120 research outputs found
On collisions with unlimited energies in the vicinity of Kerr and Schwarzschild black hole horizons
Two particle collisions close to the horizon of the rotating nonextremal
Kerr's and Schwarzschild black holes are analyzed. For the case of multiple
collisions it is shown that high energy in the centre of mass frame occurs due
to a great relative velocity of two particles and a large Lorentz factor. The
dependence of the relative velocity on the distance to horizon is analyzed, the
time of movement from the point in the accretion disc to the point of
scattering with large energy as well as the time of back movement to the Earth
are calculated. It is shown that they have reasonable order.Comment: 6 pages, 1 figure. arXiv admin note: significant text overlap with
arXiv:1105.154
Fermion Absorption Cross Section and Topology of Spherically Symmetric Black Holes
In 1997, Liberati and Pollifrone in Phys. Rev. D56 (1997) 6458
(hep-th/9708014) achieved a new formulation of the Bekenstein-Hawking formula,
where the entropy and the Euler characteristic are related by . In
this work we present a relation between the low-energy absorption cross section
for minimally coupled fermions and the Euler characteristic of
(3+1)-dimensional spherically symmetric black holes, i.e. . Based on the relation, using the Gauss--Bonnet--Chern theorem and
the -mapping method, an absorption cross section density is introduced to
describe the topology of the absorption cross section. It is shown that the
absorption cross section and its density are determined by the singularities of
the timelike Killing vector field of the spacetime and these singularities
carry the topological numbers, Hopf indices and Brouwer degrees, naturally.Comment: 16 pages, no figures, accepted by Phys. Lett.
Geometry of the extreme Kerr black holes
Geometrical properties of the extreme Kerr black holes in the topological
sectors of nonextreme and extreme configurations are studied. We find that the
Euler characteristic plays an essential role to distinguish these two kinds of
extreme black holes. The relationship between the geometrical properties and
the intrinsic thermodynamics are investigated.Comment: Latex version, 10 page
Particle Collisions on Stringy Black Hole Background
The collision of two particles in the background of a Sen black hole is
studied. With the equations of motion of the particles, the center-of-mass
energy is investigated when the collision takes place at the horizon of a Sen
black hole. For an extremal Sen black hole, we find that the center-of-mass
energy will be arbitrarily high with two conditions: (1) spin and (2)
one of the colliding particles has the critical angular momentum
. For a nonextremal Sen black hole, we show that, in order to
obtain an unlimited center-of-mass energy, one of the colliding particles
should have the critical angular momentum ( is
the radius of the outer horizon for a nonextremal black hole). However, a
particle with the angular momentum could not approach the
black hole from outside of the horizon through free fall, which implies that
the collision with arbitrarily high center-of-mass energy could not take place.
Thus, there is an upper bound of the center-of-mass energy for the nonextremal
black hole. We also obtain the maximal center-of-mass energy for a
near-extremal black hole and the result implies that the Planck-scale energy is
hard to be approached. Furthermore, we also consider the back-reaction effects.
The result shows that, neglecting the gravitational radiation, it has a weak
effect on the center-of-mass energy. However, we argue that the maximum allowed
center-of-mass energy will be greatly reduced to below the Planck-scale when
the gravitational radiation is included.Comment: 17 pages, 4 figures, published versio
The Role of Wind Waves in Dynamics of the Air-Sea Interface
Wind waves are considered as an intermediate small-scale dynamic process at
the air-sea interface,which modulates radically middle-scale dynamic processes
of the boundary layers in water and air. It is shown that with the aim of a
quantitative description of the impact said, one can use the numerical wind
wave models which are added with the blocks of the dynamic atmosphere boundary
layer (DABL) and the dynamic water upper layer (DWUL). A mathematical
formalization for the problem of energy and momentum transfer from the wind to
the upper ocean is given on the basis of the well known mathematical
representations for mechanisms of a wind wave spectrum evolution. The problem
is solved quantitatively by means of introducing special system parameters: the
relative rate of the wave energy input, IRE, and the relative rate of the wave
energy dissipation, DRE. For two simple wave-origin situations, the certain
estimations for values of IRE and DRE are found, and the examples of
calculating an impact of a wind sea on the characteristics of both the boundary
layer of atmosphere and the water upper layer are given. The results obtained
permit to state that the models of wind waves of the new (fifth) generation,
which are added with the blocks of the DABL and the DWUL, could be an essential
chain of the general model describing the ocean-atmosphere circulation.Comment: 11 pages, 4 figures, 1 tabl
An SU(2) Analog of the Azbel--Hofstadter Hamiltonian
Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and
Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the
problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce
a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a
specific spin-S Euler top and can be considered as its ``classical'' analog.
The eigenvalue problem for the proposed model, in the coherent state
representation, is described by the S-gap Lam\'e equation and, thus, is
completely solvable. We observe a striking similarity between the shapes of the
spectra of the two models for various values of the spin S.Comment: 19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and
Cartesian deformation of SU(2) and numerical results added. Final version as
will appear in J. Phys. A: Math. Ge
- …