data generated.

All of the above steps are carried out within a Jupyter notebook. This means that there are no hardware requirements for your computer.

Familiarity with the Linux command line is required, and some minimal knowledge of Python is helpful.

Note that this course replicates the material available in the online tutorial.

Steve Brandt/ Roland Haas/ Peter Diener - Building a WaveToy with NRPy

Creating a thorn for the Einstein Toolkit has been a successful collaborative framework for numerical relativity. For the last twenty-five years, researchers from institutes around the world have been contributing new physics and infrastructure thorns.

Although thorns are not difficult to create, there is still a non-trivial learning curve for new researchers.

NRPy+ is a set of Python tools that use Sympy to generate physics codes, allowing thorn authors to work with symbolic differential equations without worrying about the boilerplate code. Complicating this task is that the ET community is developing a new driver CarpetX which will required new and different knowledge than Carpet.

This tutorial is about "CactusThorn," an addition to the NRPy+ toolset which helps the authors of physics thorns cover this last mile. While the tool is still in its early stages of development, it is usable and ready for community engagement. This tutorial will show users how to create a wave equation thorn that will compile and run both for the Carpet driver and the CarpetX driver.

TUESDAY

Bruno Giacomazzo - GRHydro Tutorial

I will briefly introduce the main features of the GRHydro code, which is part of the Einstein Toolkit, and I will show how to use it in evolving a stable neutron star.

Thiago Assumpçao – An introduction to the NRPy+ framework with the NRPyElliptic initial data solver

NRPy+ is a Python-based framework that facilitates code development for numerical relativity. At its core, NRPy+ generates highly-optimized C code using CSE (common subexpression elimination) and SIMD (single instruction, multiple data) compiler intrinsics. Built atop its code generation capabilities are a large number of fully-worked examples, including fully functional numerical relativity codes in curvilinear coordinates. I will first review its tensorial equations implementation, arbitrary-order finite-difference derivative code generation, curvilinear coordinate systems support, as well as C function registration and automatic generation of Makefiles. In my tutorial, I will use the NRPyElliptic code to illustrate the typical workflow of using NRPy+ for numerical relativity applications. We will start with the mathematical formulation for puncture initial data, code up the equations using SymPy/NRPy+, generate and compile a standalone C code, visualize results, and produce diagnostics.

Wolfgang Kastaun - Post-processing for Einstein Toolkit users

I will give a broad overview of typical post-processing tasks, workflows, and requirements that arise in numerical simulations. Then I will survey the thorny situation specifically for users of the Einstein Toolkit and the tools available to those. I will also present general tools for two- and three-dimensional visualization and how to make ET simulation data usable within these. In particular, I will present the making-of a recent public outreach 3D movie created with raytracing software. Further, I will recommend some workflow related tools useful also for post-processing. The remaining time will be used for a demonstration of using the "PostCactus" Python package.

Barry Wardell - Visualisation tools

In this tutorial we will analyse a simulation of the GW150914 binary black hole merger produced using the Einstein Toolkit. We will make use of the simulation data included in the Einstein Toolkit gallery example to study the properties of the system, analyse the waveform, and visualise the spacetime. The tutorial will primarily make use of the SimulationTools analysis and visualisation package.

WEDNESDAY

Jordan Nicoules - Introduction to Kadath and featured evolution schemes.

The Kadath library is an open-source library written in C++. It relies on spectral methods to solve elliptic systems of equations in theoretical physics, and was specifically designed with numerical relativity in mind. I will first give a general introduction to the library, its main features and capabilities, as well as its original purpose. Namely, Kadath can mostly be used for the study of stationary systems or the generation of initial data. Then I will present the latest developments of the library with the implementation of time evolution schemes, and their first applications. I will illustrate the talk in order to showcase how the library can be used by novice and more advanced users, with an emphasis on its versatility. Some insights on the structure of the library itself will also be given all along.

Website : https://kadath.obspm.fr/

Karim Van Aelst - Introduction to SageMath

SageMath is a free open-source software providing a Python-based interface to many mathematics systems as well as a large number of built-in functions. In particular, the SageManifolds project extends SageMath towards differential geometry and tensor calculus. Further introduction and examples in different contexts will be provided.

Matteo Breschi - Multi-messenger studies of binary neutron stars mergers and perspectives with next-generation gravitational-wave detectors

The joint detection of GW170817 and its electromagnetic counterparts is a milestone in multi-messenger astronomy and it can provide constraints on the neutron star equation of state. We analyse GW170817 using different template models focusing on the implications for neutron star matter properties. In particular, we study the systematic tidal errors between current gravitational-wave models finding that systematics in current templates dominate over statistical errors at signal-to-noise ratio ≳ 100. We study AT2017gfo using semi-analytical model showing that observational data favour multi-component anisotropic geometries to spherically symmetric profiles. By joining the GW170817 and AT2017gfo information with the NICER measurements, we constrain the radius R1.4M⊙ of a neutron star of 1.4 M⊙ to 12.4±0.7 km (90% confidence level). Finally, we explore future extreme-matter constraints delivered by postmerger gravitational-waves from binary neutron star remnants with next-generation detectors. While inspiralling binaries inform us on the matter properties at the progenitor densities, postmerger remnants probe the high-density regimes of the nuclear equation of state, allowing the inference of the maximum neutron star mass with an accuracy of 12% (90% confidence level). Moreover, postmerger transients can be used to infer the presence of non-nucleonic matter phases through the inference of softening of the equation of state. For particular binary configurations, softening effects can lead to breaking of quasiuniversal properties and earlier collapse into black hole. These deviations can be detected for postmerger signals with signal-to-noise ratio ≳ 8.

Sarp Akcay - A brief survey of EMRIs and IMRIs:

I will begin by defining what {Extreme, Intermediate} Mass Ratio Inspirals are. Then I will delve into a detailed discussion of EMRIs starting with formation channels and event rates then going into the specifics of modelling them using black hole perturbation theory. Subsequently, I will move on to providing a similar exposition on IMRIs.

Federico Cattorini - GRMHD simulations of accretion flows onto massive binary black hole mergers

The merger of massive black hole binaries (MBHBs) is a mighty gravitational wave (GW) event, which will be detected by future space-based laser interferometers (e.g., LISA). MBHBs are a natural outcome of the hierarchical process of galaxy mergers, and their coalescence may occur in a magnetized, gas-rich environment, yielding powerful electromagnetic (EM) emission. The simultaneous observation of both GW and EM radiation emerging from such systems will provide precise measurements of cosmological parameters and help assess the evolutionary history of galaxies.

To explore the magnetohydrodynamical (MHD) features of the hot plasma surrounding these systems, we produced a suite of general-relativistic magnetohydrodynamical (GRMHD) simulations of the late-inspiral and merger of MBHBs using the Einstein Toolkit framework. Our work models for the first time the GRMHD evolution of merging binaries of spinning black holes, with spins either aligned or misaligned to the orbital angular momentum. We evolve binaries of equal- and unequal-mass black holes initialized on quasicircular orbits, and track their evolution down to coalescence, when a new black hole is formed.

Our goal is to capture the effects of spins and mass ratios on the mass accretion rates, the gas dynamics, and the EM energy emitted during the late-inspiral and merger. We observe that a higher postmerger spin of the remnant black hole corresponds to lower rates of mass accretion onto the horizon. In agreement with the Blandford-Znajek formula, we find that the postmerger value of the Poynting luminosity emitted by the remnant is proportional to the square of the spin parameter. In addition, We identify quasiperiodic modulations in the premerger accretion rate that evolve in parallel with the GW signal. This result could provide a valuable signature of EM emission concurrent to low-frequency GW detection, offering a novel outlook for future multimessenger astronomy.

Michail Chabanov - Towards the inclusion of bulk viscosity in numerical relativity simulations

Binary neutron star mergers provide the unique opportunity to study matter at densities and temperatures unreachable in laboratories on earth. Its properties are encoded in the equation of state whose influence on the gravitational wave signal of merging neutron stars can be used to constrain the physics of the strong interaction. But it is not only the equation of state which carries information about the underlying microphysics of neutron stars. Transport effects such as bulk viscosity are hypothesised to influence the dynamics binary neutron star mergers as well opening another potential window to study and constrain matter in such extreme conditions. In this talk I will present the first steps towards the inclusion of transport effects in fully general-relativistic numerical simulations. Here, I will introduce a conservative 3+1 formulation of the equations of dissipative general-relativistic hydrodynamics which enables the inclusion of dissipative effects in numerical relativity codes. As a first application of this formulation I will show standard tests in special relativity such as the Sod shock-tube problem and the Bjorken flow with bulk viscosity. To further move on to general relativity, the problem of stationary, spherically symmetric black hole accretion including bulk viscosity is solved and used as a test scenario for code validation. Finally, we present first results of oscillating neutron stars with bulk viscosity in a three-dimensional setup with a dynamically evolved spacetime.

Giulio Taiocchi - 1+1 Critical Collapse

The weak cosmic censorship conjecture (WCC) states that, for generic initial data, the maximal Cauchy development of the space-time posses a complete null-infinity, where the latter can be thought as the set of asymptotic limiting points of null geodesics. One of the most promising fields in the study of WCC is critical phenomena in gravitational collapse. Critical phenomena consist of the presence of phase transitions and critical solutions that exhibit special mathematical properties, such as self similarity, universality, and power law scaling. Firstly discovered in General Relativity by Choptuik, he studied a scalar field assuming spherical symmetry, and he individuated a critical solution via fine-tuning. This solution presented a divergence, but without the formation of a horizon. In the following years, numerical relativists tried to replicate the same study dropping symmetries and using other kinds of fields in order to generalize these results. Moreover, the study of the solutions at null infinity is necessary in order to make solid statements about the WCC. With the aim of helping the understanding of critical phenomena in a fully relativistic environment, toy models have been developed on flat space. These models are systems of semilinear partial differential equations, and present solutions with similar properties as Choptuik’s ones. Indeed, by fine-tuning the parameters that characterize the initial data, we find a phase transition, and threshold solutions that present self-similarity, universality and power law scaling. After a brief analysis of the models in spherical symmetry, I will focus on the contribution that I gave to this project in my master thesis, that is the null infinity inclusion in the analytical and computational domain. This is performed through a hyperboloidal compactification of the coordinates, and a suitable rescaling of the variables, and will lead to a comparison between our models and Choptuik’s solutions, and their critical behaviour at null infinity.

THURSDAY

Alex Vano Vinuales - Free hyperboloidal numerical evolutions

Gravitational wave radiation, our window for probing the strong field and dynamical regime of gravity, is unambiguously defined only at future null infinity - the location in spacetime where light rays arrive and thus where signals and global properties of spacetimes can be measured. A convenient way to include it in numerical relativity simulations is by evolving on hyperboloidal foliations, which are smooth spacelike slices that reach future null infinity. Among the different approaches to tackle it, I will mainly focus on conformal compactification, based on an idea by Nobel-laureate Roger Penrose, and I will also briefly describe the dual-frame method, which preserves well-posedness while using adapted coordinates. Our conformal implementation uses the BSSN and conformal Z4 formulations of the Einstein equations and has provided some very promising spherically symmetric evolutions of a massless scalar field coupled to gravity, which I will show. I will also give an update on current ongoing work towards a 3D generalization within the NRPy+ infrastructure. The final goal of this work is to provide a far-field numerical framework within the Einstein Toolkit that includes null infinity for simulations of compact object mergers with accurate gravitational wave extraction.

Niels Warburton - The Black Hole Perturbation Toolkit

The Black Hole Perturbation Toolkit brings together software and data relating to black hole perturbation theory. These can be used to model gravitational radiation from small mass ratio binaries as well as from the ringdown of black holes. The former are key sources for the future space-based gravitational wave detector, LISA. In this talk I will give an overview of the BHPToolkit, including a summary of the tools it provides.

Miguel Bezares - K-dynamics: Gravitational wave generation in Dark energy

We will discuss recent efforts to understand gravitational wave generation in Dark energy models. I will consider a class of alternative theories of gravity known as k-essence. This theory is a cosmologically relevant scalar-tensor theory that involves first-order derivative self-interactions, which pass all existing gravitational wave bounds and provides a screening mechanism. In this talk, I will present our numerical simulations of this theory considering three different scenarios: non-linear stellar oscillations, gravitational collapse and binary neutron stars.

Peter Diener - Self-force

I will explain why we would be interested in simulating Extreme Mass Ratio Inspirals (EMRIs) and the associated computational challenges. I will describe the ideas behind the self-force concept as well as several computational approaches. I will finally shortly describe SelfForce-1D, a time domain code for self-force calculations that is part of the Einstein Toolkit.

Paweł Szewczyk - Numerical studies of differentially rotating compact objects

Differentially rotating neutron stars can be produced in supernova explosions and binary neutron stars. The solution space for stationary configurations of such objects contains various types of solutions. Some of them may have extreme properties, including very high mass, a large value of spin parameter, or a quasi-toroidal shape.

In our work, we test the stability of those objects against a prompt collapse to a black hole. We employ the CoConNuT code to perform 2D hydrodynamical simulations and the FlatStar code to produce the initial data. I will present our initial results showing the stability threshold for selected degree of differential rotation and polytropic equation of state. Stable configurations with masses 2 times larger than the limit for non-rotating neutron stars were found. I will also discuss various numerical challenges that we face when performing our studies and the pseudo-spectral method used to create our initial configurations.

Benjamin Leather - Hyperboloidal method for frequency-domain self-force calculations

Gravitational self-force theory is the leading approach for modelling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands the metric of the binary in powers of the mass ratio. The source for the perturbations depends on the orbital configuration, calculational approach, and/or the order the perturbative expansion is carried too. These sources fall into three broad classes: distributional, extended and compact, and non-compact. The latter, in particular, is important for emerging second-order in the mass ratio calculations. Traditional frequency domain approaches employ the variation of parameters method and compute the perturbation on constant time slices of the spacetime with numerical boundary conditions supplied at finite radius from series expansions of the asymptotic behaviour. This approach has been very successful but the boundary conditions calculations are tedious and the approach is not well suited to non-compact sources where homogeneous solutions must be computed at all radii. In this talk I outline an alternative approach where the spacetime is foliated by horizon-penetrating hyperboloidal slices. Further compactifying the coordinates along these slices allows for simple treatment of the boundary conditions. We implement this approach with a multi-domain spectral solver with analytic mesh refinement and present results for the scalar-field self-force on circular orbits as an example problem. We find the method works efficiently for all three classes of sources encountered in self-force calculations and has some distinct advantages over the traditional approach.

Anna Heffernan - Regularising the Self-Force

A current package in development for the Black Hole Perturbation Toolkit is the new regularisation package. This uses previously derived formulae to give the ell-mode regularisation parameters required for improved convergence of self-force calculations. Here, I will give an overview of the package as well as a report on its current status.

FRIDAY

Josu Aurrekoetxea - GRChombo: Solving and evolving the initial data constraints in numerical relativity

In the first part of this talk I will give an overview of the main capabilities of GRChombo, an open-source code for numerical relativity simulations written entirely in C++14, using hybrid MPI/OpenMP parallelism and vector intrinsics. It makes use of the Chombo library for adaptive mesh refinement and is developed and maintained by a collaboration of numerical relativists with a wide range of research interests, from early universe cosmology to astrophysics and mathematical general relativity. In the second part of the talk I will introduce CTTK, a new method to solve the initial data constraints that evades the existence and uniqueness problem of solutions of the Hamiltonian constraint. This full Hamiltonian and momentum constraint solver will be soon publicly available to use with GRChombo or other existing NR evolution codes.

Boris Daszuta - GR-Athena++: puncture evolutions on vertex-centered oct-tree AMR

`GR-Athena++` is a general-relativistic, high-order, vertex-centered solver that extends the oct-tree, adaptive mesh refinement capabilities of the astrophysical (radiation) magnetohydrodynamics code `Athena++`. Dynamical spacetimes are simulated using Z4c coupled to the moving puncture gauge with robust and accurate binary black hole (BBH) mergers demonstrated. `GR-Athena++` leverages the task-based parallelism paradigm of `Athena++` to achieve excellent scalability. Strong scaling efficiencies above 95% for up to 1.2×1e4 CPUs and excellent weak scaling up to 1e5 CPUs are measured for production BBH runs. `GR-Athena++` thus allows for the robust simulation of compact binary coalescences and and offers a viable path towards numerical relativity at exascale. In this talk a general overview of features outlined above will be provided together with our recent development efforts.

Dina Traykova - Calculating environmental effects on a fixed black hole background

As compact objects are expected to interact gravitationally with their environments, we can hope to learn something of the properties of dark matter though characterising the different effects it may have on black holes and the gravitational wave signal from a merger.

In this talk I will describe how we measure some of these environmental effects from dark matter on a single static black hole and in what physical systems is fixing the background metric a good approximation. I will outline some of the main features of the (soon to be) public fixed background code, based on GRChombo, that we use for this work. And finally, taking the example of a study where we calculate the dynamical friction force on a black hole moving through a dark matter cloud, I will discuss the advantages of using a fixed background code instead of full NR.

Hayley Macpherson - Numerical relativity as a tool to study inhomogeneous cosmology

Numerical relativity (NR) is widely used for simulations of relativistic systems such as merging binary black holes. The generality of NR makes it a useful tool for any case where we may not have an analytic form of the metric tensor. One relatively new application of NR is to the study of inhomogeneous cosmology in the late-time Universe, allowing for large-scale simulations of nonlinear structure formation without any constraints on the form of the metric of spacetime. Simulations like this will eventually allow us to answer the long-term debate on the size of the backreaction effect of small-scale nonlinearities on the cosmic expansion. In addition, we are uniquely positioned to study general-relativistic effects on cosmological observables while remaining agnostic about the existence of any background metric model of spacetime. I will discuss the application of NR to late-time cosmology and present an overview of the status of the field as well as future prospects for improving current methods.

Tomas Andrade - Simulating highly eccentric black hole binaries

As a new era of gravitational wave detections rapidly unfolds, the importance of having accurate models for their signals becomes increasingly important. In this context, we will discuss numerical simulations of eccentric black hole binaries with Einstein Toolkit. Our main goal is to inform the Effective One Body code TEOBResumS, which is successful at describing quasi-circular binaries, in order to extend its regime of applicability to general orbits.

Robyn Munoz - Simulations of a quasi-spherical collapse and gravito-electromagnetic and Petrov invariant characterisation

We study a quasi-spherical collapsing structure in an inhomogeneous universe with numerical relativity simulations. We set-up fully nonlinear initial conditions by perturbing the $Lambda$CDM model with the comoving curvature perturbation $\mathcal{R}_c$, defined as a 3D sinusoidal. We then have a grid of quasi-spherical overdensities connected through filaments. This is implemented in the synchronous comoving gauge using a dust perfect fluid, then it is fully evolved with the Einstein Toolkit code.

We find that the top-hat model is an excellent approximation at the peak of the over density where we find that there is no shear. Additionally we find the electric and magnetic parts of the Weyl tensor to be strongest along and around the filaments respectively, where we see a tendency towards a spacetime of Petrov type D. While the center of the overdensity remains essentially conformally flat, in line with the spherical collapse model, in the surrounding region we see a sort of peeling-off in action, with the spacetime transitioning between different Petrov types and production of gravitational waves

John Regan - Modelling the Formation of Massive Black Holes at High Redshift

In this talk I will give an overview of how massive black holes are modelled in high resolution cosmological simulations. Cosmological simulations must attempt to model the evolution of the large scale structure of the Universe from early times (z >~ 50) down to present day epochs. In practice this means modelling the (gravitational) evolution of a virtual Universe over Mpc scales. Within this framework however many physical processes of interest (e.g. star and black hole formation and their related feedback effects) occur at sub-parsec scales introducing a spatial dynamic range of at least a factor of a million. I will discuss recent advances in the field of cosmological simulations particularly highlighting advances in our understanding of massive black hole formation.