Covariant Generalisation of Codazzi-Raychaudhuri and Area Change Equations for Relativistic Branes

TL;DR

This paper extends classical geometric equations to relativistic branes and fluids in arbitrary backgrounds, providing a fully covariant kinematic framework with projection tensors tilted to the brane worldsheets.

Contribution

It introduces covariant generalisations of Gauss-Codazzi, Raychaudhuri, and area change equations for relativistic branes and fluids in manifolds with metricity and torsion.

Findings

Derived covariant equations for relativistic branes and fluids.

Established a kinematic description using tilted projection tensors.

Applicable to arbitrary background manifolds with metricity and torsion.

Abstract

In this paper we derive the generalisations of Gauss-Codazzi, Raychaudhuri and area change equations for classical relativistic branes and multidimensional fluids in arbitrary background manifolds with metricity and torsion. The kinematical description we develop is fully covariant and based on the use of projection tensors tilted with respect to the brane worldsheets.