Gravitational Waves in General Relativity

In this paper, we write a summary about general relativity and, in particular,gravitational waves. We start by discussing the mathematics that generalrelativity uses, as well as the geometry in general relativity's spacetime. Afterwards,we explain linearized general relativity and derive the linearizedversions of Einstein's equations. From here, we construct wave solutionsand explain the polarization of gravitational waves. The quadrupole formulais derived, and generation and detection of gravitational waves is brie ydiscussed. Finally, LIGO and its latest discovery of gravitational waves isreviewed