Capabilities

Any arbitrarily chosen data for the metric and sources in the 3+1 decomposition of the Einstein Equations will not necessarily be physical. The purpose of GRTresna is to solve the initial conditions equations in the ADM formalism to generate data that is consistent with the Hamiltonian and momentum constraints of GR. This initial data can then be used in a time evolution using numerical relativity codes like GRChombo.

GRTresna takes full advantage of modern parallel computing techniques, being built on the Chombo code for the solution of general partial differential equations (here we mainly use the multigrid methods for solving elliptic equations). It allows refinement of the mesh, supporting non-trivial "many-boxes-in-many-boxes" meshing hierarchies, and massive parallelism through the Message Passing Interface (MPI).

Current features in the public code

GRTresna solves both the Hamiltonian and momentum constraints of GR under a number of specific conditions - currently it works for a superposition of two boosted and/or spinning black holes (Bowen York initial data) and/or a scalar field matter source configuration, with either asymptotically flat or periodic boundary conditions. It assumes the metric is conformally flat ($\tilde \gamma_{ij} = \delta_{ij}$). However, it has been designed to be highly adaptable and so many of these options will be extended in the future (see below for forthcoming features).

The code outputs data in an hdf5 format that can be read in as a starting checkpoint file for GRChombo time evolution (and could be adapted for other codes with hdf5 input). A regrid condition can be set to activate adaptive mesh refinement for higher resolution in areas of interest. The code currently supports 2nd order finite differencing in space and the method of solving the elliptic equations is inherently second order.

The scalar field and its time derivative can be specified generally, although for periodic spacetimes there are additional integrability constraints on the initial data that should be satisfied in order for solutions to exist. The code uses the CTTK method of solving the equations, or a method that we call CTTK Hybrid. Please refer to the documentation and to this paper for more details.

Whilst for matter sources we currently only include a scalar field, the methods are templated such that one could replace this straightforwardly with another matter type by copying the scalar field and changing the methods to calculate its energy density and momentum density appropriately.

Forthcoming features

The following are things for which we know code exists in some form with some member(s) of the collaboration. Our goal is always to add code to the public repository after a reasonable period of testing (usually within 6 months of a research article using the code has been accepted for publication). However, there is sometimes a lag in this happening since we have higher standards for public code that often necessitate a rewrite of even working and well-tested code. If you plan to develop one of these features we suggest you Contact us to see if we already have code that we can share with you (at your own risk!).

• XCTS - this alternative solution method is being implemented by Liina Chung-Jukko (KCL)

• Non conformal flatness - this is being developed by Sam Brady (QMUL)

• Proca fields - these will be added by Zipeng Wang (JHU)

• Read in data from text files - these methods will be added by Areef Waeming (QMUL)

• Compatible with the Cartoon method - this will be added by Josu Aurrekoetxea (MIT)