Existence of conserved quantities and their algebra in curved spacetime

TL;DR

This paper investigates the existence and algebra of conserved quantities in a class of dynamical systems within generic curved spacetimes, highlighting their role in understanding symmetries and geodesic behavior in General Relativity.

Contribution

It demonstrates the existence of conserved charges and their algebra for dynamical systems in generic curved spacetimes, extending understanding of symmetries in General Relativity.

Findings

Conserved quantities exist for certain dynamical systems in curved spacetime.

These conserved quantities form an algebra reflecting underlying symmetries.

The results aid in solving geodesic equations and understanding spacetime features.

Abstract

In General Relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving geodesic equations of a general spacetime manifold. Furthermore, knowing all possible conserved quantities of a system tells about the hidden symmetries of that system since, conserved quantities are deeply connected with the symmetries of the system, which are very important in their own right. Conserved quantities are also useful to capture certain features of spacetime manifold for an asymptotic observer. In this article, we show the existence of these conserved charges and their algebra for a class of dynamical systems in a generic curved spacetime.