LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – PHYSICS
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FOURTH SEMESTER – APRIL 2008
PH 4956 – GRAVITATION AND COSMOLOGY
Date : 23/04/2008 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
PART A
ANSWER ALL QUESTIONS. EACH QUESTION CARRIES 2 MARKS.
1.State Mach’s principle.
- Give the transformation law for a contra-variant tensor of rank n.
3.When is an affine connection said to be Riemannian ?
- Define the Ricci tensor. How is it related to the Einstein tensor ?
- State Birkhoff’s theorem.
6.What is Thomas precession ?
7.Define nucleonic mass of a compact spherical object.
- What is a QSO ? What is the order of magnitude of its density ?
- State Hubble’s law.
- What is the significance of the CMB ?
PART B
ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 7.5 MARKS.
- Show that the Christofel symbols do not transform like a tensor.
12.Obtain Einstein’s equation through a heuristic derivation.
13.Obtain the most general spherically symmetric line element.
- Show that in the extremely dense state of nuclear density the nucleonic mass which can be supported
in equilibrium is less than 3 solar masses.
15.How is the age of the Universe estimated?
PART C
ANSWER ANY FOUR QUESTIONS.EACH QUESTION CARRIES 12.5 MARKS.
- (a) Why is Newtonian gravitation considered unsatisfactory in the framework of modern theoretical
physics ?
(b) What is a geodesic ? Obtain the geodesic equation.
- (a) Explain the role of the Riemannian tensor in describing the geometrical properties of space-time.
(b) Use the action principle to obtain the generalized laws of dynamics.
- Explain gravitational redshift. How is Mossbauer effect used to measure it in a terrestrial experiment.
- Explain the gravitational collapse of a homogeneous dust ball. Show the variation of the scale factor
as a function of time.
- (a) Discuss the observational background of cosmology.
(b) Explain Olber’s paradox.
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