2021/03/31 by R Solanki
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #General relativity #Geodesic #Kerr metric #Linearized gravity #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Null (SQL) #Physics #Quantum field theory in curved spacetime #Quantum mechanics #Schwarzschild metric #Schwarzschild radius #Spacetime #Spherically symmetric spacetime #gr-qc
paper · pdf · doi:10.1088/1361-6382/ac3aa0
published in Classical and Quantum Gravity 39(1), 015015 (IOP Publishing) · 17 pages, 2 figures; a section on parameterization, two appendices and six footnotes added, four typos corrected
openalex publication_date 2021/11/17 · arxiv created 2021/11/19 · arxiv updated 2021/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The Kottler spacetime in isotropic coordinates is known where the metric is time-dependent. In this paper, the Kottler spacetime is given in isotropic static coordinates (i.e. the metric components are time-independent). The metric is found in terms of the Jacobian elliptic functions through coordinate transformations from the Schwarzschild–(anti-)de Sitter metric. In canonical coordinates, it is known that the unparameterized spatially projected null geodesics of the Kottler and Schwarzschild spacetimes coincide. We show that in isotropic static coordinates, the refractive indices of Kottler and Schwarzschild are not proportional, yielding spatially projected null geodesics that are different.