Quantum Area Fluctuations from Gravitational Phase Space

Abstract

We study the gravitational phase space associated to a stretched horizon within a finite-sized causal diamond in $(d+2)$-dimensional spacetimes. By imposing the Raychaudhuri equation, we obtain its constrained symplectic form using the covariant phase space formalism and derive the relevant quantum commutators by inverting the symplectic form and quantizing. Finally, we compute the area fluctuations of the causal diamond by taking a Carrollian limit of the stretched horizon in pure Minkowski spacetime, and derive the relationship $⟨(\Delta A{)}^2⟩\ge \frac{2\pi G}{d}⟨A⟩$, showing that the variance of the area fluctuations is proportional to the area itself.

28 pages, 1 figure; v2: minor edits, version to appear in JHEP

References in corpus (8)

• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Gravitational action with null boundaries
• Quasinormal spectrum and the black hole membrane paradigm
• Modular Fluctuations from Shockwave Geometries
• Quantum Null Geometry and Gravity
• An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes
• Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Modular Fluctuations in Cosmology

Cited by in corpus (3)

• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• From Asymptotically Flat Gravity to Finite Causal Diamonds
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes