Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.     

CONDUCTIVITY BEHAVIOR OF IONIC AI(OH)3-POLYACRYLAMIDE HYBRIDS IN AQUEOUS SOLUTIONS

The conductivity behavior of Al(OH)3-acrylamide hybrid polyacrylamide (hybrid PAAm) in distilled water was studied. A discontinuity phenomenon of the conductivity (k) versus concentration (c) curve of the hybrid PAAm in a certain concentration regime is found. This phenomenon is dependent on the molecular weight of the hybrid PAAm and on the particle size and content of the Al(OH)3 colloid in the hybrid PAAm. This phenomenon was accounted for assuming ionization of the hybrid PAAm.     

Exact Interior Solutions for Charged Fluid Spheres

A new method is discussed to obtain the interior solution of Einstein-Maxwell equations for a charged static sphere from a known particular solutions of a similar kind. Beginning with a charged fluid interior solution reported by Patel and Pandya [11], a new interior Reissner-Nördstrom metric is obtained using this method and physical aspects of it are extensively discussed.     

Lie Groups of Conformal Motions Acting on Null Orbits

Space-times admitting a 3-dimensional Lie group of conformal motions acting on null orbits containing a 2-dimensional Abelian subgroup of isometries are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespective of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.     

The Classical Solutions of Two-dimensional Gravity

The solutions of two-dimensional gravityfollowing from a non-linear Lagrangian =f(R)g are classified, and their symmetry andsingularity properties are described. Then a conformaltransformation is applied to rewrite these solutions as analogoussolutions of two-dimensional Einstein-dilaton gravityand vice versa.     

Invariance of the Massless Field Equations under Changes of the Metric

It is shown that the Maxwell equations with sources, expressed in terms of the covariant tensor field F_ijand the current density four-vector Jⁱ, are invariant under the change of the metric g_ijby g_ij = g_ij+ l_il_jif l_iis a principal null direction of F_ijand that an analogous result holds in the case of the massless Klein-Gordon equation if l_iis null and orthogonal to the gradient of the field and in the case of the null dust equations if l_iis parallel to the dust four-velocity. An elementary proof of the following generalization of the Xanthopoulos theorem is also given: Let (g_ij, F_ij) be an exact solution of the Einstein-Maxwell equations and let l_ibe a principal null direction of F_ij, then (g_ij+ l_il_j, F_ij) is also an exact solution of the Einstein-Maxwell equations if and only if (l_il_j, 0) satisfies the Einstein-Maxwell equations linearized about the background solution (g_ij, F_ij). Furthermore, analogous theorems, where the source of the gravitational field is a massless Klein-Gordon field or null dust, are presented.     

The GHP Formalism and a Type N Twisting Vacuum Metric with Killing Vector

It is shown that the formalism introduced byGeroch, Held and Penrose has a geometrical basis. Withthe help of the resulting insight a canonical splittingof the complex function which appears in the standard form of the Algebraically Special metrics isrealized. The results of this splitting are applied tothe problem of a (special) Type N vacuum metric with atwisting principle null direction. It is demonstrated that it is possible (but not feasable) to findthe metric without the use of differential equations. Anestimate of the size of the metric is given.     

Comment on the Roberts Solution for the Spherically-Symmetric Einstein-Scalar Field Equations

We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.     

Pulse radiolytic reduction studies of 1,4,4a,8a-tetrahydro-endo–1,4-methano-naphtha-5,8-dione (THMND): effect of tertiary structure

Radiolytic reduction of a substituted 5,8-naptha dione (THMND), synthesized in our laboratory, has been investigated by pulse radiolysis and steady-state -radiolysis in pure aqueous, aqueous-formate and in aqueous-2-propanol-acetone mixed solvent systems. The rate constants of formation of the semi-dione radicals were approx. 10⁹ dm³ mol^-1 s^-1 in aqueous-formate and aqueous-2-propanol-acetone mixed solvent. The semi-dione radicals decay by second order kinetics with rate constants (2k) of about 10⁹ and 10⁸ dm³ mol^-1 s^-1 in the above two solvents, respectively. The pK _a value of the radical was found to be 5.0 in aqueous-formate solution and 5.8 in the aqueous-2-propanol-acetone mixed solvent. The one-electron reduction potential (E ¹) value at pH 7, determined from the pulse-radiolysis experiment, was found to be –420 ± 20 mVvs. NHE at 298 K and was independent of solvent. Ab initio calculations on its one-electron reduction reaction suggest the formation of a radical, which is different from a semiquinone where the electron density is delocalised over the two oxygen atoms. Experimental absorption maxima of the radical in aqueous solution also agree very well with the ab initio calculated values. Steady-state -radiolysis of THMND produces the corresponding two-electron reduced species.     

On the singularities of solutions to 4-D semilinear dispersive wave equations

In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal