3. Tensor fields
4. Differential forms
5. Lie groups
6. Linear connections
7. Riemannian geometry
8. Matter in a gravitational field
9. Einstein's equations
11. The Schwarzschild solution
12. Cosmological solutions
These notes are for use by SISSA students.
© Roberto Percacci 2007
Version 1.00, October 2013
On differential geometry:
C.J. Isham, "Modern differential geometry for physicists", World Scientific (1999)
For the mathematically inclined, this book begins with a useful introduction to general topology, which is not covered in my notes. The rest of the book treats more or less the same material of my chapters 2-6. It does not cover Riemannian geometry.
Y. Choquet-Bruhat, C. de Witt-Morette, M. Dillard-Bleick "Analysis. manifolds and physics" North Holland (1977)
A broad review of mathematical physics including quite a bit of functional analysis.
On quantum effects in curved spacetimes:
N.D. Birrell and P.C.W. Davies "Quantum fields in curved space" Cambridge University Press (1984)
V.F. Mukhanov and S. Winitzki "Introduction to quantum effects in gravity" Cambridge University Press (2007)
L. Parker and D. Toms "Quantum field theory in curved spacetime" Cambridge University Press (2009)