Lecture 9
The connection
Objectives:
The connection
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
Lecture 10
Parallel transport
Objectives:
Parallel transport
Geodesics
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
Lecture 8
Metrics
Objectives:
More on the metric and how it transforms.
Reading: Hobson, 2.
8.1
Riemannian Geometry
The interval
ds2 = g dx dx ,
is a quadratic function of the coordinate dierentials.
This is the denition of Riemannian geometry, or more c
Lecture 7
Generalised Coordinates
Objectives:
Generalised coordinates
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
oating
Lecture 5
Tensors
Objectives:
Introduction to tensors, the metric tensor, index raising and lowering
and tensor derivatives.
Reading: Schutz, chapter 3; Hobson, chapter 4; Rindler, chapter 7
5.1
Tensors
Not all physical quantities can be represented by s
Lecture 3
Special Relativity II.
Objectives:
Four vectors
Reading: Schutz chapter 2, Rindler chapter 5, Hobson chapter 5
3.1
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 )
Lecture 4
Vectors
Objectives:
Contravariant and covariant vectors, one-forms.
Reading: Schutz chapter 3; Hobson chapter 3
4.1
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
Lecture 2
Special Relativity I.
Objectives:
To recap some basic aspects of SR
To introduce important notation.
Reading: Schutz chapter 1; Hobson chapter 1; Rindler chapter 1.
2.1
Introduction
The equivalence principle makes Special Relativity (SR) the s
Lecture 1
Introduction to GR
Requirements:
Handouts ? and ?
Lecture notes.
Objectives:
Presentation of some of the background to GR
Reading: Rindler chapter 1, Weinberg chapter 1, Foster & Nightingale
introduction.
First refer students to the website,