#### Event Title

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.