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The nonextensive parameter for the rotating astrophysical systems with power-law distributions
We study the nonextensive parameter for the rotating astrophysical systems
with power-law distributions, including both the rotating self-gravitating
system and the rotating space plasma. We extend the equation of nonextensive
parameter to complex system with arbitrary force field, and derive a general
equation of the q-parameter, most generally including both the rotating
self-gravitating systems and the rotating space plasmas. At the same time, we
reproduce the kappa-distribution in space plasmas and obtain equations of the
kappa-parameter. We show that the q-parameter is related not only to the
temperature gradient, the gravitational force and the electromagnetic force,
but also to the inertial centrifugal force and Coriolis force. Thus the
rotation introduces significant effect on nonextensivity in the systems.
Several examples are given to illustrate the nonextensive effect introduced by
the rotation.Comment: 11 pages, 56 reference
The Universal Property of the Entropy Sum of Black Holes in All Dimensions
It is proposed by Cvetic et al [Phys. Rev. Lett. 106 (2011) 121301] that the
product of all horizon areas for general rotating multi-change black holes has
universal expressions independent of the mass. When we consider the product of
all horizon entropies, however, the mass will be present in some cases, while
another new universal property [JHEP 1401 (2014) 031] is preserved, which is
more general and says that the sum of all horizon entropies depends only on the
coupling constants of the theory and the topology of the black hole. The
property has been studied in limited dimensions and the generalization in
arbitrary dimensions is not straight-forward. In this Letter, we prove a useful
formula, which makes it possible to investigate this conjectured universality
in arbitrary dimensions for the maximally symmetric black holes in general
Lovelock gravity and gravity. We also propose an approach to compute the
entropy sum of general Kerr-(anti-)de-Sitter black holes in arbitrary
dimensions. In all these cases, we prove that the entropy sum only depends on
the coupling constants and the topology of the black hole.Comment: 16 pages,no figures;v2: 17 pages, references added, minor
corrections/modifications; v3: 16 pages, added references, correct some
expressons, added equation (16) to make the context more clear, to appear in
PL
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