Entropy and Non-Collapse in Lorentzian Geometry
Abstract
In this paper, we establish a geometric correspondence between the Lorentzian Raychaudhuri equation and Perelman’s non-collapsing theorem for the Ricci flow. By interpreting the Raychaudhuri equation as a Lorentzian analogue of Ricci flow, we connect geodesic focusing in general relativity to the monotonicity and entropy functionals in geometric analysis. Through this correspondence, we derive a Lorentzian non-collapsing theorem and introduce a covariant entropy functional governing causal volume evolution. Finally, we propose the concept of geodesic entropy capacity—a curvature-bounded limit on the information that can be stored in spacetime regions—which unifies geometric, thermodynamic, and informational aspects of gravity.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Physics Letters B
- Publisher
- Elsevier BV
- Volume
- 875
- Pages
- 140355–140355
- Publication date
- 18 March 2026
- Language
- EN