LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

FG 12

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.

2. Give the transformation law  for a  contra-variant tensor of rank n.

3.When is an affine connection said to be Riemannian ?

4. Define the Ricci tensor. How is it related to the Einstein tensor ?
5. State Birkhoff’s theorem.

6.What is Thomas precession ?

7.Define nucleonic mass of a compact spherical object.

8. What is a QSO ? What is the order of magnitude of its density ?
9. State Hubble’s law.
10. What is the significance of the CMB ?

 

PART B

 

ANSWER ANY FOUR QUESTIONS. EACH QUESTION CARRIES 7.5 MARKS.

 

11. 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.

14. 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.

 

16. (a) Why is Newtonian gravitation considered unsatisfactory in the framework of modern theoretical

physics ?

(b) What is a geodesic ? Obtain the geodesic equation.

17. (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.

18. Explain gravitational redshift. How is Mossbauer effect used to measure it in a terrestrial experiment.
19. Explain the gravitational collapse of a homogeneous dust ball. Show the variation of the scale factor

as  a function of time.

20. (a) Discuss the observational background of cosmology.

(b) Explain Olber’s paradox.

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2010

    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

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

 

PART B

ANSWER ANY FOUR  QUESTIONS                                                                   4 X 7.5 = 30

11. 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

 

16. (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)

17. (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)

19. (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)

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

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

 

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – APRIL 2012

PH 3952 – GRAVITATION AND COSMOLOGY

 

 

 

Date : 28-04-2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

Answer ALL questions                                                                                                                  (10×2=20)

1. What are the desirable features of a theory of gravitation?
2. State Mach principle.
3. Define Ricci tensor.
4. When is an affine connection said to be Riemannian?
5. State Birkhoff theorem.
6. What is Thomas precession?
7. Define nucleonic mass of a compact spherical object.
8. When does the general relativistic contribution to the binding energy of a QSO become significant?
9. State Hubble’s law.
10. State the cosmological principle.

PART – B

Answer any FOUR questions                                                                                                                (4×7.5 = 30)

11. Explain why Newtonian gravitation is considered unsatisfactory in the framework of modern theoretical physics.

12 Discuss the role of energy-momentum tensors in general theory of relativity.

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 3 solar masses.

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

 

PART – C

Answer any FOUR questions                                                                                                              (4×12.5 =50)

16. (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.

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

(b) Obtain the equation for a geodesic.

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.

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

(b) Discuss Fowler’s theory of a QSO.

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

(b) Discuss the observational background of cosmology.

 

 

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