2019/01/31 by Wen-Du Li, Li, Wen-Du, Wu-Sheng Dai +1
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1901.11506
openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A duality between spacetime manifolds, the geodesic duality, is introduced. Two manifolds are geodesic dual, if the transformation between their metrics is also the transformation between their geodesics. That is, the transformation that transforms the metric to the metric of the dual manifold is also the transformation that transforms the geodesic to the geodesic of the dual manifold. On the contrary, for nondual spacetime manifolds, a geodesic is no longer a geodesic after the transformation between the metrics. We give a general result of the duality between spacetime manifolds with diagonal metrics. The geodesic duality of spherically symmetric spacetime are discussed for illustrating the concept. The geodesic dual spacetime of the Schwarzschild spacetime and the geodesic dual spacetime of the Reissner-Nordström spacetime are presented.