Topic
The aim of the workshop is to give numerical relativists the oppurtunity to learn about results in mathematical relativity beyond the level that they would typically be discussed by the numerical relativity community, to inform the mathematical community about the current state of the art in numerical simulations and finally to identify problems of common interest. Particular focus points will be:
 Global results for numerical relativists,
 The numerical treatment of nullinfinity,
 Critical collapse,
 Stateoftheart numerical methods.
This workshop is funded by the
DFG research training unit "Quantum and Gravitational Fields" (GK1523/2)
Speakers
Speakers include Matt Choptuik, Katy Clough, Piotr Chrusciel, Carsten Gundlach, Philippe LeFloch, Maciej Maliborski, Rodrigo Panosso Macedo, JuanAntonio ValienteKroon and Alex VañóViñuales.
Participants
Martin Ammon, Bernd Bruegmann, Marcus Bugner, Matt Choptuik, Piotr Chrusciel, Katy Clough, Reetika Dudi, Edgar GasperinGarcia, Carsten Gundlach, Gernot Heissel, David Hilditch, Anton Khirnov, Tomas Ledvinka, Philippe LeFloch, Rodrigo Panosso Macedo, Maciej Maliborski, Reinhard Meinel, Sebastian Moeckel, István Rácz, Jochen Roendigs, Hannes Rueter, Christian Schell, JuanAntonio ValienteKroon, Alex VañóViñuales, Gerhard Zumbusch
Program
Thursday, 08. September 2016
12:00 
13:45 
Registration and Lunch 
13:45 
14:00 
Bernd Brügmann 
Welcome and Opening Remarks 
14:00 
15:00 
Philippe LeFloch 
The Global Nonlinear Stability of Minkowski Spacetime with Massive Matter
This lecture will review recent results on the evolution of selfgravitating massive matter. A new vector field method, the Hyperboloidal Foliation Method, developed in collaboration with Yue Ma (Xian) in a series of papers, is available in order to establish globalintime results for nonlinear systems of coupled waveKleinGordon equations posed on a curved spacetime. The Hyperboloidal Foliation Method has now been extended in order to analyze the global dynamics of massive scalar fields and to establish that Minkowski spacetime is globally nonlinearly stable when the scalar fields have sufficiently small total mass. On the other hand, the pioneering method by D. Christodoulou and S. Klainerman in the 90's only applies to vacuum spacetimes or massless scalar fields.

15:00 
16:00 
Katy Clough 
GRChombo  Numerical GR with AMR: a new code and applications [pdf]
GRChombo is a new numerical relativity code which incorporates full adaptive mesh refinement (AMR), with nontrivial "manyboxesinmanyboxes" mesh hierarchies and massive parallelism through the Message Passing Interface (MPI). GRChombo evolves the Einstein equation using the standard BSSN formalism and was developed with the aim of studying of a range of new physics which has previously been computationally infeasible in a full 3+1 setting. I will present some features of the code and then talk about several applications I have worked on, including critical collapse of asymmetric scalar field “bubbles”, and inhomogeneous inflation in early universe cosmology.

16:00 
16:30 
Coffee Break 
16:30 
17:30 
Carsten Gundlach 
Critical phenomena in gravitational collapse
Phenomena such as universality, scaling and selfsimilarity arise in time evolutions of initial data that are at the threshold of black hole formation, but otherwise generic. I will review some key ideas and results since 1991, when Choptuik first studied critical collapse of a spherical scalar field, and then talk about some ongoing work with Baumgarte and Jalmuzna on rotating critical collapse.

20:00 

Buffet Dinner 
Friday, 09. September 2016
9:00 
10:00 
Piotr Chrusciel 
The many ways of the characteristic Cauchy problem
I will discuss the various ways of solving the characteristic constraint equations.

10:00 
11:00 
Matt Choptuik 
Black hole formation in RandallSundrum II braneworlds [pdf]

11:00 
11:30 
Coffee Break 
11:30 
12:30 
Rodrigo Panosso Macedo 
Spectral decomposition of blackhole perturbations on hyperboloidal slices
We present a spectral decomposition of solutions to relativistic wave equations described on horizon penetrating hyperboloidal slices within a given Schwarzschildblackhole background. The wave equation in question is Laplacetransformed which leads to a spatial differential equation with a complex parameter. For initial data which are analytic with respect to a compactified spatial coordinate, this equation is treated with the help of the Mathematicapackage in terms of a sophisticated Taylor series analysis. Thereby, all ingredients of the desired spectral decomposition arise explicitly to arbitrarily prescribed accuracy, including quasi normal modes, quasi normal mode amplitudes as well as the jump of the Laplacetransform along the branch cut. Finally, all contributions are put together to obtain via the inverse Laplace transformation the spectral decomposition in question. The paper explains extensively this procedure and includes detailed discussions of relevant aspects, such as the definition of quasi normal modes and the question regarding the contribution of infinity frequencies modes to the early time response of the black hole.

12:30 
13:00 
Gernot Heissel 
A numerical derivation of maximal Kerr trumpet initial data
The first ever detections of gravitational waves have recently been announced by the Ligo Scientific Collaboration. The sources of these signals turned out to be binary black holes mergers in all cases so far.
The mechanisms for the detection, and for the extraction of the physical source parameters heavily rely on the predictions of numerical relativity simulations. Consequently, the accuracy of these simulations puts limits to the sensitivity at which detections can be made, and to the accuracy to which the physical parameters of the black holes can be extracted from the signals.
Hence, the improvement of black hole simulations is a well motivated hot topic in current numerical relativity research; now more than ever, where it became apparent that we will observe many more signals from binary black hole mergers in upcoming higher sensitivity detector runs.
In my talk I will argue that providing Kerr initial data in what is known as trumpet geometry potentially is one such improvement, and I will present the current state of the project.

13:00 
14:30 
Lunch Break 
14:30 
15:30 
Juan ValienteKroon 
On the construction of antide Sitterlike spacetimes
In this talk I discuss a new approach to the systematic construction of vacuum 4dimensional antide Sitterlike spacetimes by means of an initialboundary value problem for Friedrich's conformal field equations. This construction allows to prescribe as Dirichlet boundary data the 3metric of the conformal boundary of the spacetime and contains, as a particular case, reflective boundary conditions. The hyperbolic reduction of the conformal equations used intros analysis leads to wave equations for the various conformal fields and makes use generalised harmonic coordinates and is close in spirit to the framework often used in numerical Relativity. Accordingly, it is hoped it will be simpler to implement numerically than other conformal approaches to the construction of antide Sitterlike spacetimes. If time allows, I will discuss how the method can be extended to the case of tracefree matter.

15:30 
16:30 
Maciej Maliborski 
On dynamics of asymptotically AdS spaces [pdf]
The antide Sitter (AdS) space is of great interest in contemporary theoretical physics due to the AdS/CFT correspondence. However, the question of stability of AdS space is unanswered till now. After giving the motivation for studies of asymptotically AdS spaces, I will review current status of the AdS instability problem. This will include: evidence for instability of AdS space, existence and properties of timeperiodic solutions, and finally the resonant approximation. If time permits I will comment on other asymptotically AdS solutions. Along with the results, I will give details of methods relevant to the topic.

16:30 
17:00 
Coffee Break 
17:00 
17:30 
Edgar Gasperin Garcia 
Zero restmass fields and the NewmanPenrose constants on flat space.
Zero restmass fields of spin 1 (the electromagnetic field) and spin 2 propagating on
flat space and their corresponding NewmanPenrose (NP) constants are studied near spatial
infinity. The aim of this analysis is to clarify the correspondence between data for these fields
on a spacelike hypersurface and the value of their corresponding NP constants at future and
past null infinity. To do so, the framework of the cylinder at spatial infinity is employed
to show that, expanding the initial data in terms spherical harmonics and powers of the
geodesic spatial distance ρ to spatial infinity, the NP constants correspond to the data for
the highest possible spherical harmonic at fixed order in ρ. In addition, it is shown that
the NP constants at future and past null infinity, for both the Maxwell and spin2 case, are
related to each other as they arise from the same terms in the initial data. Moreover, it is
shown that this observation is true for generic data (not necessarily timesymmetric). This
identification is a consequence of both the evolution and constraint equations.

20:00 

Dinner 
Saturday, 10. September 2016
9:00 
10:00 
Alex VañóViñuales 
Free evolution of the hyperboloidal IVP in spherical symmetry
We address the hyperboloidal initial value problem in numerical relativity, where the Einstein equations are evolved on hyperboloidal foliations. They consist of smooth spacelike slices that reach future null infinity (the "location" in spacetime where light rays arrive), which allow to study global properties of spacetimes, such as to unambiguously extract radiation signals. The hyperboloidal initial value problem for the Einstein equations can be addressed through conformal compactification methods, which we express in terms of unconstrained evolution schemes based on the generalized BSSN and conformal Z4 formulations. The main difficulty of the implementation is that the resulting system of PDEs includes formally diverging terms at null infinity that require a special treatment and a careful choice of gauge conditions. Among the latter, the preferred conformal gauge is especially convenient. The work in this first step is restricted to spherical symmetry, although the regularization in the radial direction is expected to also apply to the full 3D case, at least to some extent. We present stable numerical evolutions of a massless scalar field coupled to the Einstein equations for different types of initial data, including the collapse of a scalar field perturbation of flat spacetime into a black hole, as well as a scalar field perturbing a Schwarzschild trumpet geometry. In the second scenario the simulations were followed long enough to measure the scalar field's powerlaw decay tails at future null infinity at the expected convergence order. These successful results make this approach of the hyperboloidal initial value problem a good candidate for more general numerical setups.

10:00 
10:30 
István Rácz 
A new method of constructing binary black hole initial data.
By applying a parabolichyperbolic formulation of constraint equations and superposing KerrSchild black holes, a simple method is introduced to initialize time evolution of binary black hole systems. In constructing the initial data no use of boundary conditions in the strong field regime is made. The proposed new method offers a direct control on the ADM parameters of the composite system, and it could also be applied to construct initial data for multiple black holes.

10:30 
11:00 
Coffee Break 
11:00 
11:30 
Christian Schell 
Spectral approach to the numerical evolution of the axisymmetric Einstein
equations
I present a joint project with Oliver Rinne where we develop a new approach to
solving the axisymmetric vacuum Einstein equations in spherical coordinates
numerically. Controlling the coordinate singularities is a major challenge. We
use a spectral approach in spinweighted spherical harmonics in the angular
direction. In the radial direction we develop new finite difference methods to
control the origin. We demonstrate how we solve the linearized version of the
problem, analytically as well as numerically. Further we show how to benefit
from the experience gained there for the nonlinear case.

11:30 
12:00 
David Hilditch 
Dual Foliation Formulations of GR
When solving general relativity numerically we must use a formulation of the field equations for which the resulting PDE problem is wellposed. Building such a good formulation usually requires making a coordinate choice. This leads to statements like `gauge freedom in general relativity is the choice of coordinates'. The latter two facts are bothersome, because one of the first lessons in relativity is that coordinates should, in some sense, not matter. In my talk I will explain the solution to my earlier confusion. I will then explain how the resulting formalism can be exploited for practical calculations.

12:00 
14:00 
Lunch Break 
Location
The workshop will take place in Oppurg, Germany. Oppurg is located near Jena and is famous for its baroque castle which was built in the 18th century.
source: wikipedia.de
Today, the castle is used as an educational and conference center. The workshop will be held in the castle. Accommodation and food will be provided by the conference center.
Oppurg can be reached from Jena by car and train.
Rail travel is serviced by
Deutsche Bahn.
Jena is easily reached by car and train. International airports are located in Frankfurt (FRA), Berlin (BER), and Munich (MUC) which are about 3:30, 3:00 and 4:30 hours away by train, respectively. More information about getting to Jena can be found at the Jena
homepage. Rail travel between the airports and Jena is serviced by
Deutsche Bahn.
Please feel free to contact
David Hilditch with any queries.
Organising committee