{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T15:16:07Z","timestamp":1774538167518,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,9,27]],"date-time":"2020-09-27T00:00:00Z","timestamp":1601164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form of a temperature-dependent correlation over distances, of momenta oscillations about an average momentum, of vortical structures and of a positive gravitational susceptibility. In the interaction with quantum matter and below a certain range, gravity is carried by an antisymmetric, second order tensor that satisfies Maxwell-type equations. Some classical and quantum aspects of this type of \u201cgravitoelectromagnetism\u201d were investigated. Gravitational analogues of the laws of Curie and Bloch were found for a one-dimensional model. A critical temperature for a change in phase from unbound to isolated vortices can be calculated using an XY-model.<\/jats:p>","DOI":"10.3390\/e22101089","type":"journal-article","created":{"date-parts":[[2020,9,27]],"date-time":"2020-09-27T22:24:42Z","timestamp":1601245482000},"page":"1089","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Some Classical and Quantum Aspects of Gravitoelectromagnetism"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5226-955X","authenticated-orcid":false,"given":"Giorgio","family":"Papini","sequence":"first","affiliation":[{"name":"Department of Physics and Prairie Particle Physics Institute, University of Regina, Regina, SK S4S 0A2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,27]]},"reference":[{"key":"ref_1","unstructured":"DeWitt, C., and DeWitt, B. (1964). Dynamical Theory of Groups and Fields. Relativity, Groups and Topology, Les Houches Lectures 1963, Gordon and Breach, Science Publishers Inc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"073011","DOI":"10.1103\/PhysRevD.71.073011","article-title":"Neutrino optics and oscillations in gravitational fields","volume":"71","author":"Lambiase","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1103\/PhysRevLett.66.1259","article-title":"Neutrino helicity flip from gravity-spin coupling","volume":"66","author":"Cai","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rizzi, G., and Ruggiero, M.L. (2004). Relativity in Rotating Frames, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-017-0528-8"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1007\/s10714-007-0595-z","article-title":"Spin\u2013rgravity coupling and gravity-induced quantum phases","volume":"40","author":"Papini","year":"2008","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1112\/plms\/s2-32.1.87","article-title":"Taylor\u2019s theorem in the tensor calculus","volume":"32","author":"Ruse","year":"1931","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_7","unstructured":"Synge, J.L. (1966). Relativity: The General Theory, North-Holland Publishing Company."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"044022","DOI":"10.1103\/PhysRevD.75.044022","article-title":"Spin-2 particles in gravitational fields","volume":"75","author":"Papini","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1142\/S0218271809014595","article-title":"Optics of spin-1 particles from gravity-induced phases","volume":"18","author":"Papini","year":"2009","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_10","unstructured":"Feynman, R.P., and Hibbs, A.R. (1965). Quantum Mechanics and Path Integrals, McGraw-Hill."},{"key":"ref_11","unstructured":"Lanczos, C. (1970). The Variational Principles of Mechanics, Dover Publications."},{"key":"ref_12","first-page":"73","article-title":"On the influence of gravity on the light propagation","volume":"114","author":"Skrotskii","year":"1957","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"064025","DOI":"10.1103\/PhysRevD.65.064025","article-title":"Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies","volume":"65","author":"Kopeikin","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_14","unstructured":"Ballentine, L.E. (1990). Quantum Mechanics, Prentice Hall."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.physletb.2006.09.028","article-title":"Hawking temperature in the tunneling picture","volume":"642","author":"Akhmedov","year":"2006","journal-title":"Phys. Lett. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1143\/PTPS.88.1","article-title":"Vacuum noise and stress induced by uniform acceleration hawking-unruh effect in rindler manifold of arbitrary dimension","volume":"88","author":"Takagi","year":"1986","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1119\/1.3308568","article-title":"A WKB-like approach to Unruh radiation","volume":"78","author":"Singleton","year":"2010","journal-title":"Am. J. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1103\/PhysRevD.14.870","article-title":"Notes on black-hole evaporation","volume":"14","author":"Unruh","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1103\/RevModPhys.80.787","article-title":"The Unruh effect and its applications","volume":"80","author":"Crispino","year":"2008","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1550075","DOI":"10.1142\/S0217732315500753","article-title":"Unruh temperature with maximal acceleration","volume":"30","author":"Benedetto","year":"2015","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1103\/PhysRev.186.1328","article-title":"Absolute zero of time","volume":"186","author":"Misner","year":"1969","journal-title":"Phys. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1016\/j.physleta.2012.02.057","article-title":"Zitterbewegung and gravitational Berry phase","volume":"376","author":"Papini","year":"2012","journal-title":"Phys. Lett. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1450075","DOI":"10.1142\/S0217732314500758","article-title":"Covariance and gauge invariance in relativistic theories of gravity","volume":"29","author":"Papini","year":"2014","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1103\/PhysRevLett.16.1092","article-title":"Superconductors and gravitational drag","volume":"16","author":"DeWitt","year":"1966","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/BF02710584","article-title":"London moment of rotating superconductors and Lense-Thirring fields of general relativity","volume":"45","author":"Papini","year":"1966","journal-title":"Nuovo C."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"012069","DOI":"10.1088\/1742-6596\/306\/1\/012069","article-title":"Geometric quantum phase in the spacetime of topological defects","volume":"306","author":"Bakke","year":"2011","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1140\/epjc\/s10052-016-3904-4","article-title":"Noninertial effects on the quantum dynamics of scalar bosons","volume":"76","author":"Castro","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1750137","DOI":"10.1142\/S0218271817501371","article-title":"Classical and quantum aspects of particle propagation in external gravitational fields","volume":"26","author":"Papini","year":"2017","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_29","unstructured":"Itzykson, C., and Zuber, J.-B. (1980). Quantum Field Theory, McGraw-Hill."},{"key":"ref_30","unstructured":"Baxter, R.J. (1982). Exactly Solved Models in Statistical Mechanics, Academic Press."},{"key":"ref_31","unstructured":"Kittel, C. (1996). Introduction to Solid State Physics, John Wiley and Sons, Inc.. [7th ed.]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0370-1573(77)90006-0","article-title":"Gravitons in Minkowski space-time interactions and results of astrophysical interest","volume":"33","author":"Papini","year":"1977","journal-title":"Phys. Rep."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1103\/PhysRevLett.28.994","article-title":"Interpretation of Gravitational-Wave Observations","volume":"28","author":"Misner","year":"1972","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"064011","DOI":"10.1103\/PhysRevD.86.064011","article-title":"Bose-Einstein Condensate general relativistic stars","volume":"86","author":"Chavanis","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_35","unstructured":"Balian, R. (1981). Singularities in Waves And, Rays, North-Holland Publishing Company. Les Houches, Session XXXV, 1980-Physique des D\u00e9fauts\/Physics of Defects."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1089\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:14:16Z","timestamp":1760177656000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/10\/1089"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,27]]},"references-count":35,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["e22101089"],"URL":"https:\/\/doi.org\/10.3390\/e22101089","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,27]]}}}