2025/02/19 by Rossella Bartolo, Bartolo, Rossella, Erasmo Caponio +5
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2502.14108
openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent papers on spacetimes with a signature-changing metric, the concept of a Lorentzian-Euclidean black hole and new elements for Lorentzian-Riemannian signature change have been introduced. A Lorentzian-Euclidean black hole is a signature-changing modification of the Schwarzschild spacetime satisfying the vacuum Einstein equations in a weak sense. Here the event horizon serves as a boundary beyond which time becomes imaginary. We demonstrate that the proper time needed to reach the horizon remains finite, consistently with the classical Schwarzschild solution. About Lorentzian to Riemannian metric transitions, we stress that the hypersurface where the metric signature changes is naturally a spacelike hypersurface which can be identified with the future or past causal boundary of the Lorentzian sector. Moreover, a number of geometric interpretations appear, as the degeneracy of the metric corresponds to the collapse of the causal cones into a line, the degeneracy of the dual metric corresponds to collapsing into a hyperplane, and additional geometric structures on the transition hypersurface (Galilean and dual Galilean) might be explored.