6,353 research outputs found
Evaporation of Schwarzschild Black Holes in Matrix Theory
Recently, in collaboration with Susskind, we proposed a model of
Schwarzschild black holes in Matrix theory. A large Schwarzschild black hole is
described by a metastable bound state of a large number of D0-branes which are
held together by a background, whose structure has so far been understood only
in 8 and 11 dimensions. The Hawking radiation proceeds by emission of small
clusters of D0-branes. We estimate the Hawking rate in the Matrix theory model
of Schwarzschild black holes and find agreement with the semiclassical rate up
to an undetermined numerical coefficient of order 1.Comment: 9 pages, harvma
Matrix Theory Description of Schwarzschild Black Holes in the Regime N >> S
We study the description of Schwarzschild black holes, of entropy S, within
matrix theory in the regime . We obtain the most general matrix
theory equation of state by requiring that black holes admit a description
within this theory. It has a recognisable form in various cases. In some cases
a D dimensional black hole can plausibly be thought of as a
dimensional black hole, described by another auxiliary matrix theory, but in
its regime. We find what appears to be a matrix theory
generalisation to higher dynamical branes of the normalisation of dynamical
string tension, seen in other contexts. We discuss a further possible
generalisation of the matrix theory equation of state. In a special case, it is
governed by dynamical degrees of freedom.Comment: 22 pages. Latex fil
Inverse problems in the modeling of vibrations of flexible beams
The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented
Ultrarelativistic boost of spinning black rings
We study the D=5 Emparan-Reall spinning black ring under an ultrarelativistic
boost along an arbitrary direction. We analytically determine the resulting
shock pp-wave, in particular for boosts along axes orthogonal and parallel to
the plane of rotation. The solution becomes physically more interesting and
simpler if one enforces equilibrium between the forces on the ring. We also
comment on the ultrarelativistic limit of recently found supersymmetric black
rings with two independent angular momenta. Essential distinct features with
respect to the boosted Myers-Perry black holes are pointed out.Comment: 15 pages, 2 figures. v2: added multipole expansions at spatial
infinity, and a comparison with the boosted Myers-Perry solution in a new
appendix. To appear in JHE
Schwarzchild Black Holes in Matrix Theory II
We present a crude Matrix Theory model for Schwarzchild black holes in
uncompactified dimension greater than . The model accounts for the size,
entropy, and long range state interactions of black holes. The key feature of
the model is a Boltzmann gas of D0 branes, a concept which depends on certain
qualitative features of Matrix Theory which have not previously been utilized
in studies of black holes.Comment: 20 pages,harvmac,big, Some Typos corrected, 1 reference adde
Density of non-residues in Burgess-type intervals and applications
We show that for any fixed \eps>0, there are numbers and with the following property: for every prime and every integer
such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence
contains at least quadratic non-residues modulo . We use this
result to obtain strong upper bounds on the sizes of the least quadratic
non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a
co-author) to simply the proof and improve the main results of the previous
version, 14 page
Schwarzschild Black Holes from Matrix Theory
We consider Matrix theory compactified on T^3 and show that it correctly
describes the properties of Schwarzschild black holes in 7+1 dimensions,
including the energy-entropy relation, the Hawking temperature and the physical
size, up to numerical factors of order unity. The most economical description
involves setting the cut-off N in the discretized light-cone quantization to be
of order the black hole entropy. A crucial ingredient necessary for our work is
the recently proposed equation of state for 3+1 dimensional SYM theory with 16
supercharges. We give detailed arguments for the range of validity of this
equation following the methods of Horowitz and Polchinski.Comment: 9 pages, latex; minor typos correcte
Some comments about Schwarzschield black holes in Matrix theory
In the present paper we calculate the statistical partition function for any
number of extended objects in Matrix theory in the one loop approximation. As
an application, we calculate the statistical properties of K clusters of D0
branes and then the statistical properties of K membranes which are wound on a
torus.Comment: 15 page
Ten Dimensional Black Hole and the D0-brane Threshold Bound State
We discuss the ten dimensional black holes made of D0-branes in the regime
where the effective coupling is large, and yet the 11D geometry is unimportant.
We suggest that these black holes can be interpreted as excitations over the
threshold bound state. Thus, the entropy formula for the former is used to
predict a scaling region of the wave function of the latter. The horizon radius
and the mass gap predicted in this picture agree with the formulas derived from
the classical geometry.Comment: 11 pages, harvmac; v2: typos corrected, argument for the convergence
of two integrals improved, v3: one ref. adde
Supergravity and The Large N Limit of Theories With Sixteen Supercharges
We consider field theories with sixteen supersymmetries, which includes U(N)
Yang-Mills theories in various dimensions, and argue that their large N limit
is related to certain supergravity solutions. We study this by considering a
system of D-branes in string theory and then taking a limit where the brane
worldvolume theory decouples from gravity. At the same time we study the
corresponding D-brane supergravity solution and argue that we can trust it in
certain regions where the curvature (and the effective string coupling, where
appropriate) are small. The supergravity solutions typically have several
weakly coupled regions and interpolate between different limits of
string-M-theory.Comment: 24 pages, latex. v2: reference added, v3: typos correcte
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