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{\bf The Theory of Relativity:}

{\bf Special and General}
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{\bf George Efstathiou}
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{\bf CONTENTS}
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 Page &  &  \\
  1 & $\dots \dots$   & 1.$\;\;$  Introduction to Special Relativity \\ 
  9 & $\dots \dots$   & 2.$\;\;$   Tensors \\ 
  19 & $\dots \dots$  & 3.$\;\;$   Relativistic kinematics\\ 
  28 & $\dots \dots$  & 4.$\;\;$  Electromagnetism\\ 
  35 & $\dots \dots$  & 5.$\;\;$  Constructing a theory of gravity\\ 
  41 & $\dots \dots$  & 6.$\;\;$  Freely falling particles and affine connections\\ 
  48 & $\dots \dots$  & 7.$\;\;$  Riemannian geometry\\ 
  54 & $\dots \dots$  & 8.$\;\;$  Curvature\\ 
  62 & $\dots \dots$  & 9.$\;\;$  Parallel transport\\ 
  68 & $\dots \dots$  & 10. Energy-momentum tensor\\ 
  74 & $\dots \dots$  & 11. The gravitational field equations\\ 
  79 & $\dots \dots$  & 12. Are the field equations unique?\\ 
  74 & $\dots \dots$  & 11. The gravitational field equations\\ 
  84 & $\dots \dots$  & 13. The Schwarzchild metric\\ 
  89 & $\dots \dots$  & 14. Motion in the Schwarzchild metric\\ 
  96 & $\dots \dots$  & 15. Precession of planetary orbits and radar echos\\ 
  104 & $\dots \dots$  & 16. Black holes\\ 
  114 & $\dots \dots$  & 17. Do black holes exist?\\ 
  125 & $\dots \dots$  & 18. Penrose diagrams and the Kerr metric\\ 
  141 & $\dots \dots$  & 19. Gravitational waves\\ 
  150 & $\dots \dots$  & 20. Field equations in presence of matter: Cosmology\\  160 & $\dots \dots$  & 21. Cosmological models\\ 
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{\bf How to use these notes}
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There are lots of textbooks on special and general relativity.  My
personal favourite is Weinberg's book {\it Gravitation and Cosmology}
(John Wiley and Sons).
This book is a bit old now and goes to a higher level than is required
for this course. It is also expensive.  For this course I recommend
d'Inverno's book {\it Introducing Einstein's Relativity}
(Oxford University Press) . It is cheap and well written. However,
it approaches the subject from an applied mathematician's point of
view whereas I prefer to adopt a more intuitive `physics' approach.  I
have therefore written these notes for three purposes.  Firstly, I
introduce the mathematics {\it only as it is needed}. The physics
behind the theory drives the need for mathematics, not the other way
round. Secondly, although I prefer a `physical' approach to the
subject, some of the advanced mathematical techniques developed by
professional relativists ({\it e.g.} Penrose diagrams) are easy to
understand and deserve exposure to an undergraduate audience.  These
advanced techniques can help you understand some of the more bizarre
aspects of the theory that are often referred to in programmes like
Star Trek. For example:
What happens if you fall into a black hole?
What is a wormhole? Can you travel to another Universe? Are these
ideas pure science fiction, or do they have a basis in physical
theory?  Thirdly, General Relativity involves a lot of tedious
algebra. Rather than plough through this algebra on the blackboard,
which would bore you and take a long time, you can refer to these
notes. Most of the algebra is worked through here. You will have seen
cookery programmes where the cook prepares a dish, pops it in the oven,
and then immediately pulls out another one saying `here is one that
I prepared earlier'.  That is how I want to approach the
lectures. Instead of ploughing through complicated algebra, I will
sometimes work partially through examples and then pull out
results `ready made' from these notes. There is no sleight of hand,
the algebra is done in these notes. To get the most out of these
notes, I would like you {\it to work through all of the algebra}. If
you reproduce the calculations in these notes, you will gain
experience in handling tensors and in solving problems in Special and
General Relativity. In my experience, the only way of gaining an
understanding of {\it any} branch of physics
is by working through lots of examples.




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