New algorithm for isometric embedding of black hole horizons
Location
PANEL: Utilizing Mathematics to Conceptualize the Universe
Science Center A126, Nancy Schrom Dye Lecture Hall
Document Type
Presentation
Start Date
4-28-2023 2:00 PM
End Date
4-28-2023 3:00 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 presentation describes this novel algorithm and results of a finite-difference-based C++ code that we have written to implement and test it.
Keywords:
Physics, Black-holes, Embedding, Algorithm
Recommended Citation
Mendes, Iago Braz; Owen, Robert; and Zhu, Hengrui, "New algorithm for isometric embedding of black hole horizons" (2023). Research Symposium. 8.
https://digitalcommons.oberlin.edu/researchsymp/2023/presentations/8
Major
Physics; Computer Science
Project Mentor(s)
Robert Owen, Physics and Astronomy
2023
New algorithm for isometric embedding of black hole horizons
PANEL: Utilizing Mathematics to Conceptualize the Universe
Science Center A126, Nancy Schrom Dye Lecture Hall
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 presentation describes this novel algorithm and results of a finite-difference-based C++ code that we have written to implement and test it.
