# Motion of membranes in space-times with torsion

## TL;DR

This paper investigates the dynamics of membranes in space-times with torsion, deriving their equations of motion through a geometro-elastic stress tensor that accounts for curvature and torsion effects.

## Contribution

It introduces a novel stress tensor framework for membranes in torsioned space-times and derives their equations of motion, including special cases like Dirac and Onder-Tucker bubbles.

## Key findings

- Derived the membrane's equation of motion in torsioned space-times.
- Formulated a stress tensor combining intrinsic and extrinsic properties.
- Provided an example involving membranes on manifolds with generalized Killing spinors.

## Abstract

The motion of membranes interacting with external fields in space-times with curvature and torsion is considered. The intrinsic and extrinsic properties of the immersion are fused together to form a stress tensor for the corresponding material hypersurface. This geometro-elastic stress tensor is part of the total stress tensor by which it looses the symmetry and divergenceless properties because of the existence of torsion. The equation of motion of the membrane is given by equating the total stress tensor to a non-zero value determined by the curvature and torsion of the ambient space-time. Dirac and \"Onder-Tucker bubbles are considered as special cases. An example of the membrane motion on a manifold admitting a generalized Killing spinor is given.