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

More on a trace inequality in quantum information theory

It is known that for a completely positive and trace preserving (cptp) map ${\cal N}$, $\text{Tr}$ $\exp$$\{ \log \sigma$ $+$ ${\cal N}^\dagger [\log {\cal N}(\rho)$ $-\log {\cal N}(\sigma)] \}$ $\leqslant$ $\text{Tr}$ $\rho$ when $\rho$, $\sigma$, ${\cal N}(\rho)$, and ${\cal N}(\sigma)$ are strictly positive. We state and prove a relevant version of this inequality for the hitherto unaddressed case of these matrices being nonnegative. Our treatment also provides an alternate proof for the strictly positive case.Comment: 9 page

Why Einstein (Had I been born in 1844!)?

In his monumental discoveries, the driving force for Einstein was, I believe, consistency of concept and principle rather than conflict with experiment. In this spirit, I would like to look at the journey from the classical to the relativistic world as a simple and direct exercise first in recognition of universal character of universal entities and then carrying out the universalization. By this process not only the relativistic world follows most naturally but I would like to conjecture that if Einstein were born in 1844 (or had I been born in 1844 and had followed this line of thought as I do now!) it would have in fact been predicted including existence of a wave with universal constant velocity. That would have indeed been not only the greatest but most amazing and remarkable feat of human thought. Beating further on the same track of principle and concept driven ideas, we ponder over to see beyond Einstein, and ask the questions: in how many dimensions does gravity live, how many basic forces are there in nature and what are the basic building blocks of space-time?Comment: 16 pages, late

Universality, Gravity, the enigmatic Lambda and Beyond

In this essay, I wish to share a novel perspective which envisions universalization as a guide from the classical world to relativistic and quantum world. It is the incorporation of zero mass particle in mechanics which leads to special relativity while its interaction with a universal field shared by all particles leads to general relativity. We also give a very simple classical argument to show that why the universal force has to be attractive. We try to envisage what sort of directions does this principle of universality point to for the world beyond general relativity?Comment: 13 page

A duality relation : global monopole and texture

We resolve the entire gravitational field;i.e. the Riemann curvature into its electric and magnetic parts. In general, the vacuum Einstein equation is symmetric in active and passive electric parts. However it turns out that the Schwarzschild solution, which is the unique spherically symmetric vacuum solutions can be characterised by a slightly more general equation which is not symmetric. Then the duality transformation, implying interchange of active and passive parts will relate the Schwarzschlid particle with the one with global monopole charge. That is the two are dual of each-other. It further turns out that flat spacetime is dual to massless global monopole and global texture spacetimes.Comment: 10 pages, LaTeX 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

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