229 research outputs found
The Nahm Pole Boundary Condition
The Nahm pole boundary condition for certain gauge theory equations in four
and five dimensions is defined by requiring that a solution should have a
specified singularity along the boundary. In the present paper, we show that
this boundary condition is elliptic and has regularity properties analogous to
more standard elliptic boundary conditions. We also establish a uniqueness
theorem for the solution of the relevant equations on a half-space with Nahm
pole boundary conditions. These results are expected to have a generalization
involving knots, with applications to the Jones polynomial and Khovanov
homology.Comment: 60 pp, minor corrections in v.
Instantons and singularities in the Yang-Mills flow
Several results on existence and convergence of the Yang-Mills flow in
dimension four are given. We show that a singularity modeled on an instanton
cannot form within finite time. Given low initial self-dual energy, we then
study convergence of the flow at infinite time. If an Uhlenbeck limit is
anti-self-dual and has vanishing self-dual second cohomology, then no bubbling
occurs and the flow converges exponentially. We also recover Taubes's existence
theorem, and prove asymptotic stability in the appropriate sense.Comment: Published version including extended background section, minor
corrections, and many small changes, none affecting main theorems or proof
Modelling of a compact anisotropic star as an anisotropic fluid sphere in gravity
In this paper, we have studied the new exact model of anisotropic star in
theory of gravity. The dynamical equations in theory with the
anisotropic fluid have been solved by using Krori-Barua solution. We have
determined that all the obtained solutions are free from central singularity
and potentially stable. The observed values of mass and radius of the different
strange stars RX J 1856-37, Her X-1, and Vela X-12 have been used to calculate
the values of unknown constants in Krori and Barua metric. The physical
parameters like anisotropy, stability and redshift of the stars have been
investigated in detail.Comment: Accepted in the Canadian Journal of Physic
Attractor Solutions in f(T) Cosmology
In this paper, we explore the cosmological implications of interacting dark
energy model in a torsion based gravity namely . Assuming dark energy
interacts with dark matter and radiation components, we examine the stability
of this model by choosing different forms of interaction terms. We consider
three different forms of dark energy: cosmological constant, quintessence and
phantom energy. We then obtain several attractor solutions for each dark energy
model interacting with other components. This model successfully explains the
coincidence problem via the interacting dark energy scenario.Comment: 10 pages, 23 figures, version accepted for publication in European
Physical Journal C (2012
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