Holographic Evolution with Dynamical Boundary Gravity

TL;DR

This paper introduces a method to dynamically evolve a strongly coupled gauge theory coupled with four-dimensional gravity using holography, enabling the study of evolving spacetimes like expanding or collapsing universes.

Contribution

It presents a novel scheme to evolve both boundary and bulk spacetimes dynamically in holography, incorporating Einstein's equations with quantum stress tensor expectations.

Findings

Successfully evolved far-from-equilibrium states leading to expanding universes

Demonstrated collapse scenarios with dynamical boundary conditions

Provided a framework for simulating cosmological evolution holographically

Abstract

Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a four-dimensional, strongly interacting gauge theory coupled to four-dimensional dynamical gravity in the semiclassical regime. As in previous work, we use holography to evolve the quantum gauge theory stress tensor, whereas the four-dimensional metric evolves according to Einstein's equations coupled to the expectation value of the stress tensor. The novelty of our approach is that both the boundary and the bulk spacetimes are constructed dynamically, one time step at a time. We focus on Friedmann-Lema\^itre-Robertson-Walker geometries and evolve far-from-equilibrium initial states that lead to asymptotically expanding, flat or collapsing Universes