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Normal coordinates based on curved tangent space
Published in American Physical Society
2020
Volume: 101
   
Issue: 12
Abstract
Riemann normal coordinates (RNC) at a regular event p0 of a spacetime manifold M are constructed by imposing (i) gab|p0=ηab, and (ii) Γabc|p0=0. There is, however, a third, independent, assumption in the definition of RNC which essentially fixes the density of geodesics emanating from p0 to its value in flat spacetime, viz.: (iii) the tangent space Tp0(M) is flat. We relax (iii) and obtain the normal coordinates, along with the metric gab, when Tp0(M) is a maximally symmetric manifold MΛ with curvature length |Λ|-1/2. In general, the "rest"frame defined by these coordinates is noninertial with an additional acceleration a=-(Λ/3)x depending on the curvature of tangent space. Our geometric setup provides a convenient probe of local physics in a universe with a cosmological constant Λ, now embedded into the local structure of spacetime as a fundamental constant associated with a curved tangent space. We discuss classical and quantum implications of the same. © 2020 American Physical Society
About the journal
JournalData powered by TypesetPhysical Review D
PublisherData powered by TypesetAmerican Physical Society
ISSN24700010