Maulana Muhammad Ali - A Strategic Point in Indo-Muslim Politics (Comment)

‘A great man’, says Justice Oliver Wendell, Jr, ‘represents a great ganglion in the nerves of society, or to vary the figure, a strategic point in the campaign of history, and part of his greatness consists in being there’. (italic ours). And Maulana Muhammad Ali was one such nerve-centre in Indo-Muslim society during the second and third decades of the twentieth century. Indeed, he was one such strategic point in the onward march of Indo-Muslim politics that eventually found culmination and crystallization in the emergence of Pakistan. Actually no one else represented the tone, tenor and temper of the romanticist, Khilafatist era (in the 1910s and 1920s) as he did in his hectic life, his revolutionary activities his numerous discomfitures, and in his tragic death. Whether he led a hectic life, whether he took recourse to a revolutionary path, or whether he goaded himself to die a tragic death outside the frontiers of his motherland cataclysmically, in whatever he did, he, consciously or unconsciously, carried forward the campaign of Indo-Muslim history: the redemption of Islam in India and abroad. In other words, he stood, above all, for an honourable existence for Muslims in India and in the rest of the troubled Muslim world in the existential crisis that convulsed Muslim India and that world.

Noether Symmetries, Corresponding Conservation Laws and Applications

This thesis is based on a geometrical/physical analysis of the conserved quantities/forms related to each Noether symmetry of the geodetic Lagrangian of plane symmetric and spherically symmetric spacetimes. We present a complete list of such metrics along with their Noether symmetries of the geodetic Lagrangian. The conserved quantities corresponding to each Noether symmetry are obtained. Thereafter, a detailed discussion of the geometrical and physical interpretation of these quantities is given. Additionally, the structure constants of the associated Lie algebras are obtained for each case. Furthermore, we find the Ricci tensors to see which metrics are gravitational wave solutions and the scalar curvatures are obtained in each case to analyze the essential singularities. The stress-energy tensors and their traces are obtained in each case as these are the sources of spacetime curvature. The last part of this thesis is to use the symmetries to obtain the invariant solutions whenever possible. The problem of constructing the optimal system has been be used to classify invariant solutions. We intend to find the one-dimensional optimal systems of the Lie subalgebras for the system of geodesic equations by using Noether symmetries. Further, we find the invariants corresponding to each element of the optimal system. These invariants enable one to reduce the system of geodesic equations (nonlinear system of 2nd order ordinary differential equations (ODEs)) to a system of first order ODEs. The resulting systems are solved via known methods (e.g., separation of variables, integrating factor etc). In some cases, we are able to get exact solutions of the system of geodesic equations.