Numerical solution of differential equations for analyzing black hole event horizons
Location
PANEL: Physical Investigations from Galactic Phenomena to the Classroom
Adam Joseph Lewis Center Hallock Auditorium
Document Type
Presentation - Open Access
Start Date
5-13-2022 10:00 AM
End Date
5-13-2022 11:00 AM
Abstract
We present a solver capable of numerically computing the solution to a system of nonlinear partial differential equations (PDEs). Our long-term goal is to solve the embedding problem of a black hole horizon in Euclidean space by adding this solver to the Spectral Einstein Code (SpEC). Knowing that the PDEs involved in this problem are strongly nonlinear and nonstandard, we have used simple models of varying complexity to approximate the embedding conditions at each version. Current results imply a robust and efficient method combining the Newton-Raphson method (N-R) for the nonlinear equations and a generalized version of the biconjugate gradient stabilized method (BiCGSTAB) for the linear equations at each step of N-R.
Keywords:
Black hole, Embedding, Event horizon, Physics
Recommended Citation
Braz Mendes, Iago and Owen, Robert, "Numerical solution of differential equations for analyzing black hole event horizons" (2022). Research Symposium. 14.
https://digitalcommons.oberlin.edu/researchsymp/2022/presentations/14
Award
Science & Technology Research for a New Generation (STRONG)
Project Mentor(s)
Robert Owen, Physics; Computer Science
2022
Numerical solution of differential equations for analyzing black hole event horizons
PANEL: Physical Investigations from Galactic Phenomena to the Classroom
Adam Joseph Lewis Center Hallock Auditorium
We present a solver capable of numerically computing the solution to a system of nonlinear partial differential equations (PDEs). Our long-term goal is to solve the embedding problem of a black hole horizon in Euclidean space by adding this solver to the Spectral Einstein Code (SpEC). Knowing that the PDEs involved in this problem are strongly nonlinear and nonstandard, we have used simple models of varying complexity to approximate the embedding conditions at each version. Current results imply a robust and efficient method combining the Newton-Raphson method (N-R) for the nonlinear equations and a generalized version of the biconjugate gradient stabilized method (BiCGSTAB) for the linear equations at each step of N-R.
Notes
Presenter: Iago Braz Mendes