Extra talk (YouTube)

Gabriele Bozzola – A guided example of an interesting visualization with kuibit

Abstracts and presentation slides


Sascha Husa – Introduction to Numerical Relativity

I will cover the basics of Numerical Relativity, including a brief historical perspective, the major milestones in the field, the formalisms more widely used and corresponding applications.

Introduction to Numerical Relativity

Ian Hawke – Numerical Methods for matter in GR

Numerical simulations of matter in GR inherit all the problems of evolving the spacetime, alongside additional constraints. This lecture will introduce the current solutions used in the field and within the Einstein Toolkit for solving problems including discontinuous shocks and constraints linked to the magnetic field in simulations of GR(M)HD. We will also look at potential solutions for the next generation of simulations of more complex matter models on future compute resources, needed for next generation detectors.

Steven Brandt, Peter Diener – 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.

Introduction to the Einstein Toolkit

Steven Brandt, Peter Diener – Writing a Thorn for the Einstein Toolkit

This course covers the basics of writing an Einstein Toolkit thorn.

Bruno Giacomazzo – GRHydro Tutorial

I will show how to use GRHydro for simulations of single neutron star evolutions and binary neutron star mergers. I will present two example parameter files useful to simulate these scenarios and explain the most important parameters. I will also briefly discuss some simple ways to visualize the results.


Wolfgang Kastaun – Using Blender for raytracing scientific data

Visualizing 3D scientific data is no trivial task and there are only a few options, each with different strength and weaknesses. Raytracing software provides by far the most control over appearance and, arguably, can produce the most aesthetically pleasing results. The additional visual clues of photo-realistic scenes also carry across 3D structures more clearly. One freely available option for raytracing is Blender. Although it is extremely powerful, it is not geared towards scientific data. I will give a brief introduction how to employ Blender for visualizing any scientific data that can be imported to a Python environment. This will be followed by a hands-on tutorial. Participants who want to actively follow the tutorial need to install Blender and a Python3 environment on their laptops beforehand.

Using Blender for raytracing scientific data

Swapnil Shankar – GRaM-X: A new GPU-accelerated dynamical spacetime GRMHD code for Exascale computing with the Einstein Toolkit

GRaM-X (General Relativistic accelerated Magnetohydrodynamics on AMReX) is a new dynamical spacetime ideal-MHD code for Einstein Toolkit that runs on GPUs. It is capable of performing a realistic core-collapse supernova simulation with a tabulated equation of state. In this talk, I will discuss the implementation, features, performance and code tests for GRaM-X, as well as some preliminary results from a core-collapse supernova simulation.

GRaM-X: A new GPU-accelerated dynamical spacetime GRMHD code for Exascale computing with the Einstein Toolkit

Alejandra Gonzalez – Second release of the CoRe database of binary neutron star merger waveforms

We present the second data release of gravitational waveforms from binary neutron star mergers, covering a wide range of parameters and using various simulations with different equations of state. Ready-to-use fitting formulas are provided, and standard error analysis is showcased.

Second release of the CoRe database of binary neutron star merger waveforms

Peter Diener – Introduction to SelfForce1D

I will give an introduction/tutorial to the SelfForce1D code.

Introduction to SelfForce1D

Isabel Suárez-Fernandez – Coalescence of high mass ratio precessing black hole binaries using the Einstein Toolkit

Coalescences of black hole (BH) binaries are the most frequently observed Gravitational Waves (GW) sources. As members of the LIGO Scientific Collaboration we want to model the GW signals of binary BHs coalescences and, eventually, observe such signals. We use the Einstein Toolkit to carry out numerical relativity simulations of different configurations of precessing BH binaries with mass ratio between 4 and 18. The goal is to provide a publicly available catalogue of accurate GW signals of such systems.

Coalescence of high mass ratio precessing black hole binaries using the Einstein Toolkit


Samuel Tootle – Introduction to FUKA initial data

  1. Overview of FUKA
  2. Intro to Kadath spectral solver
  3. discussion of the formulations being solved in FUKA (vacuum + with matter)
  4. Additional capabilities such as eccentricity reduction
  5. tutorial and solving an isolated BH
  6. tutorial and solving an isolated NS
  7. tutorial for solving binary ID
  8. plotting the initial data using Python

Introduction to FUKA initial data

Ian Hawke – Impact of nuclear reactions on GWs from NS mergers

Multiscale approaches allow us to reformulate fast nuclear reactions as a bulk viscous pressure. Numerical simulations show the potential impact of the nuclear reaction model on GWs in next generation detectors. However, the interaction with full radiation hydrodynamics simulations makes the details complex and some results conflict. We discuss, using toy models, the potential impact of boundary layer effects, and what future numerical simulations would have to pay attention to, to resolve this.


Eric Gourgoulhon – Symbolic tensor calculus with SageMath

This hands-on session is aimed at exploring the various functionalities for tensor calculus and differential geometry available in the free Python-based mathematics software system SageMath. A special emphasis will be put on black hole spacetimes.


Those that don’t want/manage to install Sage on your own computer can open a free account on https://cocalc.com/ to be able to run SageMath notebooks (and many other scientific programs!) on this server.

Symbolic tensor calculus with SageMath

Ian Hinder – The Research Software Engineer Movement

The Research Software Engineer Movement

Hector Okada da Silva – Black hole scalarization: lessons from numerical relativity

Some theories that modify general relativity can evade Solar System constraints and yet deviate considerably from general relativity in the strong field regime of compact objects, i.e., neutron stars and black holes. This is possible through a process known as spontaneous scalarization, in which the compact object grows “scalar hair” once certain conditions are met and remains “bald” otherwise. I will review the basics of this effect and then give a bird’s-eye view of our current understanding of black hole scalarization. I will focus on what we have learned thanks to numerical relativity and also discuss what remains to be understood.

Black hole scalarization: lessons from numerical relativity

Katy Clough – GRChombo: Lessons for adaptive mesh refinement in numerical relativity

I will introduce GRChombo and discuss the opportunities and challenges of using fully general adaptive meshes.

Adaptive mesh refinement (and warp drives)

David Neilsen – Compact finite difference schemes for numerical relativity

Future advances in gravitational wave detector technology will provide both more accurate observations of merger events and observations from a wider variety of sources. One strategy for improving performance in numerical relativity is to use numerical schemes that require less communication in parallel runs. Compact finite difference stencils can do this and achieve higher accuracy than standard finite differences. I will present some initial tests of compact finite differences with the BSSN equations in Dendro-GR, including measures of accuracy and performance gains.


Stephan Rosswog – SPHINCS_BSSN: a new approach to Numerical Relativity

We have recently developed a relativistic hydrodynamics code, SPHINCS_BSSN, that solves the full set of Einstein equations (currently using the BSSN formalism), but differently from most approaches, uses a Lagrangian particle method to solve the fluid equations. I will discuss the most important methodological elements of this new approach and I will discuss some of the first applications.


Nicolas Sanchis-Gual – Evolving bosonic fields with the Einstein Toolkit: stability and gravitational waves

Bosonic stars are theoretical exotic compact objects made of ultralight bosonic particles that could explain the nature of part of the dark matter. In this talk, I will review some recent results on the stability and dynamical formation of these objects using the Einstein Toolkit. Then I will talk about bosonic star mergers, their gravitational wave emission, and what we could learn about them from a real gravitational wave event, if these stars exist in the Universe.

Claudio Lazarte – Proca stars initial data from spectral methods

In this talk, I will expound on the obtaining of initial data of non-rotating Proca stars using multi-domain spectral collocation methods. I will explain in detail a suitable decomposition of the spherically symmetric 3-dimensional space on several radial domains and the spectral decomposition of Einstein-Proca system fields using Chebyshev polynomials. Then, I will show how this implementation allows us to iteratively solve the eigenvalue problem derived from Proca stars radial equations, reproducing the same results for the spherically symmetric case of Proca stars first introduced by Brito et al.

Proca stars initial data from spectral methods

Jorge Delgado – EMRIs around j=1 black holes with synchronised hair

We study extreme mass ratio inspirals (EMRIs) due to an infalling Light Compact Object (LCO) onto a generic class of stationary and axi-symmetric massive compact objects (MCO - with or without a horizon). Using the quadrupole hybrid formalism we obtain a master formula for the evolution of the radius of the LCO and find qualitatively different behaviours depending on the geodesic structure of the MCO. We then specialize the MCO to a black hole with synchronised scalar hair (BHsSH). To allow a comparison with a highly spinning Kerr BH, we consider BHsSH with dimensionless spin, j=1. This yields two distinct sequences of solutions. The first harbours Kerr-like solutions with maximal hairiness of ∼10%. The corresponding EMRIs are Kerr-like, but the cut-off frequency can be a few times smaller than in Kerr, yielding waveforms with quantitatively significant non-Kerrness. The second sequence links the extremal Kerr black hole to a mini-boson star with j=1. Here we observe qualitative non-Kerrness, such as the non-monotonically increase of the angular velocity and stagnation endpoints, reflecting Kerr-unlike geodesic structures.

EMRIs around j=1 black holes with synchronised hair

Bradley Cownden – Examining the stability of quasinormal modes using the pseudospectrum

In this talk, we present ongoing work regarding the stability of quasinormal modes (QNMs) in black hole and kink systems. This involves two main steps: first, the application of a hyperboloidal compactification that allows for the spectral problem defining the QNMs to be written in terms of the eigenvalues of a non-self adjoint Sturm-Liouville operator. Next, we introduce the pseudospectrum, which allows us to visualize QNM instability as a topographic map of the response of the operator to perturbations. We will see how this formulation successfully reproduces the instability of the Schwarzschild black hole overtones in the case of scalar perturbations. We then employ this method to examine – for the first time – the stability of the QNMs of the Yang-Mills soliton in four dimensions.

Examining the stability of quasinormal modes using the pseudospectrum

Beyhan Karakaş – Effect of spin in binary neutron star mergers

In this talk, we will demonstrate the effect of spin (being aligned, anti-aligned and aligned-anti-aligned with the orbital angular momentum) in binary neutron star mergers by performing fully general relativistic simulations which use finite-temperature, composition dependent equation of state and take into account neutrino emission/absorption. We will investigate the effect of spin in the dynamics of the system, on the final remnant, which is a hypermassive neutron star or black hole depending on the total mass, mass ratio and spin configurations, its spin evolution, corresponding gravitational waves and ejected matter. The distinctive behaviors and their detectability by the current and future gravitational wave detectors will be discussed

Anton Khirnov – The framework paradigm - limitations and alternatives

Cactus is an example of a “framework” type of software architecture, widely used in numerical relativity codes and beyond. While this approach has a number of attractive qualities, its weaknesses are less commonly appreciated in the NR community. In my talk I will discuss limitations of framework-style architectures within the context of my recent work on vacuum critical collapse, and compare them to alternative designs.

The framework paradigm – limitations and alternatives

Raimon Luna – Machine Learning Techniques in Strong Gravity

In this talk/tutorial we will review some recent uses of machine learning techniques to perform calculations in strong gravity. These will include physics-informed neural networks (PINNs) for the solution of differential equations, and generative models such as GANs.