725 research outputs found
Exotic Smoothness and Physics
The essential role played by differentiable structures in physics is reviewed
in light of recent mathematical discoveries that topologically trivial
space-time models, especially the simplest one, , possess a rich
multiplicity of such structures, no two of which are diffeomorphic to each
other and thus to the standard one. This means that physics has available to it
a new panoply of structures available for space-time models. These can be
thought of as source of new global, but not properly topological, features.
This paper reviews some background differential topology together with a
discussion of the role which a differentiable structure necessarily plays in
the statement of any physical theory, recalling that diffeomorphisms are at the
heart of the principle of general relativity. Some of the history of the
discovery of exotic, i.e., non-standard, differentiable structures is reviewed.
Some new results suggesting the spatial localization of such exotic structures
are described and speculations are made on the possible opportunities that such
structures present for the further development of physical theories.Comment: 13 pages, LaTe
Localized Exotic Smoothness
Gompf's end-sum techniques are used to establish the existence of an infinity
of non-diffeomorphic manifolds, all having the same trivial
topology, but for which the exotic differentiable structure is confined to a
region which is spatially limited. Thus, the smoothness is standard outside of
a region which is topologically (but not smoothly) ,
where is the compact three ball. The exterior of this region is
diffeomorphic to standard . In a
space-time diagram, the confined exoticness sweeps out a world tube which, it
is conjectured, might act as a source for certain non-standard solutions to the
Einstein equations. It is shown that smooth Lorentz signature metrics can be
globally continued from ones given on appropriately defined regions, including
the exterior (standard) region. Similar constructs are provided for the
topology, of the Kruskal form of the Schwarzschild
solution. This leads to conjectures on the existence of Einstein metrics which
are externally identical to standard black hole ones, but none of which can be
globally diffeomorphic to such standard objects. Certain aspects of the Cauchy
problem are also discussed in terms of \models which are
``half-standard'', say for all but for which cannot be globally
smooth.Comment: 8 pages plus 6 figures, available on request, IASSNS-HEP-94/2
Nonminimal Couplings in the Early Universe: Multifield Models of Inflation and the Latest Observations
Models of cosmic inflation suggest that our universe underwent an early phase
of accelerated expansion, driven by the dynamics of one or more scalar fields.
Inflationary models make specific, quantitative predictions for several
observable quantities, including particular patterns of temperature anistropies
in the cosmic microwave background radiation. Realistic models of high-energy
physics include many scalar fields at high energies. Moreover, we may expect
these fields to have nonminimal couplings to the spacetime curvature. Such
couplings are quite generic, arising as renormalization counterterms when
quantizing scalar fields in curved spacetime. In this chapter I review recent
research on a general class of multifield inflationary models with nonminimal
couplings. Models in this class exhibit a strong attractor behavior: across a
wide range of couplings and initial conditions, the fields evolve along a
single-field trajectory for most of inflation. Across large regions of phase
space and parameter space, therefore, models in this general class yield robust
predictions for observable quantities that fall squarely within the "sweet
spot" of recent observations.Comment: 17pp, 2 figs. References added to match the published version.
Published in {\it At the Frontier of Spacetime: Scalar-Tensor Theory, Bell's
Inequality, Mach's Principle, Exotic Smoothness}, ed. T. Asselmeyer-Maluga
(Springer, 2016), pp. 41-57, in honor of Carl Brans's 80th birthda
Stationary Points of Scalar Fields Coupled to Gravity
We investigate the dynamics of gravity coupled to a scalar field using a
non-canonical form of the kinetic term. It is shown that its singular point
represents an attractor for classical solutions and the stationary value of the
field may occur distant from the minimum of the potential. In this paper
properties of universes with such stationary states are considered. We reveal
that such state can be responsible for modern dark energy density.Comment: H. Kroger, invited talk, FFP6, Udine (2004), revised version with
corrected author lis
A Nonsingular Brans Wormhole: An Analogue to Naked Black Holes
In a recent paper, we showed the Jordan frame vacuum Brans Class I solution
provided a wormhole analogue to Horowitz-Ross naked black hole in the wormhole
range -3/2<{\omega}<-4/3. Thereafter, the solution has been criticized by some
authors that, because of the presence of singularity in that solution within
this range, a wormhole interpretation of it is untenable. While the criticism
is correct, we show here that (i) a singularity-free wormhole can actually be
obtained from Class I solution by performing a kind of Wick rotation on it,
resulting into what Brans listed as his independent Class II solution (ii) the
Class II solution has all the necessary properties of a regular wormhole in a
revised range -2<{\omega}<-3/2 and finally, (iii) naked black holes, as
described by Horowitz and Ross, are spacetimes where the tidal forces attain
their maxima above the black hole horizon. We show that in the non-singular
Class II spacetime this maxima is attained above the throat and thus can be
treated as a wormhole analogue. Some related issues are also addressed.Comment: 20 pages, 4 figure
Black holes in the Brans-Dicke-Maxwell theory
The black hole solutions in the higher dimensional Brans-Dicke-Maxwell theory
are investigated. We find that the presence of the nontrivial scalar field
depends on the spacetime dimensions (D). When D=4, the solution corresponds to
the Reissner-Nordstr\"{o}m black hole with a constant scalar field. In higher
dimensions (D>4), one finds the charged black hole solutions with the
nontrivial scalar field. The thermal properties of the charged black holes are
discussed and the reason why the nontrivial scalar field exists are explained.
Also the solutions for higher dimensional Brans-Dicke theory are given for
comparison.Comment: Revtex, 5 pages, no figures, contents were rewritten and new
references were adde
Stellar explosion in the weak field approximation of the Brans-Dicke theory
We treat a very crude model of an exploding star, in the weak field
approximation of the Brans-Dicke theory, in a scenario that resembles some
characteristics data of a Type Ia Supernova. The most noticeable feature, in
the electromagnetic component, is the relationship between the absolute
magnitude at maximum brightness of the star and the decline rate in one
magnitude from that maximum. This characteristic has become one of the most
accurate method to measure luminosity distances to objects at cosmological
distances. An interesting result is that the active mass associated with the
scalar field is totally radiated to infinity, representing a mass loss in the
ratio of the "tensor" component to the scalar component of 1 to ( is the Brans-Dicke parameter), in agreement with a general result
of Hawking. Then, this model shows explicitly, in a dynamical case, the
mechanism of radiation of scalar field, which is necessary to understand the
Hawking result.Comment: 11 pages, no figures. Published in Class. Quantum Gravity V22 (2005
Gravitational dipole radiations from binary systems
We investigate the possibility of generating sizeable dipole radiations in
relativistic theories of gravity. Optimal parameters to observe their effects
through the orbital period decay of binary star systems are discussed.
Constraints on gravitational couplings beyond general relativity are derived.Comment: One comment added, accepted for publication in Phys. Rev.
Coupling parameters and the form of the potential via Noether symmetry
We explore the conditions for the existence of Noether symmetries in the
dynamics of FRW metric, non minimally coupled with a scalar field, in the most
general situation, and with nonzero spatial curvature. When such symmetries are
present we find general exact solution for the Einstein equations. We also show
that non Noether symmetries can be found.
Finally,we present an extension of the procedure to the Kantowski- Sachs
metric which is particularly interesting in the case of degenerate Lagrangian.Comment: 13 pages, no figure
Singularity Free (Homogeneous Isotropic) Universe in Graviton-Dilaton Models
We present a class of graviton-dilaton models in which a homogeneous
isotropic universe, such as our observed one, evolves with no singularity at
any time. Such models may stand on their own as interesting models for
singularity free cosmology, and may be studied further accordingly. They may
also arise from string theory. We discuss critically a few such possibilities.Comment: 11 pages. Latex file. Revised in response to referees' Comments.
Results remain same. To appear in Phys. Rev. Let
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