 On successful completion of the module, students should be able to:  Define the EinsteinHilbert action and derive Einstein's equations from an action principle
 Define the stressenergymomentum tensor, obtain its components in an orthonormal tetrad, and obtain explicit expressions for the stressenergymomentum tensor describing a perfect fluid matter distribution
 Derive the canonical form of the Schwarzschild solution to the vacuum field equations under the sole assumption of spherical symmetry, and hence state Birkhoff's Theorem
 Derive expressions for the gravitational redshift, perihelion advance of the planets, and light deflection in the Schwarzschild spacetime and hence discuss solar system tests of General Relativity
 Obtain the geodesic equations in arbitrary spacetimes and hence describe various trajectories such as radially infalling particles or circular geodesics
 Define spatial isotropy with respect to a universe filled with a congruence of timelike worldlines, discuss the consequences of global isotropy on the shear, vorticity and expansion of the congruence and hence construct the FriedmannRobertsonWalker metric
 Obtain the Friedmann and Raychaudhuri equations from the Einstein field equations, solve these equations for the scale factor and discuss the cosmogonical and eschatological consequences of the solutions
 Derive the Einstein equations in the linear approximation and discuss the Newtonian limit in the weakfield, slowmoving approximation
