Kamal K. Nandi

Gravitational lensing by wormholes

Gravitational lensing by traversable Lorentzian wormholes is a new possibility which is analyzed here in the strong field limit. Wormhole solutions are considered in the Einstein minimally coupled theory and in the brane world model. The observables in both the theories show significant differences from those arising in the Schwarzschild black hole lensing. As a corollary, it follows that wormholes with zero Keplerian mass exhibit lensing properties which are qualitatively (though not quantitatively) the same as those of a Schwarzschild black hole. Some special features of the considered solutions are pointed out.

Brans-Dicke wormholes in the Jordan and Einstein frames

We examine the possibility of static wormhole solutions in the vacuum Brans-Dicke theory both in the original (Jordan) frame and in the conformally rescaled (Einstein) frame. It turns out that, in the former frame, wormholes exist only in a very narrow interval of the coupling parameter, viz., -3/2<omega<-4/3. It is shown that these wormholes are not traversable in practice. In the latter frame, wormhole solutions do not exist at all unless energy conditions are violated by hand.

Charged gravastars admitting conformal motion

Abstract We propose a new model of a gravastar admitting conformal motion. While retaining the framework of the Mazur–Mottola model, the gravastar is assumed to be internally charged, with an exterior defined by a Reissner–Nordstrom instead of a Schwarzschild line element. The solutions, obtained by exploiting an assumed conformal Killing vector, involve (i) the interior region, (ii) the shell, and (iii) the exterior region of the sphere. Of these three cases the first one is of primary interest since the total gravitational mass here turns out to be an electromagnetic mass under some specific conditions. This suggests that the interior de Sitter vacuum of a charged gravastar is essentially an electromagnetic mass model that must generate gravitational mass which provides a stable configuration by balancing the repulsive pressure arising from charge with its attractive gravity to avert a singularity. Therefore the present model, like the Mazur–Mottola model, results in the construction of a compact astrophysical object, as an alternative to a black hole. We have also analyzed various other aspects such as the stress energy tensor in the thin shell and the entropy of the system.

Features of galactic halo in a brane world model and observational constraints

Several aspects of the 4d imprint of the 5d bulk Weyl radiation are investigated within a recently proposed model solution. It is shown that the solution has a number of physically interesting properties. The constraints on the model imposed by combined measurements of rotation curve and lensing are discussed. A brief comparison with a well-known scalar field model is also given.

The Optical-Mechanical Analogy in General Relativity: Exact Newtonian Forms for the Equations of Motion of Particles and Photons

In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermats principle or of Maupertuiss principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.

On the optical–mechanical analogy in general relativity

We demonstrate that the Evans–Rosenquist formulation of the optical–mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general relativity. It is possible to obtain the well‐known equations for light orbit and radar echo delay which account for two exclusive tests of Einstein’s field equations. Some remarks including suggestions for future work are also added.

Correct light deflection in Weyl conformal gravity

The conformal gravity fit to observed galactic rotation curves requires {\gamma}>0. On the other hand, conventional method for light deflection by galaxies gives a negative contribution to Schwarzschild value for {\gamma}>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for {\gamma}>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date.

BRANS DICKE THEORY: JORDAN VERSUS EINSTEIN FRAME

It is well known that, in contrast to general relativity, there are two conformally related frames, the Jordan frame and the Einstein frame, in which the Brans–Dicke theory, a prototype of generic scalar–tensor theory, can be formulated. There is a long standing debate on the physical equivalence of the formulations in these two different frames. It is shown here that gravitational deflection of light to second order accuracy may observationally distinguish the two versions of the Brans–Dicke theory.

Volume integral theorem for exotic matter

We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.

The Phase of a Quantum Mechanical Particle in Curved Spacetime

We investigate the quantum mechanical wave equations for free particles of spin 0, 1/2, 1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/ħ = ∫ pμdxμ/ħ, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple manageable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in ħ. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in ħ. For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.