In this talk we will construct a basis of quantum gravity states by cutting the Euclidean path integral. These states are made by inserting heavy dust shell operators on the asymptotic boundary. We will use this basis to resolve two puzzles :
(1) The two boundary gravity Hilbert space seemingly does not factorise, which is in tension with holography.
(2) Gibbons and Hawking proposed the gravity thermal partition function is computed by the euclidean path integral with a periodic time boundary condition. Why is does this perform a trace over gravity states?
To resolve these puzzles we will introduce some tricks that simply the evaluation of the gravity path integral in the saddle point approximation.