{"id":"https://openalex.org/W7204873436","doi":"https://doi.org/10.48550/arxiv.2608.31072","title":"Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order: aligned-spin contributions","display_name":"Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order: aligned-spin contributions","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204873436","doi":"https://doi.org/10.48550/arxiv.2608.31072"},"language":"en","primary_location":{"id":"pmh:oai:eprints.soton.ac.uk:516044","doi":null,"is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/id/eprint/516044/1/2608.31072v1.pdf","pdf_url":"https://eprints.soton.ac.uk/id/eprint/516044/1/2608.31072v1.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},"volume":null,"type":"other","is_traditional":false,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.31072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080342189","display_name":"David Trestini","orcid":"https://orcid.org/0000-0002-4140-0591","observed_orcids":["https://orcid.org/0000-0002-4140-0591"]},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Trestini, David","raw_affiliation_strings":["School of Mathematical Sciences and STAG Research Centre , University of Southampton , Southampton SO17 1BJ , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and STAG Research Centre , University of Southampton , Southampton SO17 1BJ , United Kingdom","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015174121","display_name":"Jan Steinhoff","orcid":"https://orcid.org/0000-0002-1614-0214","observed_orcids":["https://orcid.org/0000-0002-1614-0214"]},"institutions":[{"id":"https://openalex.org/I4210127646","display_name":"Max Planck Institute for Gravitational Physics","ror":"https://ror.org/03sry2h30","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127646"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Steinhoff, Jan","raw_affiliation_strings":["Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute) , Am M\u00fchlenberg 1 , 14476 Potsdam-Golm , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute) , Am M\u00fchlenberg 1 , 14476 Potsdam-Golm , Germany","institution_ids":["https://openalex.org/I4210127646"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9980000257492065,"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/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.0005000000237487257,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eccentric-orbits","display_name":"eccentric orbits","score":0.7749999761581421},{"id":"https://openalex.org/keywords/aligned-spins","display_name":"aligned spins","score":0.7480000257492065},{"id":"https://openalex.org/keywords/conserved-quantities","display_name":"first integrals","score":0.7429999709129333},{"id":"https://openalex.org/keywords/fundamental-frequency","display_name":"fundamental frequency","score":0.8410000205039978},{"id":"https://openalex.org/keywords/conservative-maps","display_name":"conservative maps","score":0.5130000114440918},{"id":"https://openalex.org/keywords/innermost-stable-circular-orbit","display_name":"innermost stable circular orbit","score":0.906000018119812},{"id":"https://openalex.org/keywords/periastron-advance","display_name":"periastron advance","score":0.8930000066757202},{"id":"https://openalex.org/keywords/scattering-angle","display_name":"scattering angle","score":0.7289999723434448},{"id":"https://openalex.org/keywords/binary-black-holes","display_name":"binary black holes","score":0.5289999842643738},{"id":"https://openalex.org/keywords/gauge-invariance","display_name":"gauge invariance","score":0.6890000104904175}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8062000274658203},{"id":"https://openalex.org/C59108619","wikidata":"https://www.wikidata.org/wiki/Q2261398","display_name":"Circular orbit","level":2,"score":0.6866000294685364},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.6108999848365784},{"id":"https://openalex.org/C81502235","wikidata":"https://www.wikidata.org/wiki/Q104225","display_name":"Precession","level":2,"score":0.5878000259399414},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.5810999870300293},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.4902999997138977},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4887999892234802},{"id":"https://openalex.org/C127635394","wikidata":"https://www.wikidata.org/wiki/Q715746","display_name":"Circular motion","level":2,"score":0.4578999876976013},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C197464742","wikidata":"https://www.wikidata.org/wiki/Q1720536","display_name":"Mean motion","level":3,"score":0.4092999994754791},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.3668000102043152},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.3345000147819519},{"id":"https://openalex.org/C158488048","wikidata":"https://www.wikidata.org/wiki/Q483400","display_name":"Gyroscope","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C173990265","wikidata":"https://www.wikidata.org/wiki/Q2268240","display_name":"Elliptic orbit","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C204610980","wikidata":"https://www.wikidata.org/wiki/Q7100079","display_name":"Orbital motion","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.28450000286102295},{"id":"https://openalex.org/C97784730","wikidata":"https://www.wikidata.org/wiki/Q272626","display_name":"Orbital elements","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C159366927","wikidata":"https://www.wikidata.org/wiki/Q647631","display_name":"Constant of motion","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C5594486","wikidata":"https://www.wikidata.org/wiki/Q161635","display_name":"Angular velocity","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C91709909","wikidata":"https://www.wikidata.org/wiki/Q583960","display_name":"Homothetic transformation","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:eprints.soton.ac.uk:516044","doi":null,"is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/id/eprint/516044/1/2608.31072v1.pdf","pdf_url":"https://eprints.soton.ac.uk/id/eprint/516044/1/2608.31072v1.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:arXiv.org:2608.31072","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31072","pdf_url":"https://arxiv.org/pdf/2608.31072","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:pure.mpg.de:item_3731797","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-8E88-2","pdf_url":"https://hdl.handle.net/21.11116/0000-0013-8E8A-0","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2608.31072","doi":"https://doi.org/10.48550/arxiv.2608.31072","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.31072","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.31072","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31072","pdf_url":"https://arxiv.org/pdf/2608.31072","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6171340896","display_name":null,"funder_award_id":"EP/Y008251/1","funder_id":"https://openalex.org/F4320314731","funder_display_name":"UK Research and Innovation"}],"funders":[{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204873436.pdf","grobid_xml":"https://content.openalex.org/works/W7204873436.grobid-xml"},"referenced_works_count":95,"referenced_works":["https://openalex.org/W1567226117","https://openalex.org/W1594002267","https://openalex.org/W1917850522","https://openalex.org/W1970762473","https://openalex.org/W1971141770","https://openalex.org/W1977684498","https://openalex.org/W1991948239","https://openalex.org/W1992785704","https://openalex.org/W1997055517","https://openalex.org/W2014203239","https://openalex.org/W2016967897","https://openalex.org/W2019184579","https://openalex.org/W2031406439","https://openalex.org/W2032576282","https://openalex.org/W2038455979","https://openalex.org/W2041161965","https://openalex.org/W2045247866","https://openalex.org/W2047177876","https://openalex.org/W2074982547","https://openalex.org/W2075631339","https://openalex.org/W2092518410","https://openalex.org/W2094546398","https://openalex.org/W2096077283","https://openalex.org/W2103395779","https://openalex.org/W2107049645","https://openalex.org/W2108976358","https://openalex.org/W2122728304","https://openalex.org/W2132564506","https://openalex.org/W2132594714","https://openalex.org/W2145981472","https://openalex.org/W2148687033","https://openalex.org/W2160734274","https://openalex.org/W2160977597","https://openalex.org/W2168158132","https://openalex.org/W2172407808","https://openalex.org/W2180326370","https://openalex.org/W2198902111","https://openalex.org/W2210870099","https://openalex.org/W2272207145","https://openalex.org/W2326021457","https://openalex.org/W2504230633","https://openalex.org/W2541407175","https://openalex.org/W2589275422","https://openalex.org/W2591745650","https://openalex.org/W2592249285","https://openalex.org/W2592633141","https://openalex.org/W2667477767","https://openalex.org/W2766167579","https://openalex.org/W2779115631","https://openalex.org/W2787204134","https://openalex.org/W2953058554","https://openalex.org/W2963044837","https://openalex.org/W2963418284","https://openalex.org/W2972780868","https://openalex.org/W2991482234","https://openalex.org/W2995579740","https://openalex.org/W3013533591","https://openalex.org/W3013590385","https://openalex.org/W3015354207","https://openalex.org/W3090848169","https://openalex.org/W3176445980","https://openalex.org/W3207935798","https://openalex.org/W3210399547","https://openalex.org/W4221144201","https://openalex.org/W4225763327","https://openalex.org/W4226336214","https://openalex.org/W4232182547","https://openalex.org/W4232444648","https://openalex.org/W4247306364","https://openalex.org/W4367060322","https://openalex.org/W4376120950","https://openalex.org/W4388540576","https://openalex.org/W4389764253","https://openalex.org/W4390607875","https://openalex.org/W4401439264","https://openalex.org/W4404569005","https://openalex.org/W4409570931","https://openalex.org/W4411794485","https://openalex.org/W4412403334","https://openalex.org/W4413080000","https://openalex.org/W4415949730","https://openalex.org/W4416339376","https://openalex.org/W4417004207","https://openalex.org/W6929164580","https://openalex.org/W6948270358","https://openalex.org/W6966542966","https://openalex.org/W6966891122","https://openalex.org/W7130425716","https://openalex.org/W7140078802","https://openalex.org/W7140755301","https://openalex.org/W7160105779","https://openalex.org/W7166706862","https://openalex.org/W7168171545","https://openalex.org/W7171556069","https://openalex.org/W7202223117"],"related_works":["https://openalex.org/W4416339376","https://openalex.org/W3199575091","https://openalex.org/W7220713527","https://openalex.org/W2504230633","https://openalex.org/W7202223117","https://openalex.org/W3199054487","https://openalex.org/W2226009251","https://openalex.org/W3146840088","https://openalex.org/W3187040208","https://openalex.org/W3098442154"],"abstract_inverted_index":{"For":[0],"eccentric":[1],"systems":[2],"with":[3,126],"aligned":[4],"spins,":[5],"we":[6,120],"compute":[7],"all":[8,127],"spin":[9,128],"contributions":[10],"to":[11,45,106],"the":[12,17,26,33,39,60,71,84,91,95,107,115,122],"gauge-invariant":[13],"conservative":[14],"map":[15,41],"between":[16],"constants":[18],"of":[19,94,117],"motion":[20],"(energy":[21],"and":[22,25,29,53,73],"angular":[23],"momentum)":[24],"fundamental":[27],"(radial":[28],"azimuthal)":[30],"frequencies":[31],"at":[32],"fourth":[34],"post-Newtonian":[35,86],"order.":[36],"This":[37],"extends":[38],"nonspinning":[40],"derived":[42,67],"in":[43,55,102,114],"[arXiv:2511.10735]":[44],"include":[46],"terms":[47],"that":[48,83,89],"are":[49],"linear,":[50],"quadratic,":[51],"cubic,":[52],"quartic":[54],"spin,":[56],"as":[57,59,70,76,78],"well":[58,77],"associated":[61],"spin-deformability":[62],"parameters.":[63],"We":[64,81],"also":[65],"obtain":[66],"quantities":[68],"such":[69],"redshift":[72],"gyroscopic":[74],"invariants,":[75],"circular":[79,98,111],"links.":[80],"notice":[82],"Blanchet-Iyer-Favata":[85],"stability":[87],"criterion":[88],"determines":[90],"dimensionless":[92],"frequency":[93],"innermost":[96],"stable":[97],"orbit":[99],"(ISCO)":[100],"is":[101],"fact":[103],"intricately":[104],"related":[105],"periastron":[108],"advance":[109],"for":[110],"orbits.":[112],"Finally,":[113],"case":[116],"unbound":[118],"orbits,":[119],"complete":[121],"4PN":[123],"scattering":[124],"angle":[125],"contributions.":[129]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
