From Asymptotically Flat Gravity to 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.

Figures (1)

• Figure 1: We draw the two relevant geometric frameworks. On the left, we have a causal diamond of radius $L$ in a Minkowski background. The edge modes are its area $A$ and its symplectic partner $\mu$, and they parametrize the spherically symmetric perturbations localized at the bifurcate horizon ${\mathcal{B}}$. On the right, we have the Penrose diagram of an asymptotically flat spacetime, with the blue ripples indicating fluctuations. We blow up spatial infinity $i^0$ and focus on its future boundary ${\mathcal{I}}^+_-$. The fluctuations are parametrized by the leading soft graviton mode $N$ and its symplectic partner $C$, and they are localized at ${\mathcal{I}}^+_-$.