Existing examples

Binary BH example

This is an example in which a binary black hole evolves in $4\partial ST$, either scalarising initially for the Type I coupling or after the merger for the Type II couplings (if the coupling is strong enough and with a negative sign). See this work and this other work for examples of how it can be used.

4∂ST Kerr BH example

This is an example for the evolution of a single spinning black hole in $4\partial ST$, which also scalarises initially for the Type I coupling or depending on the value of the coupling and the spin for Type II couplings. See this work and this other work for examples of how it can be used.

For this example we include a reference test result for the value of the normalised $L^2$ norm of the Hamiltonian $\mathcal{H}$ and momentum $\mathcal{M}=\sqrt{{\mathcal{M}}_i {\mathcal{M}}^i}$ constraints and the scalar field density $\rho^{SF}$ across all the grid for a black hole with spin parameter $a=0.8M$ and an exponential quadratic coupling of the type $\lambda(\phi)=\frac{\lambda^{GB}}{2\sigma}(1-e^{-\sigma\phi^2})$.

These results can be read from the diagnostic_norms.dat file, which is obtained by running the params.txt file, which takes in Cosma8 around 4 hours with 512 cores (256 MPI tasks and 2 OpenMP threads per task).

TestField 4∂ST Binary BH example

This is an example for the evolution of a black hole binary in the test-field limit of the $4\partial ST$ theory, where the dynamics of gravity sector is governed by Einstein equation of GR, and provides a background for the scalar field, which evolves with the full equation in $4\partial ST$ theory. This setup was used in this work.

Cubic Horndeski Binary BH example

This is an example for the evolution of a black hole binary in cubic Horndeski gravity. See this work for examples of how it can be used.