210 research outputs found
Quasi exactly solvable operators and Lie superalgebras
Linear operators preserving the direct sum of polynomial rings P(m)\oplus
P(n) are constructed. In the case |m-n|=1 they correspond to atypical
representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite
dimensional representations of the superalgebra q(2) are recovered. An example
of a Hamiltonian possessing such a hidden algebra is analyzed.Comment: 8 Revtex pages, 1 PS-figures; Section IV extended, reference adde
Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method
We propose to compute the action and global charges of the asymptotically
anti-de Sitter solutions in Einstein-Gauss-Bonnet theory by adding boundary
counterterms to the gravitational action. The general expression of the
counterterms and the boundary stress tensor is presented for spacetimes of
dimension . We apply this tehnique for several different types of
black objects. Apart from static and rotating black holes, we consider also
Einstein-Gauss-Bonnet black string solutions with negative cosmological
constant.Comment: 27 pages, 6 figures, references added, discussion extende
Charged black holes in a generalized scalar-tensor gravity model
We study 4-dimensional charged and static black holes in a generalized
scalar-tensor gravity model, in which a shift symmetry for the scalar field
exists. For vanishing scalar field the solution corresponds to the
Reissner-Nordstr\"om (RN) solution, while solutions of the full scalar-gravity
model have to be constructed numerically. We demonstrate that these black holes
support galilean scalar hair up to a maximal value of the scalar-tensor
coupling that depends on the value of the charge and can be up to roughly twice
as large as that for uncharged solutions. The Hawking temperature
of the hairy black holes at maximal scalar-tensor coupling decreases
continuously with the increase of the charge and reaches for the
highest possible charge that these solutions can carry. However, in this limit,
the scalar-tensor coupling needs to vanish. The limiting solution hence
corresponds to the extremal RN solution, which does not support regular
galilaen scalar hair due to its AdS near-horizon geometry.Comment: 11 pages including 5 figures; v2: comments on conserved Noether
current added, references added; matches version accepted for publication in
Phys. Lett.
Quasi exactly solvable matrix models in sl(n)
We reconsider the quasi exactly solvable matrix models constructed recently
by R. Zhdanov. The 22 matrix operators representing the algebra sl(2)
are generalized to matrices of arbitrary dimension and a similar construction
is achieved for the algebra sl(n).Comment: LaTeX, 8 page
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