(i) Develop a firm grasp of the physical principles behind Special and General Relativity and their main consequences;

(ii) Develop technical competence in the mathematical framework of the subjects - Lorentz transformation, coordinate transformations and geodesics in Riemann space;

(iii) Develop understanding of some of the classical tests of General Relativity - perihelion shift, gravitational deflection of light;

(iv) Develop understanding of basic concepts of black holes.

(LO1) Understand why space-time forms a non-Euclidean four-dimensional manifold.

(LO2) Develop technical competency in calculations involving Lorentz transformations, energy-momentum conservation, and the Christoffel symbols.

(LO3) Understand the arguments leading to the Einstein's field equations and how Newton's law of gravity arises as a limiting case.

(LO4) Develop technical competency in calculations of the trajectories of bodies in a Schwarzschild space-time.

(S1) Problem solving skills

(S2) Numeracy

Newtonian mechanics and its limitations.

Principles of special relativity. Lorentz transformation: derivation, properties.

Relativistic kinematics: length contraction, time dilation, velocity addition. Minkowski space formulation.

Relativistic particle mechanics: energy-mass relation, four-momentum conservation, scattering.

Riemann space, Properties of tensors. Parallel displacement, geodesics, covariant derivatives. Curvature tensor and scalar, Ricci tensor.

Equivalence principle, gravitational time dilation, non-Euclidean space-time. Freely falling bodies, weak field limit. Field equations, cosmological constant.

Schwarzschild solution and its geodesics. Classical tests of General Relativity. Black holes.