393 research outputs found
Condensation for non-relativistic matter in Ho\v{r}ava-Lifshitz gravity
We study condensation for non-relativistic matter in a Ho\v{r}ava-Lifshitz
black hole without the condition of the detailed balance. We show that, for the
fixed non-relativistic parameter (or the detailed balance parameter
), it is easier for the scalar hair to form as the parameter
(or ) becomes larger, but the condensation is not affected
by the non-relativistic parameter . We also find that the ratio of the
gap frequency in conductivity to the critical temperature decreases with the
increase of and , but increases with the increase of
. The ratio can reduce to the Horowitz-Roberts relation
obtained in the Einstein gravity and Cai's result
found in a Ho\v{r}ava-Lifshitz gravity with the
condition of the detailed balance for the relativistic matter. Especially, we
note that the ratio can arrive at the value of the BCS theory
by taking proper values of , ,
and .Comment: 16 pages, 5 figures, 2 tables. arXiv admin note: substantial text
overlap with arXiv:1001.1472; and text overlap with arXiv:0911.4867 by other
author
A quasi-optimal lower bound for skew polynomial multiplication
We establish a lower bound for the complexity of multiplying two skew
polynomials. The lower bound coincides with the upper bound conjectured by
Caruso and Borgne in 2017, up to a log factor. We present algorithms for three
special cases, indicating that the aforementioned lower bound is quasi-optimal.
In fact, our lower bound is quasi-optimal in the sense of bilinear complexity.
In addition, we discuss the average bilinear complexity of simultaneous
multiplication of skew polynomials and the complexity of skew polynomial
multiplication in the case of towers of extensions
Geometrically thick equilibrium tori around a Schwarzschild black hole in swirling universes
We study geometrically thick non-self gravitating equilibrium tori orbiting a
Schwarzschild black hole immersed in swirling universes. This solution is
axially symmetric and non-asymptotically flat, and its north and south
hemispheres spin in opposite directions. Due to repulsive effects arising from
the swirl of the background spacetime, the equilibrium torus exists only in the
case with the small swirling parameter. With the increase of the swirling
parameter, the disk structure becomes small and the excretion of matter near
the black hole becomes strong. Moreover, the odd symmetry of spacetimes
originating from the swirling parameter yields that the orientation of closed
equipotential surfaces deviates away from the horizontal axis and the
corresponding disk does not longer possess the symmetry with respect to the
equatorial plane. These significant features could help to further understand
the equilibrium tori and geometrically thick accretion disks around black holes
in swirling universes.Comment: 12 pages, 4 figure
Quasinormal modes of a scalar perturbation around a rotating BTZ-like black hole in Einstein-bumblebee gravity
We analytically study the quasinormal modes of a scalar perturbation around a
rotating BTZ-like black hole in the Einstein-bumblebee gravity. We observe that
the Lorentz symmetry breaking parameter imprints only in the imaginary parts of
the quasinormal frequencies for the right-moving and left-moving modes. The
perturbational field decays more rapidly for the negative Lorentz symmetry
breaking parameter, but more slowly for the positive one. The forms of the real
parts are the same as those in the usual BTZ black holes. Moreover, we also
discuss the correspondence from the quasinormal modes and find that
the Lorentz symmetry breaking parameter enhances the left and right conformal
weights and of the operators dual to the scalar field in the
boundary. These results could be helpful to understand the
correspondence and the Einstein-bumblebee gravity with the Lorentz symmetry
violation.Comment: 15 pages, 1 figur
- …