General Relativity in Post Independence India

The most outstanding contribution to general relativity in this era came in 1953 (published in 1955 \cite{akr}) in the form of the Raychaudhri equation. It is in 1960s that the observations began to confront the eupherial theory and thus began exploration of GR as a legitimate physical theory in right earnest. The remarkable discoveries of cosmic microwave background radiation, quasars, rotating Kerr black hole and the powerful singularity theorems heralded a new canvas of relativistic astrophysics and cosmology. I would attempt to give a brief account of Indian participation in these exciting times.Comment: 27 pages, latex, Published in Current Science: Special Issue on 100 Years of General Relativity edited by Banibrata Mukhopadhya and T P Sing

Isothermal spherical perfect fluid model: Uniqueness and Conformal mapping

We prove the theorem: The necessary and sufficient condition for a spherically symmetric spacetime to represent an isothermal perfect fluid (barotropic equation of state with density falling off as inverse square of the curvature radius) distribution without boundary is that it is conformal to the ``minimally'' curved (gravitation only manifesting in tidal acceleration and being absent in particle trajectory) spacetime.Comment: 7 pages, TeX versio

A novel derivation of the rotating black hole metric

We derive the rotating black hole metric by appealing to ellipsoidal symmetry of space and a general guiding principle of incorporation of the Newtonian acceleration for massive and no acceleration for massless particles.Comment: 4 pages, to agree with the published version except one additional reference, pubmishe

A Unified View of the Basic Forces

In this essay we wish to seek a unifying thread between the basic forces. We propose that there exists a universal force which is shared by all that physically exists. Universality is characterized by the two properties: (i) universal linkage and (ii) long range. They uniquely identify Einstein gravity as the unversal force. All other forces then arise as these properties are peeled off. For instance, relaxing (i) but retaining (ii) will lead to Maxwell electromagnetic force. This unified outlook makes interesting suggestions and predictions: if there exists a new force, it can only be a short range non-abelian vector or a scalar field, and there should exist in an appropriate space duality relations between weak and electric, and between strong and gravity.Comment: 4 pages, latex, To appear in Proceedings of the Einstein Centennial Maeting, University of Kwazulu-Natal, Durban, Sept. 25-26, 200

Universalization as a physical guiding principle

In this essay, I wish to share a novel perspective based on the principle of universalization in arriving at the relativistic and quantum world from the classical world. I also delve on some insightful discussion on going ``beyond''.Comment: RevTeX, 22 pages. This is an essay propounding a new perspective and it is open for discussion. Comments and criticism will be most welcome. It will be kept live and would be updated from time to time with proper acknowledgement to comments and criticis

Why do we live in four dimension?

We perceive the dimension of physical spacetime we live in through physical experiments and hence it is pertinent to probe the dimension in which the fundamental physical forces exist and act? In this context we shall investigate the two classical fields of gravitation and electromagnetism and argue that four dimension is necessary for spacetime but may not be sufficient. Some motivation for higher dimension would also be discussed.Comment: 14 pages, First V V Narlikar Memorial Lecture delivered on 23 January, 2009 at Jamia Millia Islamia, Ne Delh

On product spacetime with 2-sphere of constant curvature

If we consider the spacetime manifold as product of a constant curvature 2-sphere (hypersphere) and a 2-space, then solution of the Einstein equation requires that the latter must also be of constant curvature. There exist only two solutions for classical matter distribution which are given by the Nariai (anti) metric describing an Einstein space and the Bertotti - Robinson (anti) metric describing a uniform electric field. These two solutions are transformable into each other by letting the timelike convergence density change sign. The hyperspherical solution is anti of the spherical one and the vice -versa. For non classical matter, we however find a new solution, which is electrograv dual to the flat space, and describes a cloud of string dust of uniform energy density. We also discuss some interesting features of the particle motion in the Bertotti - Robinson metric.Comment: 9 pages, 1 figure, LaTex versio

Black hole : Equipartition of matter and potential energy

Black hole horizon is usually defined as the limit for existence of timelike worldline or when a spatially bound surface turns oneway (it is crossable only in one direction). It would be insightful and physically appealing to find its characterization involving an energy consideration. By employing the Brown-York [1] quasilocal energy we propose a new and novel characterization of the horizon of static black hole. It is the surface at which the Brown-York energy equipartitions itself between the matter and potential energy. It is also equivalent to equipartitioning of the binding energy and the gravitational charge enclosed by the horizon.Comment: 6 pages, LaTeX versio

On ``minimally curved spacetimes'' in general relativity

We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.Comment: 7 pages, LaTeX versio

A curious spacetime entirely free of centrifugal acceleration

In the Einstein gravity, besides the usual gravitational and centrifugal potential there is an additional attractive term that couples these two together. It is fun to enquire whether the latter could fully counteract the centrifugal repulsion everywhere making the spacetime completely free of the centrifugal acceleration. We present here such a curious spacetime metric and it produces a global monopole like stresses going as $~1/r^2$ in an AdS spacetime.Comment: 3 pages, late