Implementation of Reissner-Nordstrom metric in gr.

[karakonang]

Description:

Implemented the Reissner-Nordstrom metric and its derivatives in Cartesian-like and spherical coordinates.
metric charge parameter in code units can be interpreted as charge to mass ration (when mass1=1 in code units).
TODO: documentation

Components modified:

• Setup (src/setup)
• Main code (src/main)
• Test suite (src/tests)

Type of change:

Testing:

• GR test for precession for zero charge => equivalent to Schwarzschild.
• Custom test over various charges (partially added --need to be checked--.

Did you run the bots? yes/no

Did you update relevant documentation in the docs directory? yes/no

Did you add comments such that the purpose of the code is understandable? yes/no

Is there a unit test that could be added for this feature/bug? yes/no

If so, please describe what a unit test might check:

Related issues: #

[gemini-code-assist]

Code Review

This pull request introduces the Reissner-Nordstrom (RN) metric to the codebase, adding a new metric_rn.f90 module, integrating a charge parameter across other metric and setup files, and introducing circular orbit tests for the RN metric. Feedback on these changes highlights a critical bug where imetric is misconfigured as 4 instead of 8 in metric_rn.f90, which will cause the metric to be incorrectly identified as Kerr-Schild. Additionally, the reviewer recommends removing several unused variables in metric_cartesian_derivatives, replacing hardcoded numerical values of pi in the test suite with the imported pi constant, and replacing a Unicode en-dash with a standard hyphen in a string literal to prevent compiler compatibility issues.

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[gemini-code-assist]

The variables r5, rs_on_r3, and rs2 are declared and some are calculated (lines 185, 187) but they are never used in metric_cartesian_derivatives. Removing these unused variables and their calculations improves code maintainability and readability.

 real :: x,y,z,r,r2,r3,r4,x2,y2,z2
 real :: rs
 rs = 2.*mass1

 dgcovdx = 0.
 dgcovdy = 0.
 dgcovdz = 0.
 x = position(1)
 y = position(2)
 z = position(3)
 x2= x**2
 y2= y**2
 z2= z**2
 r2 = dot_product(position,position)
 r  = sqrt(r2)
 r3 = r*r2
 r4 = r2*r2

[gemini-code-assist]

Import the named constant pi from the physcon module to avoid hardcoding the numerical value of $\pi$ in the calculation of the orbital period.

 use io,           only:id,master
 use physcon,      only:pi
 use metric_tools, only:imetric,imet_rn
 use metric,       only:mass1,charge

[gemini-code-assist]

Use the named constant pi imported from physcon instead of the hardcoded numerical value 3.14159265358979 to ensure consistency and precision.

    period = 2.0 * pi * r0 / v0

[gemini-code-assist]

Using a standard hyphen - instead of the Unicode en-dash – (U+2013) in the string literal is safer for compatibility with older compilers or environments that might not fully support UTF-8 in source files.

 call write_inopt(charge,'charge','charge parameter for Reissner-Nordstrom metric',iunit)

[danieljprice]

@karakonang remaining failure is in metric_binarybh.f90; needs charge defined at the top of the routine. Should be minor fix...

../src/main/externalforces_gr.f90:22:26:

 22 |  use metric, only:mass1,a,charge
    |                          1

Error: Symbol ‘charge’ referenced at (1) not found in module ‘metric’