44 research outputs found
Scalar Field Probes of Power-Law Space-Time Singularities
We analyse the effective potential of the scalar wave equation near generic
space-time singularities of power-law type (Szekeres-Iyer metrics) and show
that the effective potential exhibits a universal and scale invariant leading
x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that
the metrics satisfy the strict Dominant Energy Condition (DEC). This result
parallels that obtained in hep-th/0403252 for probes consisting of families of
massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The
detailed properties of the scalar wave operator depend sensitively on the
numerical coefficient of the x^{-2}-term, and as one application we show that
timelike singularities satisfying the DEC are quantum mechanically singular in
the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We
also comment on some related issues like the near-singularity behaviour of the
scalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde
Inflationary Theory and Alternative Cosmology
Recently Hollands and Wald argued that inflation does not solve any of the
major cosmological problems. We explain why we disagree with their arguments.
They also proposed a new speculative mechanism of generation of density
perturbations. We show that in their scenario the inhomogeneities responsible
for the large scale structure observed today were generated at an epoch when
the energy density of the hot universe was 10^{95} times greater than the
Planck density. The only way to avoid this problem is to assume that there was
a stage of inflation in the early universe.Comment: 17 pages, 1 fig, a discussion of a canonical measure of probability
of inflation is adde
Hyperbolic billiards of pure D=4 supergravities
We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz
(BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as
for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find
that just as for the cases N=0 and N=8 investigated previously, these billiards
can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody
algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature
arises, however, which is that the relevant Kac-Moody algebra can be the
Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and
N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of
this property is provided by showing that the data relevant for determining the
billiards are the restricted root system and the maximal split subalgebra of
the finite-dimensional real symmetry algebra characterizing the toroidal
reduction to D=3 spacetime dimensions. To summarize: split symmetry controls
chaos.Comment: 21 page
Onset of inflation in inhomogeneous cosmology
We study how the initial inhomogeneities of the universe affect the onset of
inflation in the closed universe. We consider the model of a chaotic inflation
which is driven by a massive scalar field. In order to construct an
inhomogeneous universe model, we use the long wavelength approximation ( the
gradient expansion method ). We show the condition of the inhomogeneities for
the universe to enter the inflationary phase.Comment: 22 pages including 12 eps figures, RevTe
Topological entropy for some isotropic cosmological models
The chaotical dynamics is studied in different Friedmann-Robertson- Walker
cosmological models with scalar (inflaton) field and hydrodynamical matter. The
topological entropy is calculated for some particular cases. Suggested scheme
can be easily generalized for wide class of models. Different methods of
calculation of topological entropy are compared.Comment: Final version to appear in Phys. Rev D. Minor changes, typos
corrected; 29 pages with 2 eps figure
Kasner and Mixmaster behavior in universes with equation of state w \ge 1
We consider cosmological models with a scalar field with equation of state
that contract towards a big crunch singularity, as in recent cyclic
and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to
anisotropy and curvature are suppressed, and the contraction is described by a
homogeneous and isotropic Friedmann equation if . We generalize the
results to theories where the scalar field couples to p-forms and show that
there exists a finite value of , depending on the p-forms, such that chaotic
oscillations are suppressed. We show that orbifold compactification also
contributes to suppressing chaotic behavior. In particular, chaos is avoided in
contracting heterotic M-theory models if at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde
Chaos and Rotating Black Holes with Halos
The occurrence of chaos for test particles moving around a slowly rotating
black hole with a dipolar halo is studied using Poincar\'e sections. We find a
novel effect, particles with angular momentum opposite to the black hole
rotation have larger chaotic regions in phase space than particles initially
moving in the same direction.Comment: 9 pages, 4 Postscript figures. Phys. Rev. D, in pres
Braneworld dynamics with the BraneCode
We give a full nonlinear numerical treatment of time-dependent 5d braneworld
geometry, which is determined self-consistently by potentials for the scalar
field in the bulk and at two orbifold branes, supplemented by boundary
conditions at the branes. We describe the BraneCode, an algorithm which we
designed to solve the dynamical equations numerically. We applied the BraneCode
to braneworld models and found several novel phenomena of the brane dynamics.
Starting with static warped geometry with de Sitter branes, we found
numerically that this configuration is often unstable due to a tachyonic mass
of the radion during inflation. If the model admits other static configurations
with lower values of de Sitter curvature, this effect causes a violent
re-structuring towards them, flattening the branes, which appears as a lowering
of the 4d effective cosmological constant. Braneworld dynamics can often lead
to brane collisions. We found that in the presence of the bulk scalar field,
the 5d geometry between colliding branes approaches a universal, homogeneous,
anisotropic strong gravity Kasner-like asymptotic, irrespective of the
bulk/brane potentials. The Kasner indices of the brane directions are equal to
each other but different from that of the extra dimension.Comment: 38 pages, 10 figure
3D heterotic string theory: new approach and extremal solutions
We develop a new formalism for the bosonic sector of low-energy heterotic
string theory toroidally compactified to three dimensions. This formalism is
based on the use of some single non-quadratic real matrix potential which
transforms linearly under the action of subgroup of the three-dimensional
charging symmetries. We formulate a new charging symmetry invariant approach
for the symmetry generation and straightforward construction of asymptotically
flat solutions. Finally, using the developed approach and the established
formal analogy between the heterotic and Einstein-Maxwell theories, we
construct a general class of the heterotic string theory extremal solutions of
the Israel-Wilson-Perjes type. This class is asymptotically flat and charging
symmetry complete; it includes the extremal solutions constructed before and
possesses the non-trivial bosonic string theory limit.Comment: 20 pages in Late
The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
Quantum gravity in an AdS spacetime is described by an SU(N) Yang-Mills
theory on a sphere, a bounded many-body system. We argue that in the high
temperature phase the theory is intrinsically non-perturbative in the large N
limit. At any nonzero value of the 't Hooft coupling , an
exponentially large (in N^2) number of free theory states of wide energy range
(of order N) mix under the interaction. As a result the planar perturbation
theory breaks down. We argue that an arrow of time emerges and the dual string
configuration should be interpreted as a stringy black hole.Comment: 50 pages 3 figures uses harvma