Sudhansu Datta Majumdar

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Sudhansu Datta Majumdar
Visva Bharati

Sudhansu Datta Majumdar (1915 – 1997) was an Indian physicist, and faculty member of the

.

Biography

Born in 1915 in

Majumdar–Papapetrou solution

The phenomenon of static equilibrium for a system of point charges is well known in Newtonian theory, where the mutual gravitational and electrostatic forces can be balanced by fine-tuning the charge suitably with the particle masses. The corresponding generalisation, in the form of static solutions of the coupled, source-free Einstein-Maxwell equations, was discovered by Majumdar and Papapetrou independently^[citation needed] in 1947.^[3][4] These gravitational fields assume no spatial symmetry and also contain geodesics which are incomplete. While work continued on understanding these solutions better, a renewed interest in this metric was generated by the important observation of Israel and Wilson in 1972 that static black-hole spacetimes with the mass being equal to the magnitude of the charge are of Majumdar–Papapetrou form. In the same year, it was shown by Hartle and Hawking^[5] that these spacetimes can be analytically extended to electrovacuum black hole spacetimes with a regular domain of outer communication. They interpreted this as a system of charged black holes in equilibrium under their gravitational and electrical forces. Each one of these many black holes or the multi-black holes system has a spherical topology and hence is a fairly regular object. In a more recent development, the uniqueness of the metric was discussed by Heusler, Chrusciel and others. These and other aspects of the Majumdar–Papapetrou metric have attracted considerable attention on the classical side, as well as in the work and applications from the perspective of string theory. In particular, the mass equal to charge aspect of these models was used extensively in certain string theoretic considerations connected to black hole entropy and related issues.

Majumdar–Papapetrou geometries

Majumdar–Papapetrou geometries generalise axially symmetric solutions to Einstein-Maxwell equations found by Hermann Weyl to a completely nonsymmetric and general case. The line element is given by:

${\displaystyle ds^{2}=-U(x,y,z)^{-2}dt^{2}+U(x,y,z)^{2}(dx^{2}+dy^{2}+dz^{2}),}$

where the only nonvanishing component of the vector potential ${\displaystyle A_{\mu }\ }$ is the scalar potential ${\displaystyle \Phi (x)\ }$. The relation between the metric and the scalar potential is given by

${\displaystyle \Phi (x)=A_{t}(x)=U^{-1}(x),}$

where the electrostatic field is normalised to unity at infinity. The source-free Einstein-Maxwell equations then reduce to the Laplace equation given by:

${\displaystyle \Delta U(x,y,z)={\frac {\partial ^{2}U}{\partial x^{2}}}+{\frac {\partial ^{2}U}{\partial y^{2}}}+{\frac {\partial ^{2}U}{\partial z^{2}}}=0,}$

where U(x,y,z) can be extended in spatial directions until one encounters a singularity or U(x,y,z) vanishes.

It was later shown by Hartle and Hawking

(cancellation of NS-NS and RR forces, NS-NS being the gravitational force and RR being the generalisation of the electrostatic force), etc.

Electrodynamics of crystalline media and the Cherenkov effect

During the fifties, there was a resurgence of interest in the

.

His students and collaborators followed up his studies.^[9][10] A major contribution that resulted was the prediction of a new phenomenon called The Cherenkov analogue of conical refraction. A surprising system of intersecting Cherenkov rings in a biaxial crystal at precisely defined particle energies was predicted. These rings were later found in the photographs taken by V.P. Zrelov at the Proton Synchrotron facility at Dubna, Moscow.

Theory of group representations

Professor Majumdar's work on group theory has its origins in one of his early papers on

.

The forms of the new operators made apparent the fact that the basis states of an irreducible representation of SU(3)are linear combinations of the CG series of SU(2) with the same value of j, m and j1 – j2. Obtaining the SU(2) basis for SU(3) was thereby shown to be closely related to the theory of coupling of two angular momenta. The basic states of SU(3) were later used in deriving the matrix elements of finite transformations of SU(3). Simple analytic continuation of Majumdar's generating function of the SU(2) CGC was later understood to be the 'master function' for the solution of several problems of non-compact groups such as SU(1,1) and SL(2,C). The interpretation and domain of the complex variables, however, change from case to case. For example, in the representation theory of

these represent a pair of complex numbers i.e. spinors transforming according to the fundamental representation of SL(2,C) and the complex conjugate respectively. On the other hand, for the CG problem of SU(1,1), they transform according to two distinct SU(1,1) groups.

References

External links

• The Genius Who Touched My Life, G P Sastry at the Wayback Machine (archived 21 July 2011)
• An Homage to Sudhansu Datta Majumdar, D Basu at the Wayback Machine (archived 21 July 2011)
• The Life and Science of SDM, The Scholars Avenue, Oct 10 2007