[Phys][GRSPH] Add metric terms

[y-lapeyre]

Is it ok with tags like this or should I use templates for the choice of metric?
I think of putting all terms of all metrics in this file. Yes it will be long, but at the end of the day it's just GR formulae we will never touch again.

[github-actions]

Thanks @y-lapeyre for opening this PR!

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Summary of Changes

Hello @y-lapeyre, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request significantly enhances the shamphys library by introducing fundamental General Relativistic metric calculations. It specifically implements the Kerr metric, including its covariant and contravariant forms, along with their Cartesian derivatives. This foundational work paves the way for more advanced astrophysical simulations requiring accurate spacetime geometry. The author is also seeking input on the architectural choice for metric selection and has outlined a strategy for organizing these complex mathematical terms.

Highlights

• Introduction of General Relativistic Metrics: Adds core functionality for handling spacetime metrics within the shamphys library.
• Kerr Metric Implementation: Provides concrete implementations for the covariant and contravariant Kerr metric tensors in Cartesian-like coordinates.
• Metric Derivatives: Includes functions to compute the Cartesian derivatives of the covariant Kerr metric.
• Design Discussion: The author is considering using tags versus templates for metric selection and plans to centralize all metric terms in this file.
• Known Issue: A comment notes that the contravariant metric expressions might not be regular at certain coordinate points (x=y=0 and z=r).

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[gemini-code-assist]

Code Review

This pull request introduces calculations for the Kerr metric, including the covariant and contravariant metric tensors and their derivatives. The use of tag dispatching (e.g., struct Kerr {}) to select the metric is a good design choice.

However, the implementation has several significant issues that need to be addressed:

• Critical bugs: There are uninitialized variables in get_cartesian_cov_metric_impl and get_cartesian_contrav_metric_impl due to incorrect coordinate unpacking, which will lead to undefined behavior.
• Reusability: Metric parameters like spin and mass are hardcoded, which limits the use of these functions to a single specific black hole. These should be parameterized.
• Correctness: The implementation for the contravariant metric contains a comment highlighting a known singularity issue that has not been addressed. This could lead to incorrect results or numerical instability.
• Code Quality: There are some areas for improvement in code quality, such as very long and hard-to-read lines for the derivative calculations, and an unprofessional comment.

While I understand the sentiment that these GR formulae might not be touched again, ensuring their correctness, readability, and reusability from the start is crucial for the long-term health of the codebase. Please see the detailed comments for specific suggestions.

[tdavidcl]

Looks very nice, what do you want to use in place of Tvec in practice ? Mat4x4 from the math library with mdspan ? (I'm fine with the template signature)

[github-actions]

Workflow report

workflow report corresponding to commit a6c2863
Commiter email is yona.lapeyre@ens-lyon.fr

Light CI is enabled. This will only run the basic tests and not the full tests.
Merging a PR require the job "on PR / all" to pass which is disabled in this case.

Pre-commit check report

Pre-commit check: ✅

trim trailing whitespace.................................................Passed
fix end of files.........................................................Passed
check for merge conflicts................................................Passed
check that executables have shebangs.....................................Passed
check that scripts with shebangs are executable..........................Passed
check for added large files..............................................Passed
check for case conflicts.................................................Passed
check for broken symlinks................................................Passed
check yaml...............................................................Passed
detect private key.......................................................Passed
No-tabs checker..........................................................Passed
Tabs remover.............................................................Passed
Validate GitHub Workflows................................................Passed
clang-format.............................................................Passed
ruff check...............................................................Passed
ruff format..............................................................Passed
Check doxygen headers....................................................Passed
Check license headers....................................................Passed
Check #pragma once.......................................................Passed
Check SYCL #include......................................................Passed
No ssh in git submodules remote..........................................Passed
No UTF-8 in files (except for authors)...................................Passed

Test pipeline can run.

Doxygen diff with main

Removed warnings : 1
New warnings : 12
Warnings count : 7966 → 7977 (0.1%)

Detailed changes :

+ src/shamphys/include/shamphys/metrics.hpp:113: warning: Member get_cartesian_contravariant_metric_impl(const Kerr< Tscal > &kerr, const std::mdspan< Tscal, std::extents< SizeType, 4 >, Layout1, Accessor1 > &pos, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &g) (function) of namespace shamphys is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:181: warning: Member metric_cartesian_derivatives_impl(const Kerr< Tscal > &kerr, const std::mdspan< Tscal, std::extents< SizeType, 4 >, Layout1, Accessor1 > &pos, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &dgcovdx, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &dgcovdy, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &dgcovdz) (function) of namespace shamphys is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:27: warning: Compound shamphys::Kerr is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:29: warning: Member a (variable) of struct shamphys::Kerr is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:30: warning: Member bh_mass (variable) of struct shamphys::Kerr is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:31: warning: Member rs (variable) of struct shamphys::Kerr is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:33: warning: Member Kerr(Tscal spin=1, Tscal mass=1) (function) of struct shamphys::Kerr is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:47: warning: Member get_cartesian_covariant_metric_impl(const Kerr< Tscal > &kerr, const std::mdspan< Tscal, std::extents< SizeType, 4 >, Layout1, Accessor1 > &pos, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &g) (function) of namespace shamphys is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:480: warning: Member get_cartesian_covariant_metric(const std::mdspan< Tscal, std::extents< SizeType, 4 >, Layout1, Accessor1 > pos, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &g) (function) of namespace shamphys is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:500: warning: Member get_cartesian_contravariant_metric(const std::mdspan< Tscal, std::extents< SizeType, 4 >, Layout1, Accessor1 > pos, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &g) (function) of namespace shamphys is not documented.
+ src/shamphys/include/shamphys/metrics.hpp:520: warning: Member metric_cartesian_derivatives(const std::mdspan< Tscal, std::extents< SizeType, 4 >, Layout1, Accessor1 > pos, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &dgcovdx, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &dgcovdy, std::mdspan< Tscal, std::extents< SizeType, 4, 4 >, Layout2, Accessor2 > &dgcovdz) (function) of namespace shamphys is not documented.