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arXiv · 2208.01059

Modular Fluctuations from Shockwave Geometries

Erik Verlinde·Kathryn M. Zurek
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Abstract

Modular fluctuations have previously been shown to obey an area law $\langle ΔK^2 \rangle = \langle K \rangle = {A}/{4 G_N}$. Furthermore, modular fluctuations generate fluctuations in the spacetime geometry of empty causal diamonds. Here we demonstrate the physical origin of these fluctuations, showing that the modular area law, in $d-$dimensionsal Minkowski space, can be reproduced from shockwaves arising from vacuum fluctuations. The size of the vacuum fluctuations is fixed by commutation relations in light-ray operators, of the same form postulated by 't Hooft in the context of black hole horizons.

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Erik Verlinde, Kathryn M. Zurek. 2022-08-01. Modular Fluctuations from Shockwave Geometries. https://doi.org/10.1103/physrevd.106.106011

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