2020/11/30 by Soon-Tae Hong, Yong-Wan Kim, Young-Jai Park
Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Boundary (topology) #Classical mechanics #Cosmology and Gravitation Theories #Diagonal #Embedding #Event horizon #General relativity #Geodesic #Geometry #Gravitation #Horizon #Massive gravity #Mathematical analysis #Mathematical physics #Minkowski space #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Schwarzschild metric #Schwarzschild radius #Spacetime #Theoretical physics #gr-qc
paper · pdf · doi:10.3390/universe8010015
published as Universe 2022, 8(1), 15 · 18 pages, 3 figures, version to appear in Universe
openalex publication_date 2021/12/28 · arxiv created 2021/12/29 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Making use of the higher dimensional global embedding Minkowski spacetime (GEMS), we embed (3 + 1)-dimensional Schwarzschild and Reissner-Nordström (RN) black holes written by the Painlevé-Gullstrand (PG) spacetimes, which have off-diagonal components in metrics, into (5 + 1)- and (5 + 2)-dimensional flat ones, respectively. As a result, we have shown the equivalence of the GEMS embeddings of the spacetimes with the diagonal and off-diagonal terms in metrics. Moreover, with the aid of their geodesic equations satisfying various boundary conditions in the flat embedded spacetimes, we directly obtain freely falling temperatures. We also show that freely falling temperatures in the PG spacetimes are well-defined beyond the event horizons, while they are equivalent to the Hawking temperatures, which are obtained in the original curved ones in the ranges between the horizon and the infinity. These will be helpful to study GEMS embeddings of more realistic Kerr, or rotating BTZ black holes.