Speaker
Description
Using the Christodoulou-Ruffini and Hawking mass-energy relations as a starting point, we investigate the properties of extreme black holes from a differential-geometry perspective. The geometry of black-hole horizons is of fundamental importance, as it offers deep insight into the structure of spacetime and the behavior of gravitating systems in the strong-field regime. We present two remarkable classes of extreme black holes in which the angular momentum and electric charge are related to the irreducible mass through either an irrational constant or the golden ratio.
In the first class, the fundamental physical quantities are connected to the irreducible mass by an irrational factor. A striking consequence is that the Gaussian curvature vanishes at the poles of the horizon, implying locally flat regions on the black-hole surface. This unusual and unexpected geometric property may significantly affect the propagation of particles and light near the polar caps.
In the second class, all physical quantities, including the irreducible mass itself, are governed by the golden ratio. This special symmetry gives rise to distinctive geometric structures and suggests intriguing connections between black-hole geometry, horizon topology, and fundamental mathematical constants.
These results are derived within Smarr’s differential-geometric framework, which also allows us to analyze, in a unified way, the hidden symmetries underlying the Schwarzschild, Kerr, and Reissner–Nordström solutions. Three representative cases corresponding to irreducible masses M=10 M_{Planck}, M=3 M⊙, and M=108 M⊙ are explicitly discussed. Particular attention is devoted to the structure and properties of the umbilic points of the horizon geometry.
Finally, we estimate the extractable energy of extreme Kerr–Newman black holes through reversible and irreversible transformations, distinguishing between families of horizons that can be globally embedded in Euclidean space (E3) and those requiring pseudo-Euclidean embeddings.