Rindler Fluids from Gravitational Shockwaves

Abstract

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

arXiv comment21 pages, 1 figure

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Cited by in corpus (6)

• Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Quantum Area Fluctuations from Gravitational Phase Space
• Modular Fluctuations in Cosmology
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• Phenomenology of Holography via Quantum Coherence on Causal Horizons
• From Asymptotically Flat Gravity to Finite Causal Diamonds