428 research outputs found
The Dirac propagator in the Kerr-Newman metric
We give an alternative proof of the completeness of the Chandrasekhar ansatz
for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an
integral representation for smooth compactly supported functions which in turn
we use to derive an integral representation for the propagator of solutions of
the Cauchy problem with initial data in the above class of functions. As a
by-product, we also obtain the propagator for the Dirac equation in the
Minkowski space-time in oblate spheroidal coordinates.Comment: 29 pages, modifications in the abstract and in the introduction,
small improvements in section 2.
Velocity and velocity bounds in static spherically symmetric metrics
We find simple expressions for velocity of massless particles in dependence
of the distance in Schwarzschild coordinates. For massive particles these
expressions put an upper bound for the velocity. Our results apply to static
spherically symmetric metrics. We use these results to calculate the velocity
for different cases: Schwarzschild, Schwarzschild-de Sitter and
Reissner-Nordstr\"om with and without the cosmological constant. We emphasize
the differences between the behavior of the velocity in the different metrics
and find that in cases with naked singularity there exists always a region
where the massless particle moves with a velocity bigger than the velocity of
light in vacuum. In the case of Reissner-Nordstr\"om-de Sitter we completely
characterize the radial velocity and the metric in an algebraic way. We
contrast the case of classical naked singularities with naked singularities
emerging from metric inspired by noncommutative geometry where the radial
velocity never exceeds one. Furthermore, we solve the Einstein equations for a
constant and polytropic density profile and calculate the radial velocity of a
photon moving in spaces with interior metric. The polytropic case of radial
velocity displays an unexpected variation bounded by a local minimum and
maximum.Comment: 20 pages, 5 figure
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