# Linear and Second-order Geometry Perturbations on Spacetimes with Torsion

## TL;DR

This paper develops a method to analyze first and second-order geometric perturbations, including torsion effects, in spacetimes, revealing a new torsion-related mode that propagates under specific theories.

## Contribution

It introduces a general technique for studying linear and quadratic perturbations in spacetimes with torsion, highlighting a novel torsionon mode.

## Key findings

- Identification of a new torsionon perturbation mode
- Perturbation propagation depends on specific theories
- Framework applicable to realistic astrophysical scenarios

## Abstract

In order to study gravitational waves in any realistic astrophysical scenario, one must consider geometry perturbations up to second order. Here, we present a general technique for studying linear and quadratic perturbations on a spacetime with torsion. Besides the standard metric mode, a "torsionon" perturbation mode appears. This torsional mode will be able to propagate only in a certain kind of theories.