Professor: Fridolin Weber (UC/San Diego - EUA)

In 1905, Albert Einstein published four revolutionary papers about the world we live in. Among the ideas that would come from his work were predictions about space and time so extraordinary that even Einstein himself refused to believe they could be true. Now, one hundred years later, not only do we have actual evidence that Einstein's ideas are correct, but the study of these once wild ideas—from time travel, to the big bang, to dark energy, to compact stars—is at the cutting edge of science in the 21 st century. Astrophysicists distinguish between three different types of compact stars. These are white dwarfs, neutron stars, and black holes. The latter constitute a region of space which has so much mass-energy concentrated in it that no particles (not even light) inside the black hole's radius can escape the black hole's gravitational pull. Neutron stars are dense, neutron-packed remnants of massive stars that blew apart in supernova explosions. They are typically about ten kilometers across and spin rapidly, often making many hundred rotations per second. Finally, white dwarfs are formed from low and medium mass stars, with masses less than about eight times the mass of our Sun. A typical white dwarf is about as massive as the Sun, yet only slightly bigger than the Earth. This makes white dwarfs contain one of the densest forms of matter, surpassed only by neutron stars which may be ten to twenty times as dense as atomic nuclei. The exploration of the properties of such matter has become a forefront area of modern physics. This course constitutes an introduction into the fascinating physics of compact stars, general relativity, and the widely unknown equation of state of ultra-dense nuclear matter.

The course is designed for students at the graduate level and covers topics from different branches of physics, ranging from relativistic thermodynamics and statistical physics, to nuclear physics, to particle physics, to special and general relativity. The course begins with a review of the mathematical concepts required to develop Einsteins theory of special relativity in tensor notation. The next part of this course concentrates on the curved space-time of general relativity and on Einstein's famous field equation. The latter will be derived during the lectures and the students will learn how to solve them for spherically symmetric as well as rotationally deformed mass-energy distributions. In the last part of the course, the rapidly growing body of observed astrophysical data will be reviewed and their consequences for the interpretation of compact stars and the nuclear equation of state will be explored. The individual lectures are structured as follows:

• Lecture 1: Mathematical Background (one-forms, dual basis, definition of tensors, tensor transformations, covariant and contravariant quantities)
• Lecture 2: Special Relativity (Lorentz covariance, special relativity in tensor notation, relativistic variational principle, lagrangian of relativity theory, geodesic equation)
• Lecture 3: Curved Space-Time (derivation of Christoffel symbols, derivation of energy-momentum tensor, covariant differentiation)
• Lecture 4: Einstein's Field Equation (Parallel transport, derivation of Riemann curvature tensor, Bianci identities, Ricci tensor, derivation of Einstein's general relativistic field equation, cosmological constant, classical limit of Einstein's field equation)
• Lecture 5: Models for the Nuclear Equations of State (EOS) (lagrangians proposed for dense baryonic matter, relativistic Green's functions, Dyson equation, T-matrix approximation, relativistic mean-field approximation, quark-hadron phase transition, quark matter, color superconductivity)
• Lecture 6: Spherically Symmetric Stars (Tolman-Oppenheimer-Volkoff solution, white dwarfs, neutron stars, quark stars, Schwarzschild black holes, innermost stable orbits)
• Lecture 7: Pulsars and Kerr Black-Holes (Rotation in general relativity, Lense-Thirring (frame dragging) effect, ergospheres, criteria for stable rotation, general relativistic Kepler (mass shedding) frequency, gravitational radiation reaction driven instabilities, redshift, blueshift, moment of inertia)
• Lecture 8: Astrophysical Constraints on the Nuclear EOS (current status of neutron star observations, future instruments and observations, neutron star observables, mass-radius measurements, heavy neutron star candidates, cool compact objects, magnetars and anomalous X-ray pulsars, quasi-periodic oscillations)