# Non-relativistic geometry of holographic screens

## TL;DR

This paper proposes describing the intrinsic geometry of holographic screens using Newton-Cartan geometry and demonstrates this with covariant evolution equations derived from the Brown-York formalism.

## Contribution

It introduces a novel approach to holographic screen geometry using Newton-Cartan theory and formulates covariant evolution equations with explicit stress tensor and energy expressions.

## Key findings

- Covariant form of evolution equations for holographic screens
- Expressions for stress tensor, energy density, and momentum derived
- Validation of Newton-Cartan geometry as a suitable framework

## Abstract

We propose that the intrinsic geometry of holographic screens should be described by the Newton-Cartan geometry. As a test of this proposal, we show that the evolution equations of the screen can be written in a covariant form in terms of a stress tensor, an energy current, and a momentum one-form. We derive the expressions for the stress tensor, energy density, and momentum one-form using Brown-York action formalism.