67,113 research outputs found
Some Problems of Topology Change Description in the Theory of Space-Time
The problem of topology change description in gravitation theory is analized
in detailes. It is pointed out that in standard four-dimensional theories the
topology of space may be considered as a particular case of boundary conditions
(or constraints). Therefore, the possible changes of space topology in
(3+1)-dimensions do not admit dynamical description nor in classical nor in
quantum theories and the statements about dynamical supressing of topology
change have no sence. In the framework of multidimensional theories the space
(and space-time) may be considered as the embedded manifolds. It give the real
posibilities for the dynamical description of the topology of space or
space-time.Comment: 16 pages, LaTex; some misprints, which prevent generation of PS file,
are correcte
Cones and causal structures on topological and differentiable manifolds
General definitions for causal structures on manifolds of dimension d+1>2 are
presented for the topological category and for any differentiable one.
Locally, these are given as cone structures via local (pointwise)
homeomorphic or diffeomorphic abstraction from the standard null cone variety
in R^{d+1}. Weak and strong local cone (LC) structures refer to the cone itself
or a manifold thickening of the cone respectively.
After introducing cone (C-)causality, a causal complement with reasonable
duality properties can be defined. The most common causal concepts of
space-times are generalized to the present topological setting. A new notion of
precausality precludes inner boundaries within future/past cones.
LC-structures, C-causality, a topological causal complement, and precausality
may be useful tools in conformal and background independent formulations of
(algebraic) quantum field theory and quantum gravity.Comment: v3: 12 pages, latex+amssymb; compatibility conditions (2.5) and (3.2)
with misprints corrected and improved argumen
Exotic Differentiable Structures and General Relativity
We review recent developments in differential topology with special concern
for their possible significance to physical theories, especially general
relativity. In particular we are concerned here with the discovery of the
existence of non-standard (``fake'' or ``exotic'') differentiable structures on
topologically simple manifolds such as , \R and
Because of the technical difficulties involved in the smooth case, we begin
with an easily understood toy example looking at the role which the choice of
complex structures plays in the formulation of two-dimensional vacuum
electrostatics. We then briefly review the mathematical formalisms involved
with differentiable structures on topological manifolds, diffeomorphisms and
their significance for physics. We summarize the important work of Milnor,
Freedman, Donaldson, and others in developing exotic differentiable structures
on well known topological manifolds. Finally, we discuss some of the geometric
implications of these results and propose some conjectures on possible physical
implications of these new manifolds which have never before been considered as
physical models.Comment: 11 pages, LaTe
An Experimental Investigation of Hyperbolic Routing with a Smart Forwarding Plane in NDN
Routing in NDN networks must scale in terms of forwarding table size and
routing protocol overhead. Hyperbolic routing (HR) presents a potential
solution to address the routing scalability problem, because it does not use
traditional forwarding tables or exchange routing updates upon changes in
network topologies. Although HR has the drawbacks of producing sub-optimal
routes or local minima for some destinations, these issues can be mitigated by
NDN's intelligent data forwarding plane. However, HR's viability still depends
on both the quality of the routes HR provides and the overhead incurred at the
forwarding plane due to HR's sub-optimal behavior. We designed a new forwarding
strategy called Adaptive Smoothed RTT-based Forwarding (ASF) to mitigate HR's
sub-optimal path selection. This paper describes our experimental investigation
into the packet delivery delay and overhead under HR as compared with
Named-Data Link State Routing (NLSR), which calculates shortest paths. We run
emulation experiments using various topologies with different failure
scenarios, probing intervals, and maximum number of next hops for a name
prefix. Our results show that HR's delay stretch has a median close to 1 and a
95th-percentile around or below 2, which does not grow with the network size.
HR's message overhead in dynamic topologies is nearly independent of the
network size, while NLSR's overhead grows polynomially at least. These results
suggest that HR offers a more scalable routing solution with little impact on
the optimality of routing paths
Pre-Inflationary Spacetime in String Cosmology
Seiberg and Witten have shown that the non-perturbative stability of string
physics on conformally compactified spacetimes is related to the behaviour of
the areas and volumes of certain branes as the brane is moved towards infinity.
If, as is particularly natural in quantum cosmology, the spatial sections of an
accelerating cosmological model are flat and compact, then the spacetime is on
the brink of disaster: it turns out that the version of inflationary spacetime
geometry with toral spatial sections is marginally stable in the Seiberg-Witten
sense. The question is whether the system remains stable before and after
Inflation, when the spacetime geometry is distorted away from the inflationary
form but still has flat spatial sections. We show that it is indeed possible to
avoid disaster, but that requiring stability at all times imposes non-trivial
conditions on the spacetime geometry of the early Universe in string cosmology.
This in turn allows us to suggest a candidate for the structure which, in the
earliest Universe, forbids cosmological singularities.Comment: Final version to appear in NPB, 27 pages including 1 eps figur
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