266 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

### 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 $T_{\rm H}$
of the hairy black holes at maximal scalar-tensor coupling decreases
continuously with the increase of the charge and reaches $T_{\rm H}=0$ 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$_2\times S^2$ 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.

### 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 $d\leq 9$. 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

### Spontaneous scalarization of charged black holes at the approach to extremality

We study static, spherically symmetric and electrically charged black hole
solutions in a quadratic Einstein-scalar-Gauss-Bonnet gravity model. Very
similar to the uncharged case, black holes undergo spontaneous scalarization
for sufficiently large scalar-tensor coupling $\gamma$ - a phenomenon
attributed to a tachyonic instability of the scalar field system. While in the
uncharged case, this effect is only possible for positive values of $\gamma$,
we show that for sufficiently large values of the electric charge $Q$ two
independent domains of existence in the $\gamma$-$Q$-plane appear: one for
positive $\gamma$ and one for negative $\gamma$. We demonstrate that this new
domain for negative $\gamma$ exists because of the fact that the near-horizon
geometry of a nearly extremally charged black hole is $AdS_2\times S^2$.This
new domain appears for electric charges larger than approximately 74$\%$ of the
extremal charge. For positive $\gamma$ we observe that a singularity with
diverging curvature invariants forms outside the horizon when approaching
extremality.Comment: 13 pages including 6 figures and one tabl

### Quasi exactly solvable matrix models in sl(n)

We reconsider the quasi exactly solvable matrix models constructed recently
by R. Zhdanov. The 2$\times$2 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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