Testing a new algorithm for isometric embedding of black hole horizons
Location
Science Center: Bent Corridor
Document Type
Poster - Open Access
Start Date
4-28-2023 12:00 PM
End Date
4-28-2023 2:00 PM
Abstract
Isometric Embedding is a classic problem in differential geometry and general relativity that involves constructing a surface in Euclidean space described by a metric tensor. The results from this problem have a long history for visualization, but are also relevant for calculating quantities like black hole mass and energy. Unfortunately, in general scenarios, this problem requires a solver capable of handling a system of strongly nonlinear and nonstandard PDEs, for which there is no generally established algorithm. We have explored a radically new approach to the embedding problem, applying it to a variety of specific test cases and confirming that the results converge as expected and agree with results obtained analytically and by other algorithms. This poster presents the results of a finite-difference-based C++ code that we have written to implement and test this novel algorithm.
Keywords:
Black-holes, Relativity, Embedding, Algorithm
Recommended Citation
Mendes, Iago Braz and Owen, Robert, "Testing a new algorithm for isometric embedding of black hole horizons" (2023). Research Symposium. 19.
https://digitalcommons.oberlin.edu/researchsymp/2023/posters/19
Major
Physics; Computer Science
Project Mentor(s)
Robert Owen, Physics and Astronomy
2023
Testing a new algorithm for isometric embedding of black hole horizons
Science Center: Bent Corridor
Isometric Embedding is a classic problem in differential geometry and general relativity that involves constructing a surface in Euclidean space described by a metric tensor. The results from this problem have a long history for visualization, but are also relevant for calculating quantities like black hole mass and energy. Unfortunately, in general scenarios, this problem requires a solver capable of handling a system of strongly nonlinear and nonstandard PDEs, for which there is no generally established algorithm. We have explored a radically new approach to the embedding problem, applying it to a variety of specific test cases and confirming that the results converge as expected and agree with results obtained analytically and by other algorithms. This poster presents the results of a finite-difference-based C++ code that we have written to implement and test this novel algorithm.
