{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/13373"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/13373","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Ricci Time in Lemaître-Tolman Model and Block Universe","abstract":"It is common to think of our universe according to the \"block universe\" idea, which says that spacetime consists of many \"stacked\" 3-surfaces varied as a function of some kind of proper time Ƭ. Standard ideas do not distinguish past and future, but Ellis' \"evolving block universe\" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this work is to investigate the shape of the {Ƭ=constant} surfaces relative to the the null surfaces, and determine what makes these surfaces timelike or spacelike. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these {Ƭ=constant} surfaces to be spacelike or timelike. Furthermore, we indicate whether or not timelike surfaces appear inside black holes and other strong gravity domains, by determining the location of the timelike regions relative to the apparent horizon. Based on this idea, we find that the regions where these surfaces become timelike are often close to the apparent horizons, but always outside them, and in particular timelike regions occur outside black holes. They are always spacelike near the big bang, and at late times (near the crunch or the extreme far future), they are only timelike under special circumstances.","abstract_html":"It is common to think of our universe according to the "block universe" idea, which says that spacetime consists of many "stacked" 3-surfaces varied as a function of some kind of proper time Ƭ. Standard ideas do not distinguish past and future, but Ellis' "evolving block universe" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this work is to investigate the shape of the {Ƭ=constant} surfaces relative to the the null surfaces, and determine what makes these surfaces timelike or spacelike. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these {Ƭ=constant} surfaces to be spacelike or timelike. Furthermore, we indicate whether or not timelike surfaces appear inside black holes and other strong gravity domains, by determining the location of the timelike regions relative to the apparent horizon. Based on this idea, we find that the regions where these surfaces become timelike are often close to the apparent horizons, but always outside them, and in particular timelike regions occur outside black holes. They are always spacelike near the big bang, and at late times (near the crunch or the extreme far future), they are only timelike under special circumstances.","abstract_has_math":false,"creators":["Elmahalawy,Yasser Reda Ahmed Abdelhamid"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hellaby, Charles","Ellis, GFR"],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-22T22:23:00Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/13373","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hellaby, Charles","Ellis, GFR"]},{"key":"dc:creator","label":"Author","values":["Elmahalawy,Yasser Reda Ahmed Abdelhamid"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-07-03T10:33:42Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-07-03T10:33:42Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/13373"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["It is common to think of our universe according to the \"block universe\" idea, which says that spacetime consists of many \"stacked\" 3-surfaces varied as a function of some kind of proper time Ƭ. Standard ideas do not distinguish past and future, but Ellis' \"evolving block universe\" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this work is to investigate the shape of the {Ƭ=constant} surfaces relative to the the null surfaces, and determine what makes these surfaces timelike or spacelike. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these {Ƭ=constant} surfaces to be spacelike or timelike. Furthermore, we indicate whether or not timelike surfaces appear inside black holes and other strong gravity domains, by determining the location of the timelike regions relative to the apparent horizon. Based on this idea, we find that the regions where these surfaces become timelike are often close to the apparent horizons, but always outside them, and in particular timelike regions occur outside black holes. They are always spacelike near the big bang, and at late times (near the crunch or the extreme far future), they are only timelike under special circumstances."]},{"key":"dc:title","label":"Title","values":["Ricci Time in Lemaître-Tolman Model and Block Universe"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hellaby, Charles","Ellis, GFR"],"dc:creator":["Elmahalawy,Yasser Reda Ahmed Abdelhamid"],"dc:date.accessioned":["2015-07-03T10:33:42Z"],"dc:date.available":["2015-07-03T10:33:42Z"],"dc:date.issued":["2014"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["It is common to think of our universe according to the \"block universe\" idea, which says that spacetime consists of many \"stacked\" 3-surfaces varied as a function of some kind of proper time Ƭ. Standard ideas do not distinguish past and future, but Ellis' \"evolving block universe\" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this work is to investigate the shape of the {Ƭ=constant} surfaces relative to the the null surfaces, and determine what makes these surfaces timelike or spacelike. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these {Ƭ=constant} surfaces to be spacelike or timelike. Furthermore, we indicate whether or not timelike surfaces appear inside black holes and other strong gravity domains, by determining the location of the timelike regions relative to the apparent horizon. Based on this idea, we find that the regions where these surfaces become timelike are often close to the apparent horizons, but always outside them, and in particular timelike regions occur outside black holes. They are always spacelike near the big bang, and at late times (near the crunch or the extreme far future), they are only timelike under special circumstances."],"dc:identifier.uri":["http://hdl.handle.net/11427/13373"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Ricci Time in Lemaître-Tolman Model and Block Universe"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:00Z"}