Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2063319049', 'doi': 'https://doi.org/10.1103/physrevd.89.104056', 'title': 'Post-linear Schwarzschild solution in harmonic coordinates: Elimination of structure-dependent terms', 'display_name': 'Post-linear Schwarzschild solution in harmonic coordinates: Elimination of structure-dependent terms', 'publication_year': 2014, 'publication_date': '2014-05-27', 'ids': {'openalex': 'https://openalex.org/W2063319049', 'doi': 'https://doi.org/10.1103/physrevd.89.104056', 'mag': '2063319049'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physrevd.89.104056', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210210554', 'display_name': 'Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology', 'issn_l': '1550-2368', 'issn': ['1550-2368', '1550-7998'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320261', 'host_organization_name': 'American Physical Society', 'host_organization_lineage': ['https://openalex.org/P4310320261'], 'host_organization_lineage_names': ['American Physical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/pdf/1403.0024', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5062581437', 'display_name': 'S. A. Klioner', 'orcid': 'https://orcid.org/0000-0003-4682-7831'}, 'institutions': [{'id': 'https://openalex.org/I78650965', 'display_name': 'TU Dresden', 'ror': 'https://ror.org/042aqky30', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I78650965']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Sergei A. Klioner', 'raw_affiliation_strings': ['Lohrmann Observatory, Technische Universität Dresden, Mommsenstraße 13, 01062, Dresden, Germany'], 'affiliations': [{'raw_affiliation_string': 'Lohrmann Observatory, Technische Universität Dresden, Mommsenstraße 13, 01062, Dresden, Germany', 'institution_ids': ['https://openalex.org/I78650965']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5063360357', 'display_name': 'M. Söffel', 'orcid': 'https://orcid.org/0000-0001-8042-082X'}, 'institutions': [{'id': 'https://openalex.org/I78650965', 'display_name': 'TU Dresden', 'ror': 'https://ror.org/042aqky30', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I78650965']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Michael Soffel', 'raw_affiliation_strings': ['Lohrmann Observatory, Technische Universität Dresden, Mommsenstraße 13, 01062, Dresden, Germany'], 'affiliations': [{'raw_affiliation_string': 'Lohrmann Observatory, Technische Universität Dresden, Mommsenstraße 13, 01062, Dresden, Germany', 'institution_ids': ['https://openalex.org/I78650965']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.741, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 6, 'citation_normalized_percentile': {'value': 0.659102, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 82, 'max': 83}, 'biblio': {'volume': '89', 'issue': '10', 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11405', 'display_name': 'Geophysics and Gravity Measurements', 'score': 0.999, 'subfield': {'id': 'https://openalex.org/subfields/1910', 'display_name': 'Oceanography'}, 'field': {'id': 'https://openalex.org/fields/19', 'display_name': 'Earth and Planetary Sciences'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11405', 'display_name': 'Geophysics and Gravity Measurements', 'score': 0.999, 'subfield': {'id': 'https://openalex.org/subfields/1910', 'display_name': 'Oceanography'}, 'field': {'id': 'https://openalex.org/fields/19', 'display_name': 'Earth and Planetary Sciences'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11960', 'display_name': 'Relativity and Gravitational Theory', 'score': 0.999, '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/T10463', 'display_name': 'Pulsars and Gravitational Waves Research', 'score': 0.9984, '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/harmonic-coordinates', 'display_name': 'Harmonic coordinates', 'score': 0.61733127}, {'id': 'https://openalex.org/keywords/harmonic', 'display_name': 'Harmonic', 'score': 0.45470482}], 'concepts': [{'id': 'https://openalex.org/C52765159', 'wikidata': 'https://www.wikidata.org/wiki/Q1027847', 'display_name': 'Multipole expansion', 'level': 2, 'score': 0.6976986}, {'id': 'https://openalex.org/C48286519', 'wikidata': 'https://www.wikidata.org/wiki/Q461255', 'display_name': 'Deriving the Schwarzschild solution', 'level': 5, 'score': 0.62818575}, {'id': 'https://openalex.org/C86108249', 'wikidata': 'https://www.wikidata.org/wiki/Q2996688', 'display_name': 'Harmonic coordinates', 'level': 4, 'score': 0.61733127}, {'id': 'https://openalex.org/C136125196', 'wikidata': 'https://www.wikidata.org/wiki/Q742969', 'display_name': 'Schwarzschild metric', 'level': 3, 'score': 0.5750579}, {'id': 'https://openalex.org/C115304011', 'wikidata': 'https://www.wikidata.org/wiki/Q72755', 'display_name': 'Schwarzschild radius', 'level': 3, 'score': 0.55187684}, {'id': 'https://openalex.org/C74650414', 'wikidata': 'https://www.wikidata.org/wiki/Q11397', 'display_name': 'Classical mechanics', 'level': 1, 'score': 0.5370831}, {'id': 'https://openalex.org/C14037181', 'wikidata': 'https://www.wikidata.org/wiki/Q215007', 'display_name': 'Equations of motion', 'level': 2, 'score': 0.5313851}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.48213598}, {'id': 'https://openalex.org/C127934551', 'wikidata': 'https://www.wikidata.org/wiki/Q1148098', 'display_name': 'Harmonic', 'level': 2, 'score': 0.45470482}, {'id': 'https://openalex.org/C3768446', 'wikidata': 'https://www.wikidata.org/wiki/Q877100', 'display_name': 'Spherical harmonics', 'level': 2, 'score': 0.4530293}, {'id': 'https://openalex.org/C294558', 'wikidata': 'https://www.wikidata.org/wiki/Q366968', 'display_name': 'Newtonian fluid', 'level': 2, 'score': 0.43745196}, {'id': 'https://openalex.org/C176217482', 'wikidata': 'https://www.wikidata.org/wiki/Q860554', 'display_name': 'Metric (unit)', 'level': 2, 'score': 0.42935765}, {'id': 'https://openalex.org/C9652623', 'wikidata': 'https://www.wikidata.org/wiki/Q190109', 'display_name': 'Field (mathematics)', 'level': 2, 'score': 0.42461634}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.37223998}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.3321185}, {'id': 'https://openalex.org/C124017977', 'wikidata': 'https://www.wikidata.org/wiki/Q11412', 'display_name': 'Gravitation', 'level': 2, 'score': 0.19341356}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.1849845}, {'id': 'https://openalex.org/C95086748', 'wikidata': 'https://www.wikidata.org/wiki/Q1068747', 'display_name': 'Kerr metric', 'level': 4, 'score': 0.17699033}, {'id': 'https://openalex.org/C147452769', 'wikidata': 'https://www.wikidata.org/wiki/Q11452', 'display_name': 'General relativity', 'level': 2, 'score': 0.17526537}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.1202032}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.08663553}, {'id': 'https://openalex.org/C21547014', 'wikidata': 'https://www.wikidata.org/wiki/Q1423657', 'display_name': 'Operations management', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C195065555', 'wikidata': 'https://www.wikidata.org/wiki/Q214881', 'display_name': 'Curvature', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C12089564', 'wikidata': 'https://www.wikidata.org/wiki/Q1195879', 'display_name': 'Ricci curvature', 'level': 3, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physrevd.89.104056', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210210554', 'display_name': 'Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology', 'issn_l': '1550-2368', 'issn': ['1550-2368', '1550-7998'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320261', 'host_organization_name': 'American Physical Society', 'host_organization_lineage': ['https://openalex.org/P4310320261'], 'host_organization_lineage_names': ['American Physical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1403.0024', 'pdf_url': 'https://arxiv.org/pdf/1403.0024', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1403.0024', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1403.0024', 'pdf_url': 'https://arxiv.org/pdf/1403.0024', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W2063319049'], 'referenced_works_count': 14, 'referenced_works': ['https://openalex.org/W1611615589', 'https://openalex.org/W1979683698', 'https://openalex.org/W2013172310', 'https://openalex.org/W2026114255', 'https://openalex.org/W2030843101', 'https://openalex.org/W2033011260', 'https://openalex.org/W2038936915', 'https://openalex.org/W2063137056', 'https://openalex.org/W2099436646', 'https://openalex.org/W2113814686', 'https://openalex.org/W3099291399', 'https://openalex.org/W3101411518', 'https://openalex.org/W3105408277', 'https://openalex.org/W3173862477'], 'related_works': ['https://openalex.org/W799717315', 'https://openalex.org/W4296012609', 'https://openalex.org/W2950400809', 'https://openalex.org/W2915673819', 'https://openalex.org/W2134160070', 'https://openalex.org/W2091356062', 'https://openalex.org/W2045886921', 'https://openalex.org/W2024418890', 'https://openalex.org/W1928693544', 'https://openalex.org/W17899771'], 'abstract_inverted_index': {'The': [0, 129, 145], 'paper': [1, 77, 149], 'deals': [2], 'with': [3], 'a': [4, 47, 82], 'special': [5], 'kind': [6], 'of': [7, 13, 32, 36, 73, 84, 131, 147, 162], 'problems': [8, 53], 'that': [9, 27], 'appear': [10, 23], 'in': [11, 24, 30, 106, 110, 165], 'solutions': [12, 126], "Einstein's": [14], 'field': [15, 97, 104], 'equations': [16, 35, 105], 'for': [17, 57, 71, 81, 115], 'extended': [18], 'bodies:': [19], 'many': [20], 'structure-dependent': [21], 'terms': [22], 'intermediate': [25], 'calculations': [26], 'cancel': [28], 'exactly': [29], 'virtue': [31], 'the': [33, 59, 62, 66, 94, 103, 107, 111, 139, 143, 155, 163, 166], 'local': [34], 'motion': [37], 'or': [38], 'can': [39, 98, 150], 'be': [40, 99, 151], 'eliminated': [41], 'by': [42], 'appropriate': [43], 'gauge': [44, 113], 'transformations.': [45], 'For': [46], 'single': [48], 'body': [49], 'at': [50], 'rest': [51], 'these': [52], 'are': [54, 127], 'well': [55], 'understood': [56], 'both': [58], 'post-Newtonian': [60, 157], 'and': [61, 114, 124, 158], 'post-Minkowskian': [63, 159], 'cases.': [64], 'However,': [65], 'situation': [67], 'is': [68, 135], 'still': [69], 'unclear': [70], 'approximations': [72], 'higher': [74], 'orders.': [75], 'This': [76], 'discusses': [78], 'this': [79, 148], 'problem': [80], '"body"': [83], 'spherical': [85], 'symmetry': [86], 'to': [87, 138, 153], 'post-linear': [88, 108, 167], 'order.': [89], 'We': [90], 'explicitly': [91], 'demonstrate': [92], 'how': [93], 'usual': [95], 'Schwarzschild': [96], 'derived': [100], 'directly': [101], 'from': [102, 142], 'approximation': [109], 'harmonic': [112], 'an': [116], 'arbitrary': [117], 'spherically': [118], 'symmetric': [119], 'matter': [120], 'distribution.': [121], 'Both': [122], 'external': [123], 'internal': [125], 'considered.': [128], 'case': [130], 'static': [132], 'incompressible': [133], 'fluid': [134], 'then': [136], 'compared': [137], 'well-known': [140, 156], 'results': [141, 146], 'literature.': [144], 'applied': [152], 'generalize': [154], 'multipole': [160], 'expansions': [161], 'metric': [164], 'approximation.': [168]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2063319049', 'counts_by_year': [{'year': 2022, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 2}, {'year': 2016, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 2}], 'updated_date': '2025-01-12T04:57:56.252109', 'created_date': '2016-06-24'}