From Asymptotically Flat Gravity to Finite Causal Diamonds

TL;DR

This paper links the soft sector of asymptotically flat gravity to finite causal diamonds in Minkowski space, identifying soft modes with geometric fluctuations of the diamond's size.

Contribution

It establishes a geometric interpretation of soft graviton modes as radial and transverse fluctuations of causal diamonds in flat spacetime.

Findings

Soft graviton modes correspond to radial fluctuations of causal diamonds.

Goldstone modes involve both radial fluctuations and their symplectic partners.

The phase space of soft modes matches that of finite causal diamonds.

Abstract

We demonstrate that the phase space of the soft sector of asymptotically flat gravity in four spacetime dimensions can be identified with that of a spherically symmetric finite casual diamond in Minkowski spacetime. The leading soft graviton mode is geometrically identified with the radial fluctuation of the causal diamond size, while the Goldstone mode involves both the radial fluctuation and its symplectic partner. This allows us to relate the radial fluctuations of the causal diamond with the asymptotic transverse fluctuations parametrized by the soft modes.