Sayan Kar

Scalar kinks and fermion localization in warped spacetimes

Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realization of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localization of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink–fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling parameter ηF (with ν, the warp factor parameter, kept fixed) using appropriate, recently developed, approximation methods. In particular, the spectrum of the low-lying states and their lifetimes are obtained, with the latter being exponentially enhanced for large νηF. Our results indicate quantitatively, within this model, that it is possible to tune the nature of warping and the strength and form of the Yukawa interaction to obtain trapped massive fermion states on the brane, which, however, do have a finite (but very small) probability of escaping into the bulk.

The Raychaudhuri equations: A brief review

We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate non-Riemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein-Cartan-Sciama-Kibble theory). Finally, we give an overview of some recent applications of these equations in general relativity, quantum field theory, string theory and the theory of relativisitic membranes. We conclude with a summary and provide our own perspectives on directions of future research.

Evolving Lorentzian wormholes

Evolving Lorentzian wormholes with the required matter satisfying the energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact dimensions present in the wormhole metric is also explored and certain interesting conclusions are derived for the cases of exponential and Kaluza-Klein inflation. \textcopyright{} 1996 The American Physical Society.

Modeling galaxy halos using dark matter with pressure

We investigate whether a dark matter with substantial amounts of pressure, comparable in magnitude to the energy density, could be a viable candidate for the constituent of dark matter halos. We find that galaxy halos models, consistent with observations of flat rotation curves, are possible for a variety of equations of state with anisotropic pressures. It turns out that the gravitational bending of light rays passing through such halos is very sensitive to the pressure. We propose that combined observations of rotation curves and gravitational lensing can be used to determine the equation of state of the dark matter. Alternatively, if the equation of state is known from other observations, rotation curves and gravitational lensing can together be used to test General Relativity on galaxy scales.

Cosmology with decaying tachyon matter

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.

Quantifying energy condition violations in traversable wormholes

The ‘theoretical’ existence of traversable Lorentzian wormholes in the classical, macroscopic world is plagued by the violation of the well-known energy conditions of general relativity. In this brief article we show: (i) how the extent of violation can be quantified using certain volume integrals and (ii) whether this ‘amount of violation’ can be minimised for some specific cut-and-paste geometric constructions. Examples and possibilities are also outlined.

Does a Kalb--Ramond field make spacetime optically active?

Abstract. A spacetime with torsion produced by a Kalb–Ramond field coupled gravitationally to the Maxwell field, in accordance with a recent proposal by two of us (PM and SS), is argued to lead to optical activity in synchrotron radiation from cosmologically distant radio sources. We show that this indicates a very small, but possibly observable rotation of the plane of polarization of the radiation, above and beyond the Faraday rotation due to magnetized galactic plasma. Implications for heterotic string theory are outlined.

Braneworlds in six dimensions: new models with bulk scalars

Six-dimensional bulk spacetimes with 3- and 4-branes are constructed using certain non-conventional bulk scalars as sources. In particular, we investigate the consequences of having the phantom (negative kinetic energy) and the Brans–Dicke scalar in the bulk while obtaining such solutions. We find geometries with 4-branes with a compact on-brane dimension (hybrid compactification) which may be assumed to be small in order to realize a 3-brane world. On the other hand, we also construct, with similar sources, bulk spacetimes where a 3-brane is located at a conical singularity. Furthermore, we investigate the issue of localization of matter fields (scalar, fermion, graviton, vector) on these 3- and 4-branes and conclude with comments on our six-dimensional models.

Confinement of test particles in warped spacetimes

We investigate test particle trajectories in warped spacetimes with a thick brane warp factor, a cosmological on-brane line element, and a time dependent extra dimension. The geodesic equations are reduced to a first order autonomous dynamical system. Using analytical methods, we arrive at some useful general conclusions regarding possible trajectories. Oscillatory motion, suggesting confinement about the location of the thick brane, arises for a growing warp factor. On the other hand, we find runaway trajectories (exponential-like) for a decaying warp factor. Variations of the extra dimensional scale factor yield certain quantitative differences. Results obtained from explicit numerical evaluations match well with the qualitative conclusions obtained from the dynamical systems analysis.

de Sitter branes with a bulk scalar

We propose new brane world models arising from a scalar field in the bulk. In these examples, the induced on-brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models—one with thin branes while the other one of the thick variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the thick brane scenario the field profile resembles a kink, whereas for one or more thin branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.