{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/112043"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/112043","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Total mass of a patch of a matter-dominated Friedmann-Robertson-Walker universe","abstract":"In this thesis, I have addressed the question of how to calculate the total relativistic mass for a patch of a spherically-symmetric matter-dominated spacetime of negative curvature. This calculation provides the open-universe analogue to a similar calculation first proposed by Zel'dovich in 1962. I consider a finite, spherically-symmetric (SO(3)) spatial region of a Friedmann-Robertson-Walker (FRW) universe surrounded with a vacuum described by the Schwarzschild metric. Provided that the patch of FRW spacetime is glued along its boundary to a Schwarzschild spacetime in a sufficiently smooth manner, the result is a spatial region of FRW which transitions smoothly to an asymptotically flat exterior region such that spherical symmetry is preserved throughout. I demonstrate that this mass diverges as the size of the patch is taken to include the entire universe, and discuss the intuition provided by a classical approximation to the total mass using the formalism of Newtonian Cosmology.","abstract_html":"In this thesis, I have addressed the question of how to calculate the total relativistic mass for a patch of a spherically-symmetric matter-dominated spacetime of negative curvature. This calculation provides the open-universe analogue to a similar calculation first proposed by Zel'dovich in 1962. I consider a finite, spherically-symmetric (SO(3)) spatial region of a Friedmann-Robertson-Walker (FRW) universe surrounded with a vacuum described by the Schwarzschild metric. Provided that the patch of FRW spacetime is glued along its boundary to a Schwarzschild spacetime in a sufficiently smooth manner, the result is a spatial region of FRW which transitions smoothly to an asymptotically flat exterior region such that spherical symmetry is preserved throughout. I demonstrate that this mass diverges as the size of the patch is taken to include the entire universe, and discuss the intuition provided by a classical approximation to the total mass using the formalism of Newtonian Cosmology.","abstract_has_math":false,"creators":["Geller, Sarah (Sarah R.)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Physics.","school":null,"contributors":[],"advisors":["Alan H. Guth."],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-22T22:21:10Z","subjects":["Physics."],"languages":["eng"],"rights":["MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/112043","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Alan H. Guth."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/112043"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis: S.M., Massachusetts Institute of Technology, Department of Physics, 2017.","Cataloged from PDF version of thesis.","Includes bibliographical references (page 49)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, I have addressed the question of how to calculate the total relativistic mass for a patch of a spherically-symmetric matter-dominated spacetime of negative curvature. This calculation provides the open-universe analogue to a similar calculation first proposed by Zel'dovich in 1962. I consider a finite, spherically-symmetric (SO(3)) spatial region of a Friedmann-Robertson-Walker (FRW) universe surrounded with a vacuum described by the Schwarzschild metric. Provided that the patch of FRW spacetime is glued along its boundary to a Schwarzschild spacetime in a sufficiently smooth manner, the result is a spatial region of FRW which transitions smoothly to an asymptotically flat exterior region such that spherical symmetry is preserved throughout. I demonstrate that this mass diverges as the size of the patch is taken to include the entire universe, and discuss the intuition provided by a classical approximation to the total mass using the formalism of Newtonian Cosmology."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Total mass of a patch of a matter-dominated Friedmann-Robertson-Walker universe"]}]}],"canonical_facts":{"dc:contributor.advisor":["Alan H. Guth."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Physics."],"dc:contributor.other":["Massachusetts Institute of Technology. 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Provided that the patch of FRW spacetime is glued along its boundary to a Schwarzschild spacetime in a sufficiently smooth manner, the result is a spatial region of FRW which transitions smoothly to an asymptotically flat exterior region such that spherical symmetry is preserved throughout. I demonstrate that this mass diverges as the size of the patch is taken to include the entire universe, and discuss the intuition provided by a classical approximation to the total mass using the formalism of Newtonian Cosmology."],"dc:description.degree":["S.M."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/112043"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["MIT theses are protected by copyright. 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