14,215 research outputs found
Semi-analytical approach for the Vaidya metric in double-null coordinates
We reexamine here a problem considered in detail before by Waugh and Lake:
the solutions of spherically symmetric Einstein's equations with a radial flow
of unpolarized radiation (the Vaidya metric) in double-null coordinates. This
problem is known to be not analytically solvable, the only known explicit
solutions correspond to the constant mass case (Schwarzschild solution in
Kruskal-Szekeres form) and the linear and exponential mass functions originally
discovered by Waugh and Lake. We present here a semi-analytical approach that
can be used to discuss some qualitative and quantitative aspects of the Vaidya
metric in double-null coordinates for generic mass functions. We present also a
new analytical solution corresponding to -mass function.Comment: 5 pages, 6 figure
A possible disk mechanism for the 23d QPO in Mkn~501
Optically thin two-temperature accretion flows may be thermally and viscously
stable, but acoustically unstable. Here we propose that the O-mode instability
of a cooling-dominated optically thin two-temperature inner disk may explain
the 23-day quasi-periodic oscillation (QPO) period observed in the TeV and
X-ray light curves of Mkn~501 during its 1997 high state. In our model the
relativistic jet electrons Compton upscatter the disk soft X-ray photons to TeV
energies, so that the instability-driven X-ray periodicity will lead to a
corresponding quasi-periodicity in the TeV light curve and produce correlated
variability. We analyse the dependence of the instability-driven
quasi-periodicity on the mass (M) of the central black hole, the accretion rate
() and the viscous parameter () of the inner disk. We
show that in the case of Mkn~501 the first two parameters are constrained by
various observational results, so that for the instability occurring within a
two-temperature disk where , the quasi-period is expected to
lie within the range of 8 to 100 days, as indeed the case. In particular, for
the observed 23-day QPO period our model implies a viscosity coefficient
, a sub-Eddington accretion rate and a transition radius to the outer standard disk of , and predicts a period variation due to the
motion of the instability region.Comment: 18 pages, 1 figure, accepted by AP
A Characterization of Discrete Time Soliton Equations
We propose a method to characterize discrete time evolution equations, which
generalize discrete time soliton equations, including the -difference
Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.Comment: 13 page
Magnetic properties of an SU(4) spin-orbital chain
In this paper, we study the magnetic properties of the one-dimensional SU(4)
spin-orbital model by solving its Bethe ansatz solution numerically. It is
found that the magnetic properties of the system for the case of
differs from that for the case of . The magnetization curve and
susceptibility are obtained for a system of 200 sites. For , the
phase diagram depending on the magnetic field and the ratio of Land\'e factors,
, is obtained. Four phases with distinct magnetic properties are
found.Comment: 4 pages, 2 figure
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