{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/30860"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/30860","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Horizons, hyperbolic systems, and inner boundary conditions in numerical relativity","abstract":"\"We discuss several closely connected open questions central to Numerical Relativity. These involve computational, numerical, theoretical, and physical aspects of evolving and understanding dynamical black hole spacetimes. We discuss finding and understanding the event horizon (EH), which is the causal boundary separating the black hole interior from its exterior, in dynamical black hole spacetimes. In the EH studies, we formulate a set of tools for analyzing the behavior of the EH, including proposing a construction of the membrane paradigm suitable for numerical relativity. Moreover, we probe the geometry of the two black hole collision in detail, and investigate limits of the distortion of a single black hole EH interacting with a gravitational wave. We discuss both standard and hyperbolic formulations of the Einstein equations and how these are amenable to numerical treatment with modern parallel and adaptive computational techniques. In the course of this discussion, we present a three-dimensional implementation of the Bona-Massó hyperbolic system, and a three dimensional code we call \"\"Cactus,\"\" which we apply to several spacetimes. Finally, exploiting certain mathematical properties of the Bona-Massó system and the causal structure of horizons, we discuss and compare several methods to implement a (preliminary) apparent horizon boundary condition for evolving black hole spacetimes using the full three-dimensional Cactus code.\"","abstract_html":""We discuss several closely connected open questions central to Numerical Relativity. These involve computational, numerical, theoretical, and physical aspects of evolving and understanding dynamical black hole spacetimes. We discuss finding and understanding the event horizon (EH), which is the causal boundary separating the black hole interior from its exterior, in dynamical black hole spacetimes. In the EH studies, we formulate a set of tools for analyzing the behavior of the EH, including proposing a construction of the membrane paradigm suitable for numerical relativity. Moreover, we probe the geometry of the two black hole collision in detail, and investigate limits of the distortion of a single black hole EH interacting with a gravitational wave. We discuss both standard and hyperbolic formulations of the Einstein equations and how these are amenable to numerical treatment with modern parallel and adaptive computational techniques. In the course of this discussion, we present a three-dimensional implementation of the Bona-Massó hyperbolic system, and a three dimensional code we call ""Cactus,"" which we apply to several spacetimes. Finally, exploiting certain mathematical properties of the Bona-Massó system and the causal structure of horizons, we discuss and compare several methods to implement a (preliminary) apparent horizon boundary condition for evolving black hole spacetimes using the full three-dimensional Cactus code."","abstract_has_math":false,"creators":["Walker, Paul"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Seidel, H.E."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-17T19:45:34Z","date_published":"2012-05-17T19:45:34Z","updated_at":"2026-07-22T22:25:29Z","subjects":["numerical relativity","black hole spacetimes","event horizons"],"languages":["en"],"rights":["©1998 Paul Walker"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4162287"],"render_values":[{"text":"4162287","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/30860","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Seidel, H.E."]},{"key":"dc:creator","label":"Author","values":["Walker, Paul"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-17T19:45:34Z","10000-01-01","1998"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["numerical relativity","black hole spacetimes","event horizons"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©1998 Paul Walker"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["4162287","http://hdl.handle.net/2142/30860"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"We discuss several closely connected open questions central to Numerical Relativity. These involve computational, numerical, theoretical, and physical aspects of evolving and understanding dynamical black hole spacetimes. We discuss finding and understanding the event horizon (EH), which is the causal boundary separating the black hole interior from its exterior, in dynamical black hole spacetimes. In the EH studies, we formulate a set of tools for analyzing the behavior of the EH, including proposing a construction of the membrane paradigm suitable for numerical relativity. Moreover, we probe the geometry of the two black hole collision in detail, and investigate limits of the distortion of a single black hole EH interacting with a gravitational wave. We discuss both standard and hyperbolic formulations of the Einstein equations and how these are amenable to numerical treatment with modern parallel and adaptive computational techniques. In the course of this discussion, we present a three-dimensional implementation of the Bona-Massó hyperbolic system, and a three dimensional code we call \"\"Cactus,\"\" which we apply to several spacetimes. Finally, exploiting certain mathematical properties of the Bona-Massó system and the causal structure of horizons, we discuss and compare several methods to implement a (preliminary) apparent horizon boundary condition for evolving black hole spacetimes using the full three-dimensional Cactus code.\"","Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-17T19:45:34Z No. of bitstreams: 1 1998_walker.pdf: 9476502 bytes, checksum: e63c2ce3dbf689406a2cd626970cad20 (MD5)","Made available in DSpace on 2012-05-17T19:45:34Z (GMT). No. of bitstreams: 1 1998_walker.pdf: 9476502 bytes, checksum: e63c2ce3dbf689406a2cd626970cad20 (MD5) Previous issue date: 1998","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-17T19:45:34Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:33:04-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis","thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Horizons, hyperbolic systems, and inner boundary conditions in numerical relativity"]}]}],"canonical_facts":{"dc:contributor":["Seidel, H.E."],"dc:creator":["Walker, Paul"],"dc:date":["2012-05-17T19:45:34Z","10000-01-01","1998"],"dc:description":["\"We discuss several closely connected open questions central to Numerical Relativity. These involve computational, numerical, theoretical, and physical aspects of evolving and understanding dynamical black hole spacetimes. We discuss finding and understanding the event horizon (EH), which is the causal boundary separating the black hole interior from its exterior, in dynamical black hole spacetimes. In the EH studies, we formulate a set of tools for analyzing the behavior of the EH, including proposing a construction of the membrane paradigm suitable for numerical relativity. Moreover, we probe the geometry of the two black hole collision in detail, and investigate limits of the distortion of a single black hole EH interacting with a gravitational wave. We discuss both standard and hyperbolic formulations of the Einstein equations and how these are amenable to numerical treatment with modern parallel and adaptive computational techniques. In the course of this discussion, we present a three-dimensional implementation of the Bona-Massó hyperbolic system, and a three dimensional code we call \"\"Cactus,\"\" which we apply to several spacetimes. Finally, exploiting certain mathematical properties of the Bona-Massó system and the causal structure of horizons, we discuss and compare several methods to implement a (preliminary) apparent horizon boundary condition for evolving black hole spacetimes using the full three-dimensional Cactus code.\"","Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-17T19:45:34Z No. of bitstreams: 1 1998_walker.pdf: 9476502 bytes, checksum: e63c2ce3dbf689406a2cd626970cad20 (MD5)","Made available in DSpace on 2012-05-17T19:45:34Z (GMT). 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