Capabilities of the Einstein Toolkit

Vacuum Spacetimes

Evolution of vacuum spacetime is provided by the McLachlan code. McLachlan solves the Einstein vacuum equations in 3D Cartesian coordinates using adaptive mesh refinement and can be combined with matter codes for modeling spacetimes containing matter. McLachlan is implemented using the Kranc package. Features of McLachlan include:

  • complete implementation of the BSSNOK general relativity spacetime evolution equations including all the standard tricks that ensures stability
  • up-winding for the shift advection terms
  • standard moving puncture Gamma-driver and 1 + log gauges
  • phi- and W- methods
  • static and radiative outer boundary conditions
  • inclusion of matter through the TmunuBase interface
  • up to 8th order finite differencing
  • OpenMP parallelization through Carpet/LoopControl in addition to MPI parallelization through Carpet
  • multi-block code infrastructures by applying the Jacobian to transform local derivatives to global derivatives

Relativistic Magneto​hydrodynamics


The Einstein Toolkit GRHydro modules can evolve spacetimes with general relativistic hydrodynamics in 3D Cartesian coordinates. GRHydro was once based on the public version of the Whisky code developed originally by the EU Network on Sources of Gravitational Radiation and later by a collaboration led by AEI/SISSA, but was later expanded and cleaned up considerably. Features of GRHydro include at the moment:

  • Evolution of the equations of general relativistic magneto-hydrodynamics (GRMHD) in 3D Cartesian coordinates on a curved dynamical background.


IllinoisGRMHD solves the equations of General Relativistic MagnetoHydroDynamics (GRMHD) using a high-resolution shock capturing scheme. It is a rewrite of the Illinois Numerical Relativity (ILNR) group's GRMHD code, and generates results that agree to roundoff error with that original code. Its feature set coincides with the features of the ILNR group's recent code (ca. 2009--2014), which was used in their modeling of the following systems:

  • Magnetized circumbinary disk accretion onto binary black holes
  • Magnetized black hole--neutron star mergers
  • Magnetized Bondi flow, Bondi-Hoyle-Littleton accretion
  • White dwarf--neutron star mergers

IllinoisGRMHD is particularly good at modeling GRMHD flows into black holes without the need for excision. Its HARM-based conservative-to-primitive solver has also been modified to check the physicality of conservative variables prior to primitive inversion, and move them into the physical range if they become unphysical.

Initial Data

  • Single and binary black holes
  • Single TOV stars
  • LORENE data

Relativity Tools

  • Apparent horizon finding
  • Black hole excision


  • TrK, det(g), R_ab, R
  • ADM constraint violation
  • Basic hydrodynamics analysis routines
  • Extraction of gravitational waves

Computational Infrastructure

  • Adaptive mesh refinement
  • Reflection and rotation symmetry boundary conditions
  • Radiation boundary conditions
  • Flexible Cartesian 3-D meshes
  • Multidimensional I/O using HDF5, ASCII, Jpegs
  • Method of lines time integration
  • Courant time steeping
  • Seamless use of BLAS, GSL, HDF5, LAPACK


  • Checking for NaNs
  • Memory poisoning to identify uninitialized variables
  • Timing report by thorn, schedule bin, and method