Locally Localized Gravity: The Inside Story
Nemanja Kaloper, Lorenzo Sorbo

TL;DR
This paper derives an exact gravitational shock wave solution for a particle on an AdS 3-brane in AdS5, exploring how gravity localizes and behaves across different scales, with implications for holography and RG flow.
Contribution
It provides an exact shock wave solution in AdS5 with a brane, analyzing the scale-dependent behavior of localized gravitons and deriving the 4D Planck mass including higher-order corrections.
Findings
At short distances, the solution matches 5D gravity.
At intermediate scales, the graviton is a composite of modes.
At large scales, the ultralight mode dominates, revealing the fifth dimension.
Abstract
We derive the exact gravitational field of a relativistic particle localized on an 3-brane, with curvature radius , in bulk with radius . The solution is a gravitational shock wave. We use it to explore the dynamics of locally localized tensor gravitons over a wide range of scales. At distances below the shock wave looks exactly like the solution. Beyond the solution approximates very closely the shock wave in 4D space all the way out to distances along the brane. At distances between and , the effective 4D graviton is a composite built of the ultralight mode and heavier gravitons, whereas between and it is just the ultralight mode. Finally beyond the shock reveals a glimpse of the fifth dimension, since the ultralight mode wave function decays to zero at the rate inherited from the…
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