arXiv subjects

Sayan Kar

Publications and source records attributed to Sayan Kar.

At least 91 records · Page 5Linked to original sources

arXiv2004

Bulk phantom fields, increasing warp factors and fermion localisation

A bulk phantom scalar field (with negative kinetic energy) in a sine--Gordon type potential is used to generate an exact thick brane solution with an increasing warp factor. It is shown that the growing nature of the warp factor allows the localisation of massive as well as massless spin-half fermions on the brane even without any additional non--gravitational interactions. The exact solutions for the localised massive fermionic modes are presented and discussed. The inclusion of a fermion--scalar Yukawa coupling appears to change the mass spectrum and wave functions of the localised fermion though it does not play the crucial role it did in the case of a decreasing warp factor.

hep-th↗

arXiv2004

Diffraction of light by interfering liquid surface waves

Interfering liquid surface waves are generated by electrically driven vertical oscillations of two or more equispaced pins immersed in a liquid (water). The corresponding intensity distribution, resulting from diffraction of monochromatic light by the reflection phase grating formed on the liquid surface, is calculated theoretically and found to tally with experiments. The curious features of the diffraction pattern and its relation to the interference of waves on the liquid surface are used to measure the amplitude and wavelength of the resultant surface wave along the line joining the two sources of oscillation. Finally, a sample diffraction pattern obtained by optically probing surface regions where interference produces a lattice--like structure is demonstrated and qualitatively explained.

physics.optics↗

arXiv2004

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 (ii) whether this `amount of violation' can be minimised for some specific cut--and--paste geometric constructions. Examples and possibilities are also outlined.

gr-qc↗

arXiv2003

Modelling 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.

astro-ph↗

arXiv2003

Traversable wormholes with arbitrarily small energy condition violations

Traversable wormholes necessarily require violations of the averaged null energy condition; this being the definition of ``exotic matter''. However, the theorems which guarantee the energy condition violation are remarkably silent when it comes to making quantitative statements regarding the ``total amount'' of energy condition violating matter in the spacetime. We develop a suitable measure for quantifying this notion, and demonstrate the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of ``exotic matter''.

gr-qc↗

arXiv2003

Geodesics and geodesic deviation in a two-dimensional black hole

We introduce an exactly solvable example of timelike geodesic motion and geodesic deviation in the background geometry of a well-known two-dimensional black hole spacetime. The effective potential for geodesic motion turns out to be either a harmonic oscillator or an inverted harmonic oscillator or a linear function of the spatial variable, corresponding to the three different domains of a constant of the motion. The geodesic deviation equation also is exactly solvable. The corresponding deviation vector is obtained and the nature of the deviation is briefly discussed by highlighting a specific case.

gr-qc↗

arXiv2002

Static spherisymmetric solutions, gravitational lensing and perihelion precession in Einstein--Kalb--Ramond theory

Static, spherically symmetric solutions of the Einstein--Kalb--Ramond (KR) field equations are obtained. Besides an earlier known exact solution, we also find an approximate, asymptotically flat solution for which the metric coefficients are obtained as an infinte series in $\frac{1}{r}$. Subsequently, we study gravitational lensing and perihelion precession in these spacetimes and obtain explicit formulae which include corrections to these effects in the presence of the KR field.

hep-th↗

arXiv2002

A simple mechanical analog of the field theory of tachyon matter

In this brief note we show that the zero dimensional version of the field theory of tachyon matter proposed by Sen, provides an action integral formulation for the motion of a particle in the presence of Newtonian gravity and nonlinear damping (quadratic in velocity).

hep-th↗

arXiv2002

Asymmetrically warped R=0 braneworlds

A new family of five dimensional, R=0 braneworlds with asymmetric warp factors is proposed. Beginning with the invariance of the Ricci scalar for the general class of asymmetrically warped spacetimes we, subsequently specialise to the R=0 case. Solutions are obtained by choosing a particular relation (involving a parameter $ν$) between the warp factors. Symmetric warping arises as a special case (particular value of $ν$). Over a range of values of $ν$ the energy conditions for the matter stress energy are found to hold good. It turns out that the energy density and pressures required to support these spacetimes decay as the inverse square of the fifth (extra) coordinate. The projection of this bulk stress--energy (for symmetric warping) on the 3--brane yields an effective cosmological constant. We conclude with brief comments on spacetimes with constant Ricci scalar and the extension of our results to diverse dimensions.

gr-qc↗

arXiv2002

Geometry of theory space and RG flows

The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor--Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.

hep-th↗

arXiv2001

R=0 spacetimes and self-dual Lorentzian wormholes

A two-parameter family of spherically symmetric, static Lorentzian wormholes is obtained as the general solution of the equation $ρ=ρ_t=0$, where $ρ= T_{ij} u^iu^j$, $ρ_t = (T_{ij} - {1\over2} T g_{ij}) u^iu^j$, and $u^i u_i =- 1$. This equation characterizes a class of spacetimes which are ``self dual'' (in the sense of electrogravity duality). The class includes the Schwarzschild black hole, a family of naked singularities, and a disjoint family of Lorentzian wormholes, all of which have vanishing scalar curvature (R=0). Properties of these spacetimes are discussed. Using isotropic coordinates we delineate clearly the domains of parameter space for which wormholes, nakedly singular spacetimes and the Schwarzschild black hole can be obtained. A model for the required ``exotic'' stress-energy is discussed, and the notion of traversability for the wormholes is also examined.

gr-qc↗

arXiv2001

Cosmic optical activity from an inhomogeneous Kalb-Ramond field

The effects of introducing a harmonic spatial inhomogeneity into the Kalb-Ramond field, interacting with the Maxwell field according to a `string-inspired' proposal made in earlier work are investigated. We examine in particular the effects on the polarization of synchrotron radiation from cosmologically distant (i.e. of redshift greater than 2) galaxies, as well as the relation between the electric and magnetic components of the radiation field. The rotation of the polarization plane of linearly polarized radiation is seen to acquire an additional contribution proportional to the square of the frequency of the dual Kalb-Ramond axion wave, assuming that it is far smaller compared to the frequency of the radiation field.

hep-th↗

arXiv2001

The geometry of RG flows in theory space

Renormalisation Group (RG) flows in theory space (the space of couplings) are generated by a vector field -- the $β$ function. Using a specific metric ansatz in theory space and certain methods employed largely in the context of General Relativity, we examine the nature of the expansion, shear and rotation of geodesic RG flows. The expansion turns out to be a negative quantity inversely related to the norm of the $β$ function. This implies the focusing of the flows towards the fixed points of a given field theory. The evolution equation for the expansion along geodesic RG flows is written down and analysed. We illustrate the results for a scalar field theory with a $jϕ$ coupling and pointers to other areas are briefly mentioned.

hep-th↗

arXiv2000

Does a Kalb-Ramond field make spacetime optically active

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 an optical activity in synchrotron radiation from cosmologically distant radio sources. We suggest that this could qualitatively explain observational data from a large number of radio sources displaying such polarization asymmetry (after eliminating effects of Faraday rotation due to magnetized galactic plasma). Possible implications for heterotic string theory are also outlined.

gr-qc↗

arXiv1999

New classes of black hole spacetimes in 2+1 gravity

The electrogravity transformation is applied to the three-dimensional Einstein field equations to obtain new multi-parameter families of black hole solutions. The Bañados-Teitelboim-Zanelli black hole is shown to be a special case of one of these families. The causal structure, associated matter, as well as the mechanical and thermodynamical properties of some of the solutions are discussed.

hep-th↗

arXiv1999

Classical and quantum mechanics of a particle on a rotating loop

The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics from both exact and semi--classical standpoints. Exact solutions of the Schrodinger equation are obtained in some cases by diverse methods. Instantons, bounces are constructed and semi-classical, leading order tunneling amplitudes/decay rates are written down. We also investigate qualitatively the nature of small oscillations about the kink/bounce solutions. Finally, the connections of these toy examples with field theoretic and statistical mechanical models of relevance are pointed out.

quant-ph↗

arXiv1998

Naked singularities in low energy, effective string theory

Solutions to the equations of motion of the low energy, effective field theory emerging out of compactified heterotic string theory are constructed by making use of the well-known duality symmetries. Beginning with four-dimensional solutions of the Einstein-massless scalar field theory in the canonical frame we first rewrite the corresponding solutions in the string frame. Thereafter, using the T and S duality symmetries of the low energy string effective action we arrive at the corresponding uncharged, electrically charged and magnetically charged solutions. Brief comments on the construction of dual versions of the Kerr-Sen type using the dilatonic Kerr solution as the seed are also included. Thereafter, we verify the status of the energy conditions for the solutions in the string frame. Several of the metrics found here are shown to possess naked singularities although the energy conditions are obeyed. Dual solutions exhibit a duality in the conservation/violation of the Null and Averaged Null Energy Conditions (NEC/ANEC), a fact demonstrated earlier in the context of black holes (hep-th/9604047) and cosmologies (hep-th/9611122). Additionally, those backgrounds which conserve the NEC/ANEC in spite of possesing naked singularities serve as counterexamples to cosmic censorship in the context of low energy, effective string theory.

hep-th↗

arXiv1997

Exact solutions in two-dimensional string cosmology with back reaction

We present analytic cosmological solutions in a model of two-dimensional dilaton gravity with back reaction. One of these solutions exhibits a graceful exit from the inflationary to the FRW phase and is nonsingular everywhere. A duality related second solution is found to exist only in the ``pre-big-bang'' epoch and is singular at $τ= 0$. In either case back reaction is shown to play a crucial role in determining the specific nature of these geometries.

hep-th↗