Anyone Walking into my room can see me reading a lot of Research Papers on Arxiv. So, these papers[Find them in the Reference Section of the Paper] I was reading these days, so thought to prepare some notes and add some views
We explore numerical stability issues and hyperboloidal coordinate choices for solving the wave equation on Schwarzschild-de Sitter (SdS) spacetime. In particular, we consider the treatment of the origin with a spherical symmetry boundary condition and use finite differences to discretize the equation. We demonstrate that a direct discretization is numerically unstable and propose an alternative stable approach by employing a suitable identity. We then introduce hyperboloidal coordinates and explore different choices for the height function to remove the metric singularity at the roots of