Derivation of the Raychaudhuri Equation

As a homage to A K Raychaudhuri, I derive in a straightforward way his famous equation and also indicate the problems he was last engaged in.Comment: 8 pages, latex file, Pedagogical, One technical incorrect statement corrected and some minor rephrasin

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

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

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

Universal Velocity and Universal Force

In his monumental discoveries, the driving force for Einstein was, I believe, consistency of concept and principle rather than conflict with experiment. Following this Einsteinian dictum, we would first argue that homogeneity (universal character) of space and time characterizes 'no force' (absence of force) and leads to existence of a universal velocity while inhomogeneity (again a universal property) characterizes curved spacetime and presence of a universal force which is present everywhere and always. The former gives rise to Special Relativity while the latter to General Relativity.Comment: 12 pages, latex. arXiv admin note: substantial text overlap with physics/050509

The gravitational equation in higher dimensions

Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the Riemann curvature, and then the trace of its Bianchi derivative yields the corresponding polynomial analogue of the divergence free Einstein tensor defining the differential operator for the equation of motion. We propose that the general equation of motion is $G^{(n)}_{ab} = -\Lambda g_{ab} +\kappa_n T_{ab}$ for $d=2n+1, \, 2n+2$ dimensions with the single coupling constant $\kappa_n$, and $n=1$ is the usual Einstein equation. It turns out that gravitational behavior is essentially similar in the critical dimensions for all $n$. All static vacuum solutions asymptotically go over to the Einstein limit, Schwarzschild-dS/AdS. The thermodynamical parameters bear the same relation to horizon radius, for example entropy always goes as $r_h^{d-2n}$ and so for the critical dimensions it always goes as $r_h, \, r_h^2$. In terms of the area, it would go as $A^{1/n}$. The generalized analogues of the Nariai and Bertotti-Robinson solutions arising from the product of two constant curvature spaces, also bear the same relations between the curvatures $k_1=k_2$ and $k_1=-k_2$ respectively.Comment: latex, 5pages, Contribution to the Proceedings of the Conference, Relativity and Gravitation: 100 years after Einstein in Prague, June 25-28, 201

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