The gravitational field of a global monopole

We present an exact solution to the non-linear equation which describes a global monopole in the flat space. We re-examine the metric and the geodesics outside the global monopole. We will see that a global monopole produces a repulsive gravitational field outside the core in addition to a solid angular deficit. The lensing property of the global monopole and the global monopole-antimonopole annihilation mechanism are studied.Comment: 8 pages, no figure

Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular derivations, difference and $q$-difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin-Radul super KdV equation, studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140, (1997). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Ma\~nas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solutions to the Main-Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic

Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states

We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to a simple way of partitioning pure n-qubit states into inequivalent families and distinguishing degenerate families from one another under SLOCC. Moreover, the classification scheme via the ranks of coefficient matrices can be combined with other schemes to build a more refined classification scheme. To exemplify we classify the nine families of four qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further into inequivalent subfamilies via the ranks of coefficient matrices, and as a result, we find 28 genuinely entangled families and all the degenerate classes can be distinguished up to permutations of the four qubits. We also discuss the completeness of the classification of four qubits into nine families

Disk Accretion onto Magnetized Neutron Stars: The Inner Disk Radius and Fastness Parameter

It is well known that the accretion disk around a magnetized compact star can penetrate inside the magnetospheric boundary, so the magnetospheric radius \ro does not represent the true inner edge \rin of the disk; but controversies exist in the literature concerning the relation between \ro and \rin. In the model of Ghosh & Lamb, the width of the boundary layer is given by \delta=\ro-\rin\ll\ro, or \rin\simeq\ro, while Li & Wickramasinghe recently argued that \rin could be significantly smaller than \ro in the case of a slow rotator. Here we show that if the star is able to absorb the angular momentum of disk plasma at \ro, appropriate for binary X-ray pulsars, the inner disk radius can be constrained by 0.8\lsim \rin/\ro\lsim 1, and the star reaches spin equilibrium with a relatively large value of the fastness parameter ($\sim 0.7-0.95$). For accreting neutron stars in low-mass X-ray binaries (LMXBs), \ro is generally close to the stellar radius \rs so that the toroidal field cannot transfer the spin-up torque efficiently to the star. In this case the critical fastness parameter becomes smaller, but \rin is still near \ro.Comment: 7 pages, 2 figures, to appear in Ap