SciPost Submission Page
Pseudospectral implementation of the Einstein-Maxwell system
by Jorge Expósito Patiño, Hannes Robert Rüter, David Hilditch
Submission summary
| Authors (as registered SciPost users): | Jorge Expósito Patiño · Hannes Rüter |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202505_00035v2 (pdf) |
| Date accepted: | Sept. 30, 2025 |
| Date submitted: | Sept. 22, 2025, 2:49 p.m. |
| Submitted by: | Jorge Expósito Patiño |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Electromagnetism plays an important role in a variety of applications in gravity that we wish to investigate. To that end, in this work, we present an implementation of the Maxwell equations within the adaptive-mesh pseudospectral numerical relativity code BAMPS. We perform a thorough analysis of the evolution equations as a first order symmetric hyperbolic system of PDEs. This includes both the construction of the characteristic variables for use in our penalty boundary communication scheme, as well as radiation controlling, constraint preserving outer boundary conditions which, for the first time in a numerical context, are shown to be boundary-stable. After choosing a formulation of the Maxwell constraints that we may solve for initial data, we move on to show a suite of numerical tests. Our simulations, both within the Cowling approximation, and in full non-linear evolution, demonstrate rapid convergence of error with resolution, as well as consistency with known quasinormal decay rates on the Kerr background. Finally we evolve the electrovacuum equations of motion with strong data, a good representation of typical critical collapse runs.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
Overview of changes requested by referee 1
The typo in Eq. 4 is fixed.
A new paragraph (lines 357-379) is added to explain the infrastructure.
The definition of \(E^A\) and \(B^A\) is added (line 150).
The typo (extra constraint word) is fixed.
Extra information is added to clarify that \(\psi\) is not freely specifiable.
A new figure 5 is added to show clearly the convergence, and the explanation of what happens after \(t/\sigma > 20\) is added also to the caption of figure 3, not just in the text.
The new paragraph that explains the infrastructure (lines 357-379) also includes a description of the excision method.
We have added the cost in core-hours of each simulation.
Overview of changes requested by referee 2
in the same order that the comments were given:
We have added the specifier of Gaussian units, and explicitely added which quantities are set to one in which cases.
The convention is now explicitly stated.
We have added the formula explicitly, both for vectors and scalars. We felt that giving the general formula instead of the two cases separately will be counterproductive if the objective is to be as explicit as possible.
The formula for the spatial covariant derivative \(D_i\) is given explicitly in terms of the four covariant derivative \(\nabla_i\).
The surface plots (now figures 2 and 9) are now colored with respect to the absolute value, which is equivalent to centering at zero with the same color at the maximum and the minimum. We believe this is a good way to color this plot, since the sign of the field is more clear in the elevation of the surface plot.
The approximate time of the pulse reaching the outer boundary is added both in the text, and in the label to figure 3.
For all surface plots (now figures 2 and 9) a label is included next to the color bar. We have kept the same colormap for the Kretschmann scalar and the electric field, for visual consistency, since with the new label the difference between the two is clearer.
The missing "r" that was missing in "electrovacuum" has been fixed.
Published as SciPost Phys. 19, 112 (2025)