1,976 research outputs found

### Primordial Inflation

A macroscopic universe may emerge naturally from a Planck cell fluctuation by
unfolding through a stage of exponential expansion towards a homogeneous
cosmological background. Such primordial inflation requires a large and
presumably infinite degeneracy at the Planck scale, rooted in the unbounded
negative gravitational energy stored in conformal classes. This complex Planck
structure is consistent with a quantum tunneling description of the transition
from the Planck scale to the inflationary era and implies, in the limit of
vanishing Planck size, the Hartle-Hawking no-time boundary condition. On the
other hand, string theory give credence to the holographic principle and the
concomitant depletion of states at the Planck scale. The apparent
incompatibility of primordial inflation with holography either invalidates one
of these two notions or relegates the nature of the Planck size outside the
realm of quantum physics, as we know it.Comment: LaTeX, 24 pages, 4 figures, presented at the Erice International
School on Basics and Highlights in Fundamental Physics, August 199

### On the black hole unitarity issue

I discuss features required for preserving unitarity in black hole decay and
concepts underlying such a perspective. Unitarity requires that correlations
extend on the scale of the horizon. I show, in a toy model inspired by string
theories, that such correlations can indeed arise. The model suggests that,
after a time of order 4M ln M following the onset of Hawking radiation, quantum
effects could maintain throughout the decay a collapsing star within a Planck
distance of its Schwarzschild radius. In this way information loss would be
avoided. The concept of black hole ``complementarity'', which could reconcile
these macroscopic departures from classical physics with the equivalence
principle, is interpreted in terms of weak values of quantum operators.Comment: 14 pages, latex, no figures. Talk presented at the Puri workshop
(December 1996

### OPERATOR WEAK VALUES AND BLACK HOLE COMPLEMENTARITY

In conventional field theories, the emission of Hawking radiation in the
background of a collapsing star requires transplanckian energy fluctuations.
These fluctuations are encoded in the weak values of the energy-momentum
operator constructed from matrix elements between both -in and -out states. It
is argued that taming of these weak values by back-reaction may lead to
geometrical backgrounds which are also build from weak values of the
gravitational field operators. This leads to different causal histories of the
black hole as reconstructed by observers crossing the horizon at different
times but reduces, in accordance with the equivalence principle, to the
classical description of the collapse for the proper history of the star as
recorded by an observer comoving with it. For observers never crossing the
horizon, the evaporation would be interpreted within a topologically trivial
``achronon geometry" void of horizon and singularity: after the initial
ignition of the radiation from pair creation out of the vacuum of the
collapsing star of mass M, as in the conventional theory, the source of the
thermal radiation would shift gradually to the star itself in a time at least
of order $4M\ln 2M$. The burning of the star could be consistent with a quantum
unitary evolution along the lines suggested by 't Hooft. A provisional formal
expression of general black hole complementarity is proposed and its possible
relevance for testing features of a theory of quantum gravity is suggested.Comment: presented at the Oskar Klein Centenary Symposium (September 1994); 29
pages, phyzzx, no figure

### Black Hole Tunneling Entropy and the Spectrum of Gravity

The tunneling approach for entropy generation in quantum gravity is applied
to black holes. The area entropy is recovered and shown to count only a tiny
fraction of the black hole degeneracy. The latter stems from the extension of
the wave function outside the barrier. In fact the semi-classical analysis
leads to infinite degeneracy. Evaporating black holes leave then infinitely
degenerate "planckons" remnants which can neither decay into, nor be formed
from, ordinary matter in a finite time. Quantum gravity opens up at the Planck
scale into an infinite Hilbert space which is expected to provide the
ultraviolet cutoff required to render the theory finite in the sector of large
scale physics.Comment: 26 pages + 3 figures, phyzzx macropackage, figures available from
Author

### Statistical Entropy of Schwarzschild Black Holes

The entropy of a seven dimensional Schwarzschild black hole of arbitrary
large radius is obtained by a mapping onto a near extremal self-dual
three-brane whose partition function can be evaluated. The three-brane arises
from duality after submitting a neutral blackbrane, from which the
Schwarzschild black hole can be obtained by compactification, to an infinite
boost in non compact eleven dimensional space-time and then to a Kaluza-Klein
compactification. This limit can be defined in precise terms and yields the
Bekenstein-Hawking value up to a factor of order one which can be set to be
exactly one with the extra assumption of keeping only transverse brane
excitations. The method can be generalized to five and four dimensional black
holes.Comment: 11 pages, LaTex, no figures, corrected typ

### G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

We present a tentative formulation of theories of gravity with suitable
matter content, including in particular pure gravity in D dimensions, the
bosonic effective actions of M-theory and of the bosonic string, in terms of
actions invariant under very-extended Kac-Moody algebras G+++. We conjecture
that they host additional degrees of freedom not contained in the conventional
theories. The actions are constructed in a recursive way from a level expansion
for all very-extended algebras G+++. They constitute non-linear realisations on
cosets, a priori unrelated to space-time, obtained from a modified Chevalley
involution. Exact solutions are found for all G+++. They describe the algebraic
properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein
monopoles. They illustrate the generalisation to all G+++ invariant theories of
the well-known duality properties of string theories by expressing duality as
Weyl invariance in G+++. Space-time is expected to be generated dynamically. In
the level decomposition of E8+++ = E11, one may indeed select an A10
representation of generators Pa which appears to engender space-time
translations by inducing infinite towers of fields interpretable as field
derivatives in space and time.Comment: Latex 45 pages, 1 figure. Discussion on pages 19 and 20 altered.
Appendix B amplified. 4 footnotes added. 2 references added. Acknowledgments
updated. Additional minor correction

### Representations of G+++ and the role of space-time

We consider the decomposition of the adjoint and fundamental representations
of very extended Kac-Moody algebras G+++ with respect to their regular A type
subalgebra which, in the corresponding non-linear realisation, is associated
with gravity. We find that for many very extended algebras almost all the A
type representations that occur in the decomposition of the fundamental
representations also occur in the adjoint representation of G+++. In
particular, for E8+++, this applies to all its fundamental representations.
However, there are some important examples, such as An+++, where this is not
true and indeed the adjoint representation contains no generator that can be
identified with a space-time translation. We comment on the significance of
these results for how space-time can occur in the non-linear realisation based
on G+++. Finally we show that there is a correspondence between the A
representations that occur in the fundamental representation associated with
the very extended node and the adjoint representation of G+++ which is
consistent with the interpretation of the former as charges associated with
brane solutions.Comment: 45 pages, 9 figures, 9 tables, te

### Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories

A description of the bosonic sector of ten-dimensional N=1 supergravity as a
non-linear realisation is given. We show that if a suitable extension of this
theory were invariant under a Kac-Moody algebra, then this algebra would have
to contain a rank eleven Kac-Moody algebra, that can be identified to be a
particular real form of very-extended D_8. We also describe the extension of
N=1 supergravity coupled to an abelian vector gauge field as a non-linear
realisation, and find the Kac-Moody algebra governing the symmetries of this
theory to be very-extended B_8. Finally, we discuss the related points for the
N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields

### E10 and SO(9,9) invariant supergravity

We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc

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