The Geometry of Small Causal Cones

Abstract

We derive a formula for the spacetime volume of a small causal cone. We use this formula within the context of causal set theory to construct causal set expressions for certain geometric quantities relating to a spacetime with a spacelike hypersurface. We also consider a scalar field on the causal set, and obtain causal set expressions relating to its normal derivatives with respect to the hypersurface.

References in corpus (5)

• Entanglement Equilibrium and the Einstein Equation
• Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
• Directions in Causal Set Quantum Gravity
• The Discrete Geometry of a Small Causal Diamond
• Boundary Terms for Causal Sets

Cited by in corpus (4)

• The causal set approach to quantum gravity
• Geometry of small causal diamonds
• Area deficits and the Bel-Robinson tensor
• Horizon Molecules in Causal Set Theory