{"id":"https://openalex.org/W1024040355","doi":null,"title":"On Causal Geometries","display_name":"On Causal Geometries","publication_year":2015,"publication_date":"2015-06-19","ids":{"openalex":"https://openalex.org/W1024040355","mag":"1024040355"},"language":"en","primary_location":{"id":"pmh:oai:d-scholarship.pitt.edu:24007","doi":null,"is_oa":true,"landing_page_url":"https://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","pdf_url":"http://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102932036","display_name":"Jonathan Holland","orcid":"https://orcid.org/0000-0003-0235-0891","observed_orcids":["https://orcid.org/0000-0003-0235-0891"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jonathan Holland","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0235-0891","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5102932036"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.010599999688565731,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/causal-geometry","display_name":"causal geometry","score":0.9919999837875366},{"id":"https://openalex.org/keywords/light-cone","display_name":"light cone","score":0.9290000200271606},{"id":"https://openalex.org/keywords/huygens-principle","display_name":"Huygens' principle","score":0.9200000166893005},{"id":"https://openalex.org/keywords/conformal-geometry","display_name":"conformal geometry","score":0.8659999966621399},{"id":"https://openalex.org/keywords/null-geodesics","display_name":"null geodesics","score":0.800000011920929},{"id":"https://openalex.org/keywords/weyl-tensor","display_name":"Weyl tensor","score":0.9860000014305115},{"id":"https://openalex.org/keywords/raychaudhuri-equation","display_name":"Raychaudhuri equation","score":0.8830000162124634},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"projective geometry","score":0.8410000205039978},{"id":"https://openalex.org/keywords/third-order-ordinary-differential-equations","display_name":"third-order ordinary differential equations","score":0.8820000290870667},{"id":"https://openalex.org/keywords/incidence-geometry","display_name":"incidence geometry","score":0.6639999747276306},{"id":"https://openalex.org/keywords/manifolds","display_name":"manifolds","score":0.5809999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7507414221763611},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6398777961730957},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.5900797247886658},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.5620713233947754},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5184364318847656},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.49956798553466797},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44887733459472656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44796139001846313},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.438687264919281},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.4182325303554535},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:d-scholarship.pitt.edu:24007","doi":null,"is_oa":true,"landing_page_url":"https://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","pdf_url":"http://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"mag:1024040355","doi":null,"is_oa":false,"landing_page_url":"http://d-scholarship.pitt.edu/24007/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:d-scholarship.pitt.edu:24007","doi":null,"is_oa":true,"landing_page_url":"https://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","pdf_url":"http://d-scholarship.pitt.edu/24007/1/On_Causal_Geometries%2C_Jonathan_Holland%2C_PhD_Disstertation_1.pdf","source":{"id":"https://openalex.org/S4306402372","display_name":"D-Scholarship@Pitt (University of Pittsburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170201317","host_organization_name":"University of Pittsburgh","host_organization_lineage":["https://openalex.org/I170201317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1024040355.pdf","grobid_xml":"https://content.openalex.org/works/W1024040355.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W765753736","https://openalex.org/W790503037","https://openalex.org/W1511670827","https://openalex.org/W1547403762","https://openalex.org/W1603988537","https://openalex.org/W1628031632","https://openalex.org/W1707552160","https://openalex.org/W1789645782","https://openalex.org/W1969454298","https://openalex.org/W1981375877","https://openalex.org/W1992541079","https://openalex.org/W1995194735","https://openalex.org/W2000600180","https://openalex.org/W2004784025","https://openalex.org/W2028590532","https://openalex.org/W2033123657","https://openalex.org/W2036954048","https://openalex.org/W2046070628","https://openalex.org/W2052045615","https://openalex.org/W2058136136","https://openalex.org/W2059386043","https://openalex.org/W2062999682","https://openalex.org/W2063268956","https://openalex.org/W2094297722","https://openalex.org/W2126847907","https://openalex.org/W2147468466","https://openalex.org/W2162155934","https://openalex.org/W2282901172","https://openalex.org/W2322187432","https://openalex.org/W2325204850","https://openalex.org/W2962783575","https://openalex.org/W3106087840","https://openalex.org/W3164592651","https://openalex.org/W4235693166","https://openalex.org/W4302293532"],"related_works":["https://openalex.org/W1588961358","https://openalex.org/W1707552160","https://openalex.org/W2607112426","https://openalex.org/W1964549476","https://openalex.org/W2907557271","https://openalex.org/W2052369571","https://openalex.org/W2889704215","https://openalex.org/W2119398127","https://openalex.org/W3035120298","https://openalex.org/W3004830081"],"abstract_inverted_index":{"Causal":[0,28],"geometries":[1,29,36,45,48],"are":[2,30,72],"geometric":[3],"structures":[4],"on":[5,75],"manifolds":[6],"for":[7,46],"which":[8],"a":[9,23,31],"(non-degenerate)":[10],"null":[11,20,62,77],"cone":[12],"exists":[13],"at":[14],"every":[15],"point,":[16],"such":[17],"that":[18],"the":[19,67,76],"cones":[21],"satisfy":[22],"version":[24],"of":[25,34],"Huygen's":[26],"principle.":[27],"natural":[32],"generalization":[33],"conformal":[35,60],"(in":[37],"non-Euclidean":[38],"signature).":[39],"They":[40],"appear":[41],"naturally":[42],"as":[43,65],"incidence":[44],"projective":[47],"in":[49],"three-dimensions,":[50],"and":[51,70],"third-order":[52],"ordinary":[53],"differential":[54],"equations.":[55],"These":[56],"share":[57],"features":[58],"with":[59],"geometries:":[61],"geodesics":[63],"exist,":[64],"does":[66],"Weyl":[68],"tensor,":[69],"there":[71],"Raychaudhuri":[73],"conditions":[74],"geodesic":[78],"deviation.":[79]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}