caa a22 4500 445385537 CHVBK 20180317143031.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10714-010-1086-1 doi (NATIONALLICENCE)springer-10.1007/s10714-010-1086-1 Static observers in curved spaces and non-inertial frames in Minkowski spacetime [Elektronische Daten] [F. Dahia, P. da Silva] Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically, we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. We also determine, from the Einstein equations, a covariant field equation that regulates the behavior of the proper acceleration of static observers in curved spacetimes. It corresponds to an exact relativistic version of the Newtonian gravitational field equation. In the specific case in which the level surfaces of the norm of the acceleration field of the static observers are maximally symmetric two-dimensional spaces, the energy-momentum tensor of the source is analyzed. Springer Science+Business Media, LLC, 2010 Non-inertial frames nationallicence Simultaneity nationallicence Static observers nationallicence Dahia F. Departamento de Física, Universidade Federal de Campina Grande, 58109-970, Campina Grande, PB, Brazil aut da Silva P. Departamento de Física, Universidade Federal de Campina Grande, 58109-970, Campina Grande, PB, Brazil aut General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/1(2011-01-01), 269-292 0001-7701 43:1<269 2011 43 10714 https://doi.org/10.1007/s10714-010-1086-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-010-1086-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dahia F. Departamento de Física, Universidade Federal de Campina Grande, 58109-970, Campina Grande, PB, Brazil aut NATIONALLICENCE 700 1- da Silva P. Departamento de Física, Universidade Federal de Campina Grande, 58109-970, Campina Grande, PB, Brazil aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/1(2011-01-01), 269-292 0001-7701 43:1<269 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer