PH 3952 – GRAVITATION AND COSMOLOGY

Date : 09-11-10 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

PART A

ANSWER ALL QUESTIONS 10 X 2 = 20

What are the two approaches to General Relativity ?
State Mach principle.
What are pseudo tensors ? Give an example.
When is an affine connection said to be Riemannian ?
State Birkhoff theorem.
What is Thomas precession ?
Define nucleonic mass of a compact spherical object.
When does the general relativistic contribution to the binding energy of a QSO become significant ?
State Hubble’s law.
State the cosmological principle.

PART B

ANSWER ANY FOUR QUESTIONS 4 X 7.5 = 30

Explain the conflict between Newtonian gravitation and special Relativity.

12 Deduce the conservation law for the energy-momentum tensor..

13 Derive the most general spherically symmetric line element.

14 Show that in the extremely dense state of nuclear density the nucleonic mass which can be supported in equilibrium is less than three solar masses.

15 Explain Olber’s paradox.How is it resolved?

PART C

ANSWER ANY FOUR QUESTIONS 4 X 12.5 = 50

(a)Explain and interpret the Lie derivative of A along B , where A and B are two vector fields.

(b) Show that the Christofel symbols do not transform like a tensor. (5+7.5)

(a)Explain the two important properties of a geodesic.

(b) Obtain the equation for a geodesic . (6+6.5)

18 (a) Discuss particle orbits in the Schwarzschild space-time using Newtonian approximation.

(b) Calculate the radar echo delay due to the Sun’s gravitational field. (7.5+5)

(a) Discuss the Schwarzschild solution of Einstein’s equation and obtain the exterior Schwarzschild metric.

(b) Discuss Fowler’s theory of a QSO. (7.5+5)

(a) Explain the significance of the cosmic microwave background.

(b) Discuss the observational background of cosmology. (6+6.5)

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