Author ORCID Identifier

http://orcid.org/0009-0007-9845-8448

Degree Year

2024

Document Type

Thesis - Oberlin Community Only

Degree Name

Bachelor of Arts

Department

Physics and Astronomy

Advisor(s)

Robert Owen
Roberto Hoyle

Committee Member(s)

Robert Owen
Yumi Ijiri
Jason Stalnaker
Dan Stinebring
Dan Styer

Keywords

Isometric embedding, Black hole, Apparent horizon, Euclidean space, Numerical method

Abstract

Isometric embeddings consist in describing surfaces in a desired space such that infinitesimal distances from a given geometry are preserved. The isometric embedding of black hole apparent horizons in flat geometry is useful both for visualizing the horizon structure and for computing quasilocal quantities such as mass, energy, and angular momentum. However, finding these embeddings requires solving a system of nonlinear partial differential equations for which there is no generally established algorithm. In this context, we have developed two novel, robust numerical methods for finding isometric embeddings. Both of them were developed in the Spectral Einstein Code (SpEC), where they were tested and applied to binary black hole merger simulations. From the embedding results, we gained insight into the intrinsic shape of such horizons and how their embeddability possibly behaves.

Notes

Additional Department: Computer Science

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