Reading: Schutz 5; Hobson 3; Rindler 10.
Apart from the change from to its more general counterpart, g , we have
not had to change much in moving from SR to more general coordinates, but
this comes to a
Equations of motion
Reading: Schutz 6; Hobson 3; Rindler 10.
In this lecture we are nally going to see how the metric determines the
motion of particles. First we discuss the concep
More on the metric and how it transforms.
Reading: Hobson, 2.
ds2 = g dx dx ,
is a quadratic function of the coordinate dierentials.
This is the denition of Riemannian geometry, or more c
Transformations between coordinates
Reading: Schutz, 5 and 6; Hobson, 2; Rindler, 8.
Consider the following situation:
Figure: A freely falling laboratory with two small masses
Introduction to tensors, the metric tensor, index raising and lowering
and tensor derivatives.
Reading: Schutz, chapter 3; Hobson, chapter 4; Rindler, chapter 7
Not all physical quantities can be represented by s
Special Relativity II.
Reading: Schutz chapter 2, Rindler chapter 5, Hobson chapter 5
The interval of SR
To cope with shifts of origin, restrict to the interval between two events
s2 = (ct2 ct1 )2 (x2 x1 )2 (y2 y1 )
Contravariant and covariant vectors, one-forms.
Reading: Schutz chapter 3; Hobson chapter 3
Scalar or dot product
We have had
V V = V V .
If A and B are four-vectors then V with components
V = A + B ,
is also a four-vect
Special Relativity I.
To recap some basic aspects of SR
To introduce important notation.
Reading: Schutz chapter 1; Hobson chapter 1; Rindler chapter 1.
The equivalence principle makes Special Relativity (SR) the s
Introduction to GR
Handouts ? and ?
Presentation of some of the background to GR
Reading: Rindler chapter 1, Weinberg chapter 1, Foster & Nightingale
First refer students to the website,