About the Fundations of the Black Holes Theory

Hicham Zejli (1) , Florent Margnat (2, 3) , Jean-Pierre Petit (1)

1 LAM - Laboratoire d'Astrophysique de Marseille
2 PPrime [Poitiers] - Institut Pprime [UPR 3346]
3 UP - Université de Poitiers = University of Poitiers

In a broad overview, we discuss the two interpretations that have been given of the outer Schwarzschild solution, depending on whether one opts for uniqueness, in which case the geometric object has a single layer, a structure of a variety with an edge, or non-uniqueness of the solution, i.e. for a configuration in which there are two metrics, each referring to one of the layers of a covering structure with two sheets, joined by a groove sphere. In these two interpretations, the object is non-contractile. The black hole model, as described in Chandrasekhar's 1992 book entitled "Mathematics of Black Holes", is based on the central hypothesis of including in the real world particles whose geodesic trajectories are traversed with pure imaginary proper time, which goes hand in hand with the hypothesis of contractibility of the geometric object, which is then equipped with a central singularity.

Keywords: black hole; Schwarzschild metric; proper time; space bridge; throat sphere; Flamm surface; time factor; two-folds cover; bimetric; Birkhoff theorem; unicity; free fall time; staticity; physical criticity; geometrical criticity; signature; imaginary proper time; crossed term

Domains: Sciences of the Universe [physics]

Hicham Zejli, Florent Margnat, Jean-Pierre Petit. About the Fundations of the Black Holes Theory. 2024. ⟨hal-04637824⟩