45 research outputs found
Gauge fields as composite boundary excitations
We investigate representations of the conformal group that describe
"massless" particles in the interior and at the boundary of anti-de Sitter
space. It turns out that massless gauge excitations in anti-de Sitter are gauge
"current" operators at the boundary. Conversely, massless excitations at the
boundary are topological singletons in the interior. These representations lie
at the threshold of two "unitary bounds" that apply to any conformally
invariant field theory. Gravity and Yang-Mills gauge symmetry in anti-De Sitter
is translated to global translational symmetry and continuous -symmetry of
the boundary superconformal field theory.Comment: Latex 2 figures in one eps fil
Heat and gravitation. II. Stability
In this second article of a series we propose to base criteria of stability
on the hamiltonian functional that is provided by the variational principle, to
replace the reliance that has often been placed on {\it ad hoc} definitions of
the "energy". We introduce a new virial principle that is formulated entirely
within the Eulerian description of hydrodynamics, which allows a simpler
derivation of a well known stability criterion for polytropic stellar
configurations. Boundary conditions are based entirely on mass conservation.Comment: 19 pages, plain te
On entropy in eulerian thermodynamics
To the student of thermodynamics the most difficult subject is entropy. In
this paper we examine the actual, practical application of entropy to two
simple systems, the homogeneous slab with fixed boundary values of the
temperature, and an isolated atmosphere in the presence of the static
gravitational field. The first gives valuable insight into the nature of
entropy that is subsequently applied to the second system.
It is a basic tenet of thermodynamics that the equilibrium of an extended,
homogeneous and isolated system is characterized by a uniform temperature
distribution and it is a strongly held belief that this remains true in the
presence of gravity. We find that this is consistent with the equations of
extended thermodynamics but that entropy enters in an essential way. The
principle of equivalence takes on a new aspect.Comment: Paper presented the AIP Conference on the second law of
thermodynamics, June 2011. Plaintex 20 page
On N=8 Supergravity on and N=4 Superconformal Yang-Mills theory
We discuss the spectrum of states of IIB supergravity on in a manifest invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in and superconformal invariant singleton theory at the boundary is formulated in an N=4 superfield covariant language
Reissner-Nordstrom and charged gas spheres
The main point of this paper is a suggestion about the proper treatment of
the photon gas in a theory of stellar structure and other plasmas. This problem
arises in the study of polytropic gas spheres, where we have already introduced
some innovations. The main idea, already advanced in the contextof neutral,
homogeneous, polytropic stellar models, is to base the theory firmly on a
variational principle. Another essential novelty is to let mass distribution
extend to infinity, the boundary between bulk and atmosphere being defined by
an abrupt change in the polytropic index, triggered by the density. The logical
next step in this program is to include the effect of radiation, which is a
very significant complication since a full treatment would have to include an
account of ionization, thus fieldsrepresenting electrons, ions, photons,
gravitons and neutral atoms as well. In way of preparation, we consider models
that are charged but homogeneous, involving only gravity, electromagnetism and
a single scalar field that represents both the mass and the electric charge; in
short, anon-neutral plasma. While this work only represents a stage in the
development of a theory of stars, without direct application to physical
systems, it does shed some light on the meaning of the Reissner-Nordstrom
solution of the modified Einstein-Maxwell equations., with an application to a
simple system.Comment: 19 pages, plain te
Ideal Stars and General Relativity
We study a system of differential equations that governs the distribution of
matter in the theory of General Relativity. The new element in this paper is
the use of a dynamical action principle that includes all the degrees of
freedom, matter as well as metric. The matter lagrangian defines a relativistic
version of non-viscous, isentropic hydrodynamics. The matter fields are a
scalar density and a velocity potential; the conventional, four-vector velocity
field is replaced by the gradient of the potential and its scale is fixed by
one of the eulerian equations of motion, an innovation that significantly
affects the imposition of boundary conditions. If the density is integrable at
infinity, then the metric approaches the Schwarzschild metric at large
distances. There are stars without boundary and with finite total mass; the
metric shows rapid variation in the neighbourhood of the Schwarzschild radius
and there is a very small core where a singularity indicates that the gas laws
break down. For stars with boundary there emerges a new, critical relation
between the radius and the gravitational mass, a consequence of the stronger
boundary conditions. Tentative applications are suggested, to certain Red
Giants, and to neutron stars, but the investigation reported here was limited
to polytropic equations of state. Comparison with the results of Oppenheimer
and Volkoff on neutron cores shows a close agreement of numerical results.
However, in the model the boundary of the star is fixed uniquely by the
required matching of the interior metric to the external Schwarzschild metric,
which is not the case in the traditional approach.Comment: 26 pages, 7 figure
Growth of a Black Hole
This paper studies the interpretation of physics near a Schwarzschild black
hole. A scenario for creation and growth is proposed that avoids the conundrum
of information loss. In this picture the horizon recedes as it is approached
and has no physical reality. Radiation is likely to occur, but it cannot be
predicted.Comment: 12 pages, 2 figures, TeX fil
Quantization on Curves
Deformation quantization on varieties with singularities offers perspectives
that are not found on manifolds. Essential deformations are classified by the
Harrison component of Hochschild cohomology, that vanishes on smooth manifolds
and reflects information about singularities. The Harrison 2-cochains are
symmetric and are interpreted in terms of abelian -products. This paper
begins a study of abelian quantization on plane curves over \Crm, being
algebraic varieties of the form R2/I where I is a polynomial in two variables;
that is, abelian deformations of the coordinate algebra C[x,y]/(I).
To understand the connection between the singularities of a variety and
cohomology we determine the algebraic Hochschild (co-)homology and its
Barr-Gerstenhaber-Schack decomposition. Homology is the same for all plane
curves C[x,y]/(I), but the cohomology depends on the local algebra of the
singularity of I at the origin.Comment: 21 pages, LaTex format. To appear in Letters Mathematical Physic