Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W3101625225', 'doi': 'https://doi.org/10.1088/0264-9381/28/23/235009', 'title': 'A note on the post-Newtonian limit of quasi-local energy expressions', 'display_name': 'A note on the post-Newtonian limit of quasi-local energy expressions', 'publication_year': 2011, 'publication_date': '2011-11-16', 'ids': {'openalex': 'https://openalex.org/W3101625225', 'doi': 'https://doi.org/10.1088/0264-9381/28/23/235009', 'mag': '3101625225'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1088/0264-9381/28/23/235009', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S171172751', 'display_name': 'Classical and Quantum Gravity', 'issn_l': '0264-9381', 'issn': ['0264-9381', '1361-6382'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320083', 'host_organization_name': 'IOP Publishing', 'host_organization_lineage': ['https://openalex.org/P4310311669', 'https://openalex.org/P4310320083'], 'host_organization_lineage_names': ['Institute of Physics', 'IOP Publishing'], '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/1102.1867', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5030228602', 'display_name': 'Jörg Frauendiener', 'orcid': 'https://orcid.org/0000-0003-2796-5323'}, 'institutions': [{'id': 'https://openalex.org/I184942183', 'display_name': 'University of Oslo', 'ror': 'https://ror.org/01xtthb56', 'country_code': 'NO', 'type': 'education', 'lineage': ['https://openalex.org/I184942183']}, {'id': 'https://openalex.org/I80281795', 'display_name': 'University of Otago', 'ror': 'https://ror.org/01jmxt844', 'country_code': 'NZ', 'type': 'education', 'lineage': ['https://openalex.org/I80281795']}], 'countries': ['NO', 'NZ'], 'is_corresponding': False, 'raw_author_name': 'Jörg Frauendiener', 'raw_affiliation_strings': ['Centre of Mathematics for Applications, University of Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway', 'Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9010, New Zealand'], 'affiliations': [{'raw_affiliation_string': 'Centre of Mathematics for Applications, University of Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway', 'institution_ids': ['https://openalex.org/I184942183']}, {'raw_affiliation_string': 'Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9010, New Zealand', 'institution_ids': ['https://openalex.org/I80281795']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5101702557', 'display_name': 'László B Szabados', 'orcid': 'https://orcid.org/0000-0001-7738-8726'}, 'institutions': [{'id': 'https://openalex.org/I4210090693', 'display_name': 'Institute for Particle and Nuclear Physics', 'ror': 'https://ror.org/008mx9f83', 'country_code': 'HU', 'type': 'facility', 'lineage': ['https://openalex.org/I4210090693', 'https://openalex.org/I4210126225', 'https://openalex.org/I7597260']}], 'countries': ['HU'], 'is_corresponding': False, 'raw_author_name': 'László B Szabados', 'raw_affiliation_strings': ['Research Institute for Particle and Nuclear Physics, H–1525 Budapest 114, PO Box 49, Hungary'], 'affiliations': [{'raw_affiliation_string': 'Research Institute for Particle and Nuclear Physics, H–1525 Budapest 114, PO Box 49, Hungary', 'institution_ids': ['https://openalex.org/I4210090693']}]}], 'institution_assertions': [], 'countries_distinct_count': 3, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 3, 'citation_normalized_percentile': {'value': 0.599044, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 76, 'max': 78}, 'biblio': {'volume': '28', 'issue': '23', 'first_page': '235009', 'last_page': '235009'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10025', 'display_name': 'Black Holes and Theoretical Physics', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/3106', 'display_name': 'Nuclear and High Energy Physics'}, '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/T10025', 'display_name': 'Black Holes and Theoretical Physics', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/3106', 'display_name': 'Nuclear and High Energy Physics'}, '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/T10095', 'display_name': 'Cosmology and Gravitation Theories', 'score': 0.9999, '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/T11415', 'display_name': 'Noncommutative and Quantum Gravity Theories', 'score': 0.9988, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, '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/newtonian-limit', 'display_name': 'Newtonian limit', 'score': 0.75726396}, {'id': 'https://openalex.org/keywords/newtonian-potential', 'display_name': 'Newtonian potential', 'score': 0.6539069}, {'id': 'https://openalex.org/keywords/expression', 'display_name': 'Expression (computer science)', 'score': 0.5328252}, {'id': 'https://openalex.org/keywords/flatness', 'display_name': 'Flatness (cosmology)', 'score': 0.5281503}], 'concepts': [{'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.89103293}, {'id': 'https://openalex.org/C2778654791', 'wikidata': 'https://www.wikidata.org/wiki/Q7020536', 'display_name': 'Newtonian limit', 'level': 3, 'score': 0.75726396}, {'id': 'https://openalex.org/C147452769', 'wikidata': 'https://www.wikidata.org/wiki/Q11452', 'display_name': 'General relativity', 'level': 2, 'score': 0.7256583}, {'id': 'https://openalex.org/C70920666', 'wikidata': 'https://www.wikidata.org/wiki/Q4328383', 'display_name': 'Newtonian potential', 'level': 3, 'score': 0.6539069}, {'id': 'https://openalex.org/C294558', 'wikidata': 'https://www.wikidata.org/wiki/Q366968', 'display_name': 'Newtonian fluid', 'level': 2, 'score': 0.60200125}, {'id': 'https://openalex.org/C151201525', 'wikidata': 'https://www.wikidata.org/wiki/Q177239', 'display_name': 'Limit (mathematics)', 'level': 2, 'score': 0.5656434}, {'id': 'https://openalex.org/C90559484', 'wikidata': 'https://www.wikidata.org/wiki/Q778379', 'display_name': 'Expression (computer science)', 'level': 2, 'score': 0.5328252}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.53056335}, {'id': 'https://openalex.org/C2778530986', 'wikidata': 'https://www.wikidata.org/wiki/Q5457948', 'display_name': 'Flatness (cosmology)', 'level': 3, 'score': 0.5281503}, {'id': 'https://openalex.org/C74650414', 'wikidata': 'https://www.wikidata.org/wiki/Q11397', 'display_name': 'Classical mechanics', 'level': 1, 'score': 0.51799}, {'id': 'https://openalex.org/C124017977', 'wikidata': 'https://www.wikidata.org/wiki/Q11412', 'display_name': 'Gravitation', 'level': 2, 'score': 0.48802653}, {'id': 'https://openalex.org/C22492302', 'wikidata': 'https://www.wikidata.org/wiki/Q2297853', 'display_name': 'Gravitational energy', 'level': 3, 'score': 0.44209826}, {'id': 'https://openalex.org/C72169020', 'wikidata': 'https://www.wikidata.org/wiki/Q194404', 'display_name': 'Monotonic function', 'level': 2, 'score': 0.43922982}, {'id': 'https://openalex.org/C14257148', 'wikidata': 'https://www.wikidata.org/wiki/Q558066', 'display_name': 'Gravitational field', 'level': 2, 'score': 0.42512083}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.41918814}, {'id': 'https://openalex.org/C186370098', 'wikidata': 'https://www.wikidata.org/wiki/Q442787', 'display_name': 'Energy (signal processing)', 'level': 2, 'score': 0.41046226}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.22636682}, {'id': 'https://openalex.org/C26405456', 'wikidata': 'https://www.wikidata.org/wiki/Q338', 'display_name': 'Cosmology', 'level': 2, 'score': 0.20204362}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.1885767}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.073096246}, {'id': 'https://openalex.org/C78458016', 'wikidata': 'https://www.wikidata.org/wiki/Q840400', 'display_name': 'Evolutionary biology', '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}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1088/0264-9381/28/23/235009', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S171172751', 'display_name': 'Classical and Quantum Gravity', 'issn_l': '0264-9381', 'issn': ['0264-9381', '1361-6382'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320083', 'host_organization_name': 'IOP Publishing', 'host_organization_lineage': ['https://openalex.org/P4310311669', 'https://openalex.org/P4310320083'], 'host_organization_lineage_names': ['Institute of Physics', 'IOP Publishing'], '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/1102.1867', 'pdf_url': 'https://arxiv.org/pdf/1102.1867', '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.1102.1867', '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/1102.1867', 'pdf_url': 'https://arxiv.org/pdf/1102.1867', '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': [{'id': 'https://metadata.un.org/sdg/7', 'display_name': 'Affordable and clean energy', 'score': 0.88}], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W2167755433', 'https://openalex.org/W3101625225'], 'referenced_works_count': 24, 'referenced_works': ['https://openalex.org/W1542765289', 'https://openalex.org/W1549416275', 'https://openalex.org/W1789645782', 'https://openalex.org/W2013191528', 'https://openalex.org/W2015106666', 'https://openalex.org/W2029403139', 'https://openalex.org/W2032003775', 'https://openalex.org/W2044665434', 'https://openalex.org/W2046357915', 'https://openalex.org/W2052709408', 'https://openalex.org/W2062756503', 'https://openalex.org/W2064191127', 'https://openalex.org/W2070051532', 'https://openalex.org/W2071725611', 'https://openalex.org/W2078171821', 'https://openalex.org/W2086051335', 'https://openalex.org/W2105973581', 'https://openalex.org/W2123823073', 'https://openalex.org/W2139496359', 'https://openalex.org/W2234725005', 'https://openalex.org/W2263517427', 'https://openalex.org/W4206689951', 'https://openalex.org/W4234933822', 'https://openalex.org/W4249276713'], 'related_works': ['https://openalex.org/W4221113306', 'https://openalex.org/W3183872805', 'https://openalex.org/W3147075703', 'https://openalex.org/W3146120274', 'https://openalex.org/W2985822684', 'https://openalex.org/W2936120896', 'https://openalex.org/W2228757726', 'https://openalex.org/W2173849148', 'https://openalex.org/W2077493895', 'https://openalex.org/W152640756'], 'abstract_inverted_index': {'An': [0], "'effective'": [1, 111], 'quasi-local': [2, 103], 'energy': [3, 69, 89, 104, 112], 'expression,': [4], 'motivated': [5], 'by': [6], 'the': [7, 19, 24, 28, 32, 47, 51, 55, 67], '(relativistically': [8], 'corrected)': [9], 'Newtonian': [10, 33, 56], 'theory,': [11], 'is': [12], 'introduced': [13], 'in': [14, 27, 35, 46, 50, 83, 114], 'exact': [15], 'general': [16], 'relativity': [17], 'as': [18, 73], 'volume': [20], 'integral': [21], 'of': [22], 'all': [23], 'source': [25, 48], 'terms': [26], 'field': [29, 52], 'equation': [30, 53], 'for': [31, 54], 'potential': [34], 'static': [36], 'spacetimes.': [37], 'In': [38, 59], 'particular,': [39], 'we': [40], 'exhibit': [41], 'a': [42, 74], 'new': [43], 'post-Newtonian': [44], 'correction': [45], 'term': [49], 'gravitational': [57], 'potential.': [58], 'asymptotically': [60], 'flat': [61], 'spacetimes,': [62], 'this': [63, 110, 115], 'expression': [64, 105, 113], 'tends': [65], 'to': [66], 'Arnowitt–Deser–Misner': [68], 'at': [70], 'spatial': [71], 'infinity': [72], 'monotonically': [75], 'decreasing': [76], 'set': [77], 'function.': [78], 'We': [79, 97], 'prove': [80], 'its': [81, 93], 'positivity': [82], 'spherically': [84], 'symmetric': [85], 'spacetimes': [86], 'under': [87], 'certain': [88], 'conditions,': [90], 'and': [91], 'that': [92, 99], 'vanishing': [94], 'characterizes': [95], 'flatness.': [96], 'argue': [98], 'any': [100], 'physically': [101], 'acceptable': [102], 'should': [106], 'behave': [107], 'qualitatively': [108], 'like': [109], 'limit.': [116]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3101625225', 'counts_by_year': [{'year': 2019, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}], 'updated_date': '2025-01-05T09:08:46.080603', 'created_date': '2020-11-23'}