14,049 research outputs found
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
Finitely Generated Nil but Not Nilpotent Evolution Algebra
To use evolution algebras to model population dynamics that both allow
extinction and introduction of certain gametes in finite generations,
nilpotency must be built into the algebraic structures of these algebras with
the entire algebras not to be nilpotent if the populations are assumed to
evolve for a long period of time. To adequately address this need, evolution
algebras over rings with nilpotent elements must be considered instead of
evolution algebras over fields. This paper develops some criteria, which are
computational in nature, about the nilpotency of these algebras, and shows how
to construct finitely generated evolution algebras which are nil but not
nilpotent
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