108 research outputs found
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
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
Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry
We derive a transformation of the noncommutative geometry inspired
Schwarzschild solution into new coordinates such that the apparent unphysical
singularities of the metric are removed. Moreover, we give the maximal
singularity-free atlas for the manifold with the metric under consideration.
This atlas reveals many new features e.g. it turns out to describe an infinite
lattice of asymptotically flat universes connected by black hole tunnels.Comment: 17 pages LaTex, 2 figure
The generalized Heun equation in QFT in curved space-times
In this article we give a brief outline of the applications of the
generalized Heun equation (GHE) in the context of Quantum Field Theory in
curved space-times. In particular, we relate the separated radial part of a
massive Dirac equation in the Kerr-Newman metric and the static perturbations
for the non-extremal Reissner-Nordstr\"{o}m solution to a GHE.Comment: 7 pages, some small improvements in section
Quantum Mechanical Corrections to the Schwarzschild Black Hole Metric
Motivated by quantum mechanical corrections to the Newtonian potential, which
can be translated into an -correction to the component of the
Schwarzschild metric, we construct a quantum mechanically corrected metric
assuming . We show how the Bekenstein black hole entropy
receives its logarithmic contribution provided the quantum mechanical
corrections to the metric are negative. In this case the standard horizon at
the Schwarzschild radius increases by small terms proportional to
and a remnant of the order of Planck mass emerges. We contrast these results
with a positive correction to the metric which, apart from a corrected
Schwarzschild horizon, leads to a new purely quantum mechanical horizon.Comment: 14 pages Latex, enlarged version as compared to the published on
A new development cycle of the Statistical Toolkit
The Statistical Toolkit is an open source system specialized in the
statistical comparison of distributions. It addresses requirements common to
different experimental domains, such as simulation validation (e.g. comparison
of experimental and simulated distributions), regression testing in the course
of the software development process, and detector performance monitoring.
Various sets of statistical tests have been added to the existing collection to
deal with the one sample problem (i.e. the comparison of a data distribution to
a function, including tests for normality, categorical analysis and the
estimate of randomness). Improved algorithms and software design contribute to
the robustness of the results. A simple user layer dealing with primitive data
types facilitates the use of the toolkit both in standalone analyses and in
large scale experiments.Comment: To be published in the Proc. of CHEP (Computing in High Energy
Physics) 201
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