Algebra of conserved quantities in curved spacetime
In General Relativity (GR) finding out geodesics of a given spacetime manifold is an important task because it determines what are the classical processes which 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 a system which is not apparent, since conserved quantities are deeply connected with symmetry properties of the system, which are very important in their own right. This connection is more transparent due to Noether's theorem with the development of the Lagrangian and Hamiltonian formulations of Newtonian mechanics. Conserved quantities are also useful to capture certain features of spacetime manifold for an asymptotic observer. In this report, we have found out the possible methods of finding conserved quantities and their algebra in the dynamics of an object in curved spacetime both in presence and absence of spin of that object which will help in analyzing dynamics of objects in curved spacetime in future run of advanced LIGO with the help of gravitational memory effect and gravitational lensing effect using principles of electromagnetism and GR.