Anadijiban Das

Bio: Anadijiban Das is an academic researcher from Simon Fraser University. The author has contributed to research in topics: Scalar field & General relativity. The author has an hindex of 21, co-authored 71 publications receiving 1000 citations. Previous affiliations of Anadijiban Das include University of British Columbia & Indian Institute of Technology Kharagpur.

Stationary Riemannian space-times with self-dual curvature

Abstract: Riemannian space-times with self-dual curvature and which admit at least one Killing vector field (stationary) are examined. Such space-times can be classified according to whether a certain scalar fieldψ (which is the difference between the Newtonian and NUT potentials) reduces to a constant or not. In the former category (called here KSD) are the multi-TaubNUT and multi-instanton space-times. Nontrivial examples of the latter category have yet to be discovered. It is proved here that the static self-dual metrics are flat. It is also proved that each stationary metric for which the Newtonian and nut potentials are functionally related admits a Killing vector field relative to which the metric is KSD. It has also been proved that the regularity of theψ field everywhere implies that the metric is KSD. Finally it is proved that for non-KSD space-times every regular compact level surface of theψ field encloses the total NUT charge, which must be proportional to the Euler number of the surface.

A class of exact solutions of certain classical field equations in general relativity

Abstract: This paper deals with certain model statical universes representing exact solutions of some field equations in general relativity. Three universes of this type are discussed. They correspond to combinations of gravitation respectively with (i) electromagnetic field, (ii) scalar or pseudo-scalar field, (iii) Maxwell-Dirac field. Such statical solutions are possible in the first two cases only if mass density and charge density are equal in magnitude, and in the third case only if mass and charge are equal in magnitude, so that matter is in equilibrium under the action of gravitation and other forces. The field equations, in this work, are classical in the sense that no second quantization is involved.

Cosmology with decaying tachyon matter

Abstract: We investigate the case of a homogeneous tachyon field coupled to gravity in a spatially flat Friedmann-Robertson-Walker spacetime.Assuming the field evolution to be exponentially decaying with time we solve the field equations and show that, under certain conditions, the scale factor represents an accelerating universe, following a phase of decelerated expansion. We make use of a model of dark energy (withp=-rho) and dark matter (p=0) where a single scalar field (tachyon) governs the dynamics of both the dark components. We show that this model fits the current supernova data as well as the canonical Lambda CDM model. We give the bounds on the parameters allowed by the current data.

Cellular space-time and quantum field theory

Abstract: A simple cellular model of space-time is introduced which incorporates a fundamental length in a natural way. The usual concept of field quantities as functions of geometrical points is rejected in favour of the concept of field quantities as functionals of elementary cells. Consequently the usual field equations in the form of partial differential equations are replaced by corresponding partial difference equations. Subsequent quantization yields anS-matrix which is not vitiated by the presence of serious divergences. The basic space-time structure and theS-Matrix (which does not involve derivative coupling) are shown to be integral Lorentz covariant. The semi-convergence or asymptotic behaviour of theS-matrix series is established, and a meaningful Borel-sum of the « gross »S-matrix series is presented.

Dynamics of dark energy

Abstract: We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Bubbling AdS space and 1/2 BPS geometries

Abstract: We consider all 1/2 BPS excitations of AdS × S configurations in both type-IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of AdS5 compactifications of M-theory preserving = 2 superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.

On Continued Gravitational Contraction

Abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

Advanced Calculus I

Abstract: WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.