• Volume 51, Issue 6

December 1998,   pages  663-771

• Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell’s equations for static spheres assuming the matter content to be a charged perfect fluid of null-conductivity. Defining three new variablesu=4πεr2,ν=4πpr22 andw=(4π/3)(ρ+ε)r2 whereε, ρ andε denote respectively energy densities of the electric, matter and free gravitational fields whereasp is the fluid pressure, Einstein’s field equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5,6], Xingxiang [7], Patino and Rago [8] are all shown to possess simple relations betweenu, v, andw whereas Pant and Sah’s [9] solution for which all the three functions,u, v, andw are constants is a trivial case of the present formalism, We have presented six new solutions with ε = 2ρ. For the first three solutionsw andu are constants withv as a variable whereas the remaining three solutions satisfy the equation of state for isothermal gas;v =kw =-ku where (i)k is an arbitrary constant but not equal to 1 or 1/3 (ii)k = 1 and (iii)k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz’s [3] solution which is regular for 2ρ &gt; ε but singular for 2ρ ≤ ε.

• Collapsing void in a spatially flat Robertson-Walker universe

We consider here a model of the spherical void (or its precursor) containing low density conducting fluid surrounded by a thick spherical shell of radiation embedded in a RobertsonWalker (RW) universe with flat space sections. The underdense region has a metric which is the special case of a solution given by Maiti [1] surrounded by Vaidya metric. We also assume the RW universe to be filled with a perfect fluid with a linear equation of state. The matching conditions indicate that if the time coordinate in each region is future directed then the underdense region appears to go on contracting to a comoving observer in the universe as the latter expands until it disappears. However, if the pressure in the RW universe vanishes, (approximately the present day condition), the underdense region remains static. We have also extended the space-time coordinates of Vaidya metric to the interior of the underdense region as well as the RW universe. It remains to be seen if the region having Vaidya metric disappears earlier than the interior or vice versa.

• Motion of test particles around global monopoles in Brans-Dicke theory

A detailed analysis of the motion of test particles around global monopole in Brans-Dicke theory of gravity has been prescribed using the Hamilton-Jacobi (H-J) formalism. The trajectory of the test particles are trapped by the monopole with some restriction on the coupling parameter ω.

• Physical nature of the event horizon

It is shown by arguments based on the uncertainty principle that large fluctuations of the metric occur near the event horizon of a Schwarzschild black hole on a scale much larger than Planck length. The width of the transition layer about the event horizon and the associated surface tension are also estimated.

• Einstein equations and the joining of discontinuous metrics

We consider the problem of joining of metrics when these are not continuous across the joining (hyper-) surface. We confine ourselves to static, spherically symmetric metrics which join without requiring gradients of a δ-function in the energy-momentum tensor. It is found that a surface tension is always associated in cases where the metrics are discontinuous. In some cases, the joined metrics satisfy Einstein equations (in the sense of distributions) while, in others, the surface tension associated with the limiting discontinuous metric depends on the interpolating functions used to produce it suggesting sensitivity to short distance effects beyond general relativity.

• Mass and decay constant of the (qq)-pion in a relativistic-potential model of independent quarks

Under the assumption that a meson is an assembly of independent quark and antiquark, confined in a first approximation by an effective potential$$V_q (r) = \raise.5ex\hbox{\scriptstyle 1}\kern-.1em/ \kern-.15em\lower.25ex\hbox{\scriptstyle 2} (1 + \gamma ^0 )(a^2 r + V_0 )$$ which presumably represents the non-perturbative gluon interactions, the mass and decay constant of the (qq)-pion together with the masses of ρ and ω-mesons are calculated by considering perturbatively the corrections due to the possible residual interaction such as quark-pion coupling arising out of the requirement of chiral symmetry and quark-gluon coupling arising out of one-gluon exchange and that due to the spurious motion of center of mass of the meson core.This results in the physical mass of the (qq)-pion in consistency with that of the PCAC-pion and the pion decay constant in a reasonable agreement with experiment.

• T = 0 versusT = 1 pairing in 0(36) limit of IBM-4 for heavyN = Z nuclei

In theO(36) limit of the interacting boson model including spin-isospin degrees of freedom (IBM-4), starting with a group chain that preservess andd boson spins and isospins together with a simple mixing hamiltonian, it is shown that the model generates, for heavyN =Z nuclei, even-even to odd-odd staggering in the number ofT = 0 pairs in the ground states for moderate difference in the basicT = 0 andT = 1s-boson pair energies; the staggering disappears when the energy difference is large.

• Vertex function and coupling constant for the virtual decay of7Li

The alpha-triton relative wave function with various nucleon exchange contributions and their asymptotic normalization are considered in the framework of the generator coordinate method (GCM). The asymptotic normalization of relative wave function provide the estimate of the coupling constant. The relative wave function is also used to obtain7Li-α-t vertex function in the virtual decay of7Li. The extrapolation of vertex function for negative values ofq2 up to the alpha-triton pole provide the vertex constant, which is compared with the experimentally determined estimates 0.67 FM and 0.72 FM. Our calculated value is 0.656 FM which is in close agreement with the above estimates.

• Near-barrier fusion reactions induced by α on197Au,193Ir,191Ir,185Re,181Ta,121Sb and69Ga nuclei

Fusion-evaporation cross-sections for the α-induced reactions upon197Au,193Ir,191Ir,185Re,181Ta,121Sb and69Ga nuclei at bombarding energies near the Coulomb barrier have been measured by off-line observation of the γ-rays emitted in the radioactive decay of the residual nuclei using stacked foil technique. The total fusion cross-section for the systems have been compared with simple statistical model calculations using the code ALICE/91 as well as with the coupled channel calculations that include the β2 and ν4 slatic deformations and dynamic couplings of the vibrational/rotational states of the target and the projet tile using the code CCDEF.

• Calculation of triple differential cross-sections ofK-shell ionization of medium-heavy atoms by electrons for symmetric geometry

Triple differential cross-section forK-shell ionization of medium-heavy atoms by relativistic electrons has been calculated for coplanar symmetric geometry. In this calculation the final state is described by a non-relativistic wave function of Das and Seal [Phys. Rev.A47 (1993) 2978] multiplied with suitable spinors. Results of the present calculation are compared with the available experimental data and with other theoretical calculations.

• Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 106 cm-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.

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