The light-cone theorem

Abstract

We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light-cone.

24 pages, 1 figure. Minor changes to match published version

References in corpus (1)

• Uniqueness of de Sitter space

Cited by in corpus (15)

• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
• The cosmological constant and the energy of gravitational radiation
• The next detectors for gravitational wave astronomy
• Area Law Unification and the Holographic Event Horizon
• Geometry of small causal diamonds
• Comparison theorems for causal diamonds
• Local causal structures, Hadamard states and the principle of local covariance in quantum field theory
• The mass of light-cones
• A comparison theorem for cosmological lightcones
• Hawking-type singularity theorems for worldvolume energy inequalities
• Mathematical general relativity: a sampler
• Optimal transport on null hypersurfaces and the null energy condition
• Applications of the Hawking Energy in Inhomogeneous Cosmology
• A Scale-Dependent Distance Functional between Past Light Cones in Cosmology
• Integral transform approach to solving Klein-Gordon equation with variable coefficients