2026-09-18T21:14:31Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1599402025-07-08T03:07:15Zcom_1721.1_7582com_1721.1_7581col_1721.1_131024
Hughes, Scott A.
Leonard, Aidan J.
Massachusetts Institute of Technology. Department of Physics
2025-07-07T17:39:41Z
2025-07-07T17:39:41Z
2025-05
2025-05-19T13:39:20.621Z
https://hdl.handle.net/1721.1/159940
In general relativity, problems with high degrees of symmetry often serve as illustrative simplifications of complicated scenarios. Oppenheimer-Snyder collapse, an exact solution for the gravitational collapse of a uniform, pressure-less ball of dust into a black hole, provides valuable insight into the collapse of realistic mass distributions such as stars. Early numerical relativity simulations demonstrated that a rotating ball of dust collapses into a Kerr black hole. In this thesis, we formulate the collapse of a slowly rotating dust-ball using the BSSN framework from numerical relativity, with the aim of reproducing this result in a simple manner. By perturbing the Oppenheimer-Snyder solution in isotropic coordinates, we find semi-analytic solutions to the constraint equations at linear order in angular momentum. In addition, we develop a Mathematica simulation code for modeling of spherical vacuum systems using the BSSN formalism. Diagnostics provide comparison of our results with theoretical predictions for the simplified case of a stationary black hole. Further work is required to introduce matter terms and move from spherical to axial symmetry.
S.B.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright retained by author(s)
https://rightsstatements.org/page/InC-EDU/1.0/
Oppenheimer-Snyder Collapse in the BSSN Formalism
Thesis
application/pdf
Bachelor
Bachelor of Science in Physics
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="96852bf3-8ac0-46c3-ab27-08e48dded3a8">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>Oppenheimer-Snyder Collapse in the BSSN Formalism</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2025-05</PublicationDate>
<Authors>
<Author>
<DisplayName>Leonard, Aidan J.</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://rightsstatements.org/page/InC-EDU/1.0/</License>
<Abstract>In general relativity, problems with high degrees of symmetry often serve as illustrative simplifications of complicated scenarios. Oppenheimer-Snyder collapse, an exact solution for the gravitational collapse of a uniform, pressure-less ball of dust into a black hole, provides valuable insight into the collapse of realistic mass distributions such as stars. Early numerical relativity simulations demonstrated that a rotating ball of dust collapses into a Kerr black hole. In this thesis, we formulate the collapse of a slowly rotating dust-ball using the BSSN framework from numerical relativity, with the aim of reproducing this result in a simple manner. By perturbing the Oppenheimer-Snyder solution in isotropic coordinates, we find semi-analytic solutions to the constraint equations at linear order in angular momentum. In addition, we develop a Mathematica simulation code for modeling of spherical vacuum systems using the BSSN formalism. Diagnostics provide comparison of our results with theoretical predictions for the simplified case of a stationary black hole. Further work is required to introduce matter terms and move from spherical to axial symmetry.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>