Geometry Seminar: E. Minguzzi (Università degli Studi di Pisa)
Geometry Seminar (Geometric Analysis)
Speaker: Ettore Minguzzi (Università degli Studi di Pisa)
Title: On the constancy of surface gravity (temperature) for non-degenerate compact null hypersurfaces
Speaker: Ettore Minguzzi (Università degli Studi di Pisa)
Title: On the constancy of surface gravity (temperature) for non-degenerate compact null hypersurfaces
Abstract: In Lorentzian geometry, a generic compact null hypersurface may not admit a tangential lightlike geodesic vector field. A classical conjecture (Isenberg-Moncrief) states that a lightlike pregeodesic vector field of constant surface gravity can be found in the totally geodesic case, provided suitable energy or convergence conditions are imposed.
Surface gravity is significant due to its physical interpretation as temperature, particularly in the context of black hole physics. In this talk, I motivate interest in this problem and outline a recent proof of the conjecture in the non-degenerate case (i.e., under the existence of at least one incomplete generator).