The Development of GR in India

With emphasis on Early Days

Main thrust area

• In the period between two world wars the general theory of relativity was a subject of research in the mathematics departments of Indian universities

• The main reason was that GR with its base in differential geometry, was looked upon as a hard mathematical exercise

The role of physics?

• The lack of many experiments in GR also played a role in turning physicists away

• But there was an exception: the experiment organized by Eddington of

measuring the bending of light by

gravity…how was it seen in India?

The physicist M.N. Saha intervened…

Saha’s article in the Statesman,Calcutta, Nov. 13, 1919

• Statesman: November 13, 1919• “A Scientific Sensation – Certainty of Ages Overthrown by Recent Experiments” “The announcement conveyed in yesterday’s

Reuter’s cable that Professor Einstein’s theory of the equivalence of Time and Space has at last been verified by observations made during the last total solar eclipse will be hailed with joy by scientific circles all over the world…

Query by a reader “Simplicimus”

…but I confess myself still completely at a loss…apparently,on this view, an inch is not always an inch but more or less according to circumstances. Obviously I am talking nonsense, which may be regarded as the pathological effect of Reuter’s and Dr Saha’s explanations of things on an average mind. Can nobody help?

Sir Oliver Lodge’s reaction

Lodge had been pro-Newton in the controversy

and had predicted the Newtonian value for the

bending of light. Also he had tried to explain

the shift of the Perihelion of Mercury

by arguing that masses vary with speed.

Eddington shot that approach down. “Traps may

lie in wait for the Unwary” warned Lodge !

GR in India: the Early Days

The new theory (GR) was highly

Mathematical and flourished more in

Maths departments of Indian universities!

Thus two criteria mattered:

1. The field equations should be solvable exactly

2. There should be some symmetries

Pioneers in GR in India

GR took off in India mainly in two places because of specific persons who played a leadership role…

1. Calcutta University : Nikhil Ranjan Sen (1924---)

2. Benares Hindu University: Vishnu Vasudeva Narlikar (1932---)

The Calcutta School

1911 saw three boys scoring high marks in the Intermediate examination at Rajsahi Cillege in Dacca. They were in order of merit: 1. S.N. Bose 2. M.N. Saha 3. N.R. Sen

The first two went to theoretical physics while Sen went to applied mathematics. Sen studied relativity and cosmogony at Berlin University under Von Laue

The Calcutta School

Sen’s works involved theoretical models

as solutions of Einstein’s equations with

some physical property. Well known

amongst these are:

1. Static solution with spherical symmetry in most general form

2. Spherical shell with surface matter

The Calcutta School

3. Relationship to de Sitter universe: A transformation of the solution inside the shell leads to the de Sitter model4. Equilibrium of a charged particle with a definite spherical boundary[ For any distribution of charge inside representable by an analytical function ¾ of the energy of the particle is electrical and ¼ gravitational]

The Calcutta School

Who was B. Datt?B.Datt has a paper on gravitational collapse of a spherically symmetric mass distribution [ 1938 : Z. Phys. 108, 314] This came before the much cited paperBy Oppenheimer and Snyder [1939: Phys. Rev. 56, 455] covering the same topic.

Who was B. Datt?

My enquiries so far have drawn a

blank!

Was he part of N.R. Sen’s school?

Any information would be welcome!

Unified Field Theory

In the latter half of his life Einstein Was keen to find a unified field Theory. S.N. Bose also tried his hand but no specific result emerged.Others from Calcutta school Included Gangopadhyaya, Dutta etc.

The Benares School

V.V. Narlikar joined BHU in 1932 as the Head of Maths Department after a brightCareer in Cambridge as student of Eddington.

The episode of cosmological models now known as Friedmann-Lemaitre Robertson-Walker models

Some highlights of the BHU work

Curvature invariants T.Y.Thomas had proved that in 4D Riemannian spacetime only 14 curvature invariants can be constructed. In 1946 the work of Narlikar and Karmarkar first showed how to construct them. In 1952 Gehanau and Debevar did the same work but now credit is given to N+K.

The Vaidya Solution

• P.C. Vaidya wanted to do research under VVN but had no scholarship to support this work. He used his savings instead and stayed in Benares until they ran out. He was married with a child and thus had a family to support.

• He was able to live this way for a year and had good interaction with VVN during 1942-43.

The Vaidya Solution

• VVN suggested the problem of the gravitational field of a radiating star

• After many trial-error attempts PCV suggested writing the exterior as made up of ‘radiation fluid’ representing flow of radiation outwards from the star.

• VVN liked the suggestion and immediately derived the first equation.

The Vaidya Solution

• There were two equations remaining.• PCV describes that he managed to

write the two equations and solve them also without help from VVN as he was away…thanks to VVN’s strategy of introducing ‘silent’ phases in his lectures to allow the students ‘time to ponder’.Thus came the Vaidya solution.

• VVN gave all the credit to PCV

Research areas in BHU

• Exact solutions• Solutions of equations of unified field theory

of Einstein and Schrödinger• Equations of motion derived from EIH

method applied to field equations• The geometrical and physical properties of

metrics satisfying the GR equations• Ramji Tiwari, K.P. Singh, B.R. Rao,...• VVN’s query to Chandra

Concluding Remarks

• GR provided ample scope to anyone interested in a mathematical problem.

• The rather negative response of SC may have delayed the origin of the subject of relativistic astrophysics.

• Datt’s solution in Calcutta and the Vaidya solution in BHU represent the highlights of early GR work in India