4,609 research outputs found
Exact solution for two unequal counter-rotating black holes
The complete solution for two unequal counter-rotating black holes separated
by a massless strut, is developed in terms of four arbitrary parameters
involving two quantities \sigma 1 and \sigma 2 as the half length of the two
rods representing the black hole horizons, the total mass M and the relative
distance R between the centers of the horizons. A further attempt for
describing the explicit form of this solution in terms of the physical
parameters: The two Komar masses M1 and M2, Komar angular momenta per unit mass
a1 and a2 (a1 and a2 have opposite sign), and the coordinate distance R, guided
us to a 4-parameter subclass in which the five physical parameters satisfy a
simple algebraic relation and the interaction force in this scheme looks like
Schwarzschild type.Comment: This paper has been withdrawn for changes on i
Hidden Symmetries, AdS_D x S^n, and the lifting of one-time-physics to two-time-physics
The massive non-relativistic free particle in d-1 space dimensions has an
action with a surprizing non-linearly realized SO(d,2) symmetry. This is the
simplest example of a host of diverse one-time-physics systems with hidden
SO(d,2) symmetric actions. By the addition of gauge degrees of freedom, they
can all be lifted to the same SO(d,2) covariant unified theory that includes an
extra spacelike and an extra timelike dimension. The resulting action in d+2
dimensions has manifest SO(d,2) Lorentz symmetry and a gauge symmetry Sp(2,R)
and it defines two-time-physics. Conversely, the two-time action can be gauge
fixed to diverse one-time physical systems. In this paper three new gauge fixed
forms that correspond to the non-relativistic particle, the massive
relativistic particle, and the particle in AdS_(d-n) x S^n spacetime will be
discussed. The last case is discussed at the first quantized and field theory
levels as well. For the last case the popularly known symmetry is SO(d-n-1,2) x
SO(n+1), but yet we show that it is symmetric under the larger SO(d,2). In the
field theory version the action is symmetric under the full SO(d,2) provided it
is improved with a quantized mass term that arises as an anomaly from operator
ordering ambiguities. The anomalous cosmological term vanishes for AdS_2 x S^0
and AdS_n x S^n (i.e. d=2n). The strikingly larger symmetry could be
significant in the context of the proposed AdS/CFT duality.Comment: Latex, 23 pages. The term "cosmological constant" that appeared in
the original version has been changed to "mass term". My apologies for the
confusio
The Fractality of the Hydrodynamic Modes of Diffusion
Transport by normal diffusion can be decomposed into the so-called
hydrodynamic modes which relax exponentially toward the equilibrium state. In
chaotic systems with two degrees of freedom, the fine scale structure of these
hydrodynamic modes is singular and fractal. We characterize them by their
Hausdorff dimension which is given in terms of Ruelle's topological pressure.
For long-wavelength modes, we derive a striking relation between the Hausdorff
dimension, the diffusion coefficient, and the positive Lyapunov exponent of the
system. This relation is tested numerically on two chaotic systems exhibiting
diffusion, both periodic Lorentz gases, one with hard repulsive forces, the
other with attractive, Yukawa forces. The agreement of the data with the theory
is excellent
The fractality of the relaxation modes in deterministic reaction-diffusion systems
In chaotic reaction-diffusion systems with two degrees of freedom, the modes
governing the exponential relaxation to the thermodynamic equilibrium present a
fractal structure which can be characterized by a Hausdorff dimension. For long
wavelength modes, this dimension is related to the Lyapunov exponent and to a
reactive diffusion coefficient. This relationship is tested numerically on a
reactive multibaker model and on a two-dimensional periodic reactive Lorentz
gas. The agreement with the theory is excellent
A Two-Form Formulation of the Vector-Tensor Multiplet in Central Charge Superspace
A two-form formulation for the N=2 vector-tensor multiplet is constructed
using superfield methods in central charge superspace. The N=2 non-Abelian
standard supergauge multiplet in central charge superspace is also discussed,
as is with the associated Chern-Simons form. We give the constraints, solve the
Bianchi identities and present the action for a theory of the vector-tensor
multiplet coupled to the non-Abelian supergauge multiplet via the Chern-Simons
form.Comment: 16 pages, LaTeX2e with AMS-LaTe
Fractals and dynamical chaos in a random 2D Lorentz gas with sinks
Two-dimensional random Lorentz gases with absorbing traps are considered in
which a moving point particle undergoes elastic collisions on hard disks and
annihilates when reaching a trap. In systems of finite spatial extension, the
asymptotic decay of the survival probability is exponential and characterized
by an escape rate, which can be related to the average positive Lyapunov
exponent and to the dimension of the fractal repeller of the system. For
infinite systems, the survival probability obeys a stretched exponential law of
the form P(c,t)~exp(-Ct^{1/2}). The transition between the two regimes is
studied and we show that, for a given trap density, the non-integer dimension
of the fractal repeller increases with the system size to finally reach the
integer dimension of the phase space. Nevertheless, the repeller remains
fractal. We determine the special scaling properties of this fractal.Comment: 40 pages, 10 figures, preprint for Physica
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