SpheriCo.jl

A Julia package for the Spherical Collapse of a scalar field in classical and semiclassical gravity.

  • Combined the method of lines and summation-by-parts finite difference operators to solve stiff equations and resolve instabilities.
  • Reduced runtime and resource requirements, enabling longer and more extensive simulations compared to what was possible before.
  • Achieved clear second-order convergence in numerical solutions, improving reliability and accuracy.
Keywords: Julia, Numerical Simulations, Black Holes
Repository:
SpheriCo.jl
Published: 24 March 2025

Hyperbolicity

Investigated the hyperbolicity of the characteristic setup in general relativity and its impact in applications.

  • Found that common characteristic formulations are only weakly hyperbolic, contrary to expectations.
  • Analysed the effect of weak hyperbolicity in numerical simulations through suitable convergence test.
  • Discussed the implications in applications such as gravitational waveform modelling, and specifically the well-posedness of the CCE and CCM methods.
Keywords: Differential Equations, Numerical Convergence, General Relativity
Repository:
model_CCE_CCM
,
PhD_thesis
,
Bondi_Toy
Published: 3 January 2024