484 research outputs found
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 Statistical Mechanics of Horizons and Black Hole Thermodynamics
Although we know that black holes are characterized by a temperature and an
entropy, we do not yet have a satisfactory microscopic ``statistical
mechanical'' explanation for black hole thermodynamics. I describe a new
approach that attributes the thermodynamic properties to ``would-be gauge''
degrees of freedom that become dynamical on the horizon. For the
(2+1)-dimensional black hole, this approach gives the correct entropy. (Talk
given at the Pacific Conference on Gravitation and Cosmology, Seoul, February
1996.)Comment: 11 pages, LaTe
Hall viscosity from gauge/gravity duality
In (2+1)-dimensional systems with broken parity, there exists yet another
transport coefficient, appearing at the same order as the shear viscosity in
the hydrodynamic derivative expansion. In condensed matter physics, it is
referred to as "Hall viscosity". We consider a simple holographic realization
of a (2+1)-dimensional isotropic fluid with broken spatial parity. Using
techniques of fluid/gravity correspondence, we uncover that the holographic
fluid possesses a nonzero Hall viscosity, whose value only depends on the
near-horizon region of the background. We also write down a Kubo's formula for
the Hall viscosity. We confirm our results by directly computing the Hall
viscosity using the formula.Comment: 12 page
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
The article reviews the current status of a theoretical approach to the
problem of the emission of gravitational waves by isolated systems in the
context of general relativity. Part A of the article deals with general
post-Newtonian sources. The exterior field of the source is investigated by
means of a combination of analytic post-Minkowskian and multipolar
approximations. The physical observables in the far-zone of the source are
described by a specific set of radiative multipole moments. By matching the
exterior solution to the metric of the post-Newtonian source in the near-zone
we obtain the explicit expressions of the source multipole moments. The
relationships between the radiative and source moments involve many non-linear
multipole interactions, among them those associated with the tails (and
tails-of-tails) of gravitational waves. Part B of the article is devoted to the
application to compact binary systems. We present the equations of binary
motion, and the associated Lagrangian and Hamiltonian, at the third
post-Newtonian (3PN) order beyond the Newtonian acceleration. The
gravitational-wave energy flux, taking consistently into account the
relativistic corrections in the binary moments as well as the various tail
effects, is derived through 3.5PN order with respect to the quadrupole
formalism. The binary's orbital phase, whose prior knowledge is crucial for
searching and analyzing the signals from inspiralling compact binaries, is
deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review
article originally published in 2002; available on-line at
http://www.livingreviews.org
Higher Dimensional Cylindrical or Kasner Type Electrovacuum Solutions
We consider a D dimensional Kasner type diagonal spacetime where metric
functions depend only on a single coordinate and electromagnetic field shares
the symmetries of spacetime. These solutions can describe static cylindrical or
cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on
electrovacuum solutions and four different types of solutions are obtained in
which one of them has no four dimensional counterpart. We also consider the
properties of the general solution corresponding to the exterior field of a
charged line mass and discuss its several properties. Although it resembles the
same form with four dimensional one, there is a difference on the range of the
solutions for fixed signs of the parameters. General magnetic field vacuum
solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic
universe for a special choice of the parameters. The Kasner forms of the
general solution are also presented for the cylindrical or cosmological cases.Comment: 16 pages, Revtex. Text and references are extended, Published versio
The Origin of Black Hole Entropy in String Theory
I review some recent work in which the quantum states of string theory which
are associated with certain black holes have been identified and counted. For
large black holes, the number of states turns out to be precisely the
exponential of the Bekenstein-Hawking entropy. This provides a statistical
origin for black hole thermodynamics in the context of a potential quantum
theory of gravity.Comment: 18 pages (To appear in the proceedings of the Pacific Conference on
Gravitation and Cosmology, Seoul, Korea, February 1-6, 1996.
Fast Scramblers Of Small Size
We investigate various geometrical aspects of the notion of `optical depth'
in the thermal atmosphere of black hole horizons. Optical depth has been
proposed as a measure of fast-crambling times in such black hole systems, and
the associated optical metric suggests that classical chaos plays a leading
role in the actual scrambling mechanism. We study the behavior of the optical
depth with the size of the system and find that AdS/CFT phase transitions with
topology change occur naturally as the scrambler becomes smaller than its
thermal length. In the context of detailed AdS/CFT models based on D-branes,
T-duality implies that small scramblers are described in terms of matrix
quantum mechanics.Comment: 14 pages, 3 figures. Added reference
Which Distributions (or Families of Distributions) Best Represent Interval Uncertainty: Case of Permutation-Invariant Criteria
In many practical situations, we only know the interval containing the quantity of interest, we have no information about the probability of different values within this interval. In contrast to the cases when we know the distributions and can thus use Monte-Carlo simulations, processing such interval uncertainty is difficult -- crudely speaking, because we need to try all possible distributions on this interval. Sometimes, the problem can be simplified: namely, it is possible to select a single distribution (or a small family of distributions) whose analysis provides a good understanding of the situation. The most known case is when we use the Maximum Entropy approach and get the uniform distribution on the interval. Interesting, sensitivity analysis -- which has completely different objectives -- leads to selection of the same uniform distribution. In this paper, we provide a general explanation of why uniform distribution appears in different situations -- namely, it appears every time we have a permutation-invariant objective functions with the unique optimum. We also discuss what happens if there are several optima
The holographic fluid dual to vacuum Einstein gravity
We present an algorithm for systematically reconstructing a solution of the
(d+2)-dimensional vacuum Einstein equations from a (d+1)-dimensional fluid,
extending the non-relativistic hydrodynamic expansion of Bredberg et al in
arXiv:1101.2451 to arbitrary order. The fluid satisfies equations of motion
which are the incompressible Navier-Stokes equations, corrected by specific
higher derivative terms. The uniqueness and regularity of this solution is
established to all orders and explicit results are given for the bulk metric
and the stress tensor of the dual fluid through fifth order in the hydrodynamic
expansion. We establish the validity of a relativistic hydrodynamic description
for the dual fluid, which has the unusual property of having a vanishing
equilibrium energy density. The gravitational results are used to identify
transport coefficients of the dual fluid, which also obeys an interesting and
exact constraint on its stress tensor. We propose novel Lagrangian models which
realise key properties of the holographic fluid.Comment: 31 pages; v2: references added and minor improvements, published
versio
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