FYSS7320 General Relativity (9 cr)

• Special relativity and differential geometry in the flat spacetime

• Differential geometry in curved spacetimes

• Covariant derivative, parallel transport, geodesics, Riemann tensor

• Einstein equations, Newtonian limit, action of general relativity

• Schwarzschild solution: dynamics, applications

• Schwarzschild black hole: event horizon, causal structure, coordinate transformations, maximally extended solution

• Gravitational waves: linear perturbations around the Minkowski spacetime, equation of motion for gravitational waves, impacts on test masses, sources of gravitational waves  
  
• Maximally symmetric spacetimes, RW metric
  

After the course the student should be able to:

• Explain the basic features of the special and general relativity and their differences.

• Compute the transformation of tensor components under coordinate transformations, take covariant derivatives of tensors, compute distances in the space-time and compute the connection coefficients and components of the Riemann tensor.

• Determine the geodesic equations, explain their meaning and solve them in specific cases.

• Explain the structure and contents of the Einstein equations, derive them by varying the action.

• Write down the solution for the Schwarzschild spacetime, compute trajectories of test particles and gravitational redshifts in it.

• Write down the metric for a Schwarzschild black hole inside the event horizon, form the maximally extended solutio and explain its causal structure.

• Derive equations of motion for gravitational waves around the Minkowski solution, investigate how gravitational waves distort mutual distances of test masses, and compute the gravitational wave signal of a circular binary star system.  

FYSA2004 Modern Physics, part B (special general relativity might be useful)

lecture notes, course book