# Time evolving fluid from Vaidya spacetime

## TL;DR

This paper constructs a time-evolving fluid model on a boundary in Vaidya spacetime, extending gravity/fluid correspondence to dynamic settings with explicit relations between fluctuations and fluid properties.

## Contribution

It introduces a novel method to derive time-dependent fluid equations from Vaidya spacetime using Petrov type I conditions, expanding the gravity/fluid duality to non-static scenarios.

## Key findings

- Derived explicit relations between fluctuation modes and fluid quantities.
- Formulated a time-dependent compressible Navier-Stokes equation.
- Established a sourced continuity equation governing the fluid evolution.

## Abstract

A time evolving fluid system is constructed on a timelike boundary hypersurface at finite cutoff in Vaidya spacetime. The approach used to construct the fluid equations is a direct extension of the ordinary Gravity/Fluid correspondence under the constrained fluctuation obeying Petrov type I conditions. The explicit relationships between the time dependent fluctuation modes and the fluid quantities such as density, velocity field and kinematic viscosity parameters are established, and the resulting fluid system is governed by a system of a sourced continuity equation and a compressible Navier-Stokes equation with non-trivial time evolution.