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Journ�es Relativistes University
College Dublin
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Abstracts of Contributed Talks (in speaking order) |
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J. Novak (and E. Gourgoulhon)(Paris): Covariant Conformal Decomposition of Einstein Equations P.
Nurowski (Warsaw): Conformal Connection and Equivalence Problem for
Third Order ODEs B.
Edgar (Sweden): Finding Conformal Killing Vectors from the Invariant
Classification Scheme G. Valent (and P-.Y. Casteill) (Paris): Some Self-Dual Einstein Metrics from Harmonic Super-Space P. S. Florides (Dublin): Einstein�s Equivalence Principle and the Gravitational Red Shift P. Spindel (Mons): Scalar Perturbations in a Primordial Inflationary Scenario Alan
A. Coley (Dalhousie): Assisted Inflation P.
Teyssandier (Paris): Non-Minimal Coupling, Variable Speed of Light
and Cosmology M. R. Martinez (Paris): Brane Cosmology with a Bulk Scalar Field J.
C. Thorwart (and J. J. Halliwell) (London): Timeless Properties for
Quantum Models M. E. Guimaraes (Brazil): String�s Current Induced by the Dilatonic Coupling of Gravity D. Birmingham (Dublin): Choptuik
Scaling and Quasi Normal Modes in the AdS/CFT Correspondence Alessandro
Fabbri (Bologna): 2D Black Holes and Dimensional Reduction S.
Mignemi (Cagliari): Primary Scalar Hair of Black Holes in String
Theory R.
Steinbauer (Vienna): Generalised Pseudo-Riemannian Geometry for
General Relativity R.
Garattini (Bergamo): Wormholes and Space-Time Foam: the case with a
cosmological constant J-.W.
van Holten (Amsterdam): World-Line Deviations R.
Colistete (Paris): Higher-Order Geodesic Deviations with the Kerr
Metric
FRIDAY: G.
Bergqvist(Sweden): Causal Tensors and Simple Forms J.M.M. Senovilla (Bilbao): Causal
Tensors and Rainich Conditions R.
Casadio (Bologna): Gamma-Ray Bursts from Gravitational Collapse C.
Barrab�s (and P. A. Hogan) (Tours): Impulsive Light-Like Signals L.
Villain (Paris): Concerning r-Modes in Neutron Stars C.
Ringeval (Paris): Fermionic Currents Along Cosmic Strings S.
Kaniel (Jerusalem): On The Derivation of the Equations of Motion B.
C. Nolan (Dublin): Weak Solutions for Weak Singularities J.
Vickers (Southampton): Weak Singularities in General Relativity J.
Melanson (and P. Gravel) (New Brunswick): Energy Conditions for
Primordial Warp Drives D.
Puetzfeld (Cologne): A Cosmological Model in Weyl-Cartan Space-Time
Y.
Itin (Jerusalem): Conserved Currents for General Teleparallel Models M. Carmeli (Beer Sheva): Cosmological Constant and Dark Matter: Theory versus Experiment J. C. Fabris (Brazil): Classical Analogue of Quantum Cosmological Perfect Fluid Model |
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| ABSTRACTS: | |
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J.
Novak (and E. Gourgoulhon)(Paris): Covariant Conformal
Decomposition of Einstein Equations A
3+1 type formalism is presented to decompose Einstein�s equations.
This decomposition is motivated by the aim of stable numerical
implementation and resolution of the equations. We introduce the
conformal 3-�metric� (scaled by the determinant of the usual
3-metric) which is a tensor density of weight �2/3. The Einstein
equations are then derived in terms of this �metric�, of the
conformal extrinsic curvature and in terms of the associated
derivative. We also introduce a flat 3-metric (the asymptotic metric
for isolated systems) and the associated derivative. Finally, the
generalised Dirac gauge is introduced in this formalism and some
examples are shown. P.
Nurowski (Warsaw): Conformal Connection and
Equivalence Problem for Third Order ODEs The
equivalence problem for the third order ODEs solved by E. Cartan and
S. S. Chern is reconsidered. We consider third order ODEs of the form
y'''=F(x,y,y',y'') for which the Wunshman invariant I vanishes.
All such ODEs split into equivalence classes with respect to the
contact transformations of the variables. As shown by E. T. Newman and
collaborators such equations are also in one-to-one correspondence
with conformal classes of Lorentian three-metrics. We supplement
Cartan-Chern-Newman results by providing explicit expressions for all
the contact invariants of an ODE with I=0. The invariants
are explicitly written in terms of the function F and its
partial derivatives. Explicit expression for the associated Cartan's
O(2,3) connection is also given. The curvature of this
conformal connection is reinterpreted in terms of the Cotton-York
tensor of the Lorentzian three-metric associated with the equation. B.
Edgar (Sweden): Finding Conformal Killing
Vectors from the Invariant Classification Scheme As
a by-product of the invariant classification (Karlhede classification)
of a particular metric, it has been shown how to determine the number
of Killing vectors which
exist and whether a proper homothetic vector exists. In this talk we
will show how to exploit this information to find the explicit forms
of these vectors by a very concise method. Furthermore, we shall give
an algorithm for determining the existence of proper conformal Killing
vectors, as well as a method to find such vectors explicitly. G. Valent (and P-.Y.
Casteill) (Paris): Some Self-Dual Einstein Metrics from Harmonic
Super-Space Using ideas from supergravity and techniques from the harmonic superspace formalism, it has been possible to derive the explicit form of a family of Euclidean Einstein metrics, with isometries U(1)xU(1), and which involves two parameters besides the Einstein constant. Their novelty stems from the fact that their limits for vanishing Einstein constant are Riemann self-dual. Comparison with other known results by Plebanski and Demianski on the one hand and Israel, Perjes and Wilson on the other hand is given. P.
S. Florides (Dublin): Einstein�s
Equivalence Principle and the Gravitational Red Shift Since
the inception of the general theory of relativity in 1907 it is widely
claimed that arguments based entirely on Einstein�s Equivalence
Principle predict the well-known gravitational red shift. Here we
show, contrary to these claims, these arguments are false and that
only the full theory of general relativity can correctly predict the
observed gravitational red shift. P.
Spindel (Mons): Scalar Perturbations in a
Primordial Inflationary Scenario We
compute the spectral index for scalar perturbations generated in a
primordial inflationary model. In this model, the transition of the
inflationary phase to the radiative era is achieved through the decay
of the cosmological term leading a second order phase transition and
the characteristics of the model allow to implement a set of initial
conditions where the perturbations display a thermal spectrum when
they emerge from the horizon. The obtained value for the spectral
index is equal to 2, a result that depends very weakly on the various
parameters of the model and on the initial conditions used. Alan
A. Coley (Dalhousie): Assisted Inflation We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed. The early-time and intermediate behaviour of the models is also studied. P.
Teyssandier (Paris): Non-Minimal
Coupling, Variable Speed of Light and Cosmology M.
R. Martinez (Paris): Brane Cosmology with a
Bulk Scalar Field In
the last couple of years, cosmological models with extra dimensions
have been actively studied: in particular, scenarios where the
ordinary matter is confined in a (3+1)-dimensional surface (the
world-sheet of a 3-brane) embedded in a higher dimensional space-time.
In this talk, I will consider a five-dimensional spacetime with a
scalar field coupled to a 3-brane
representing our universe. I will give explicit solutions of Einstein
equations and then explore the induced cosmology in the brane,
characterized by a non-standard Friedmann equation. J.
C. Thorwart (and J. J. Halliwell) (London): Timeless
Properties for Quantum Models Using
the decoherent histories approach to quantum theory, we investigate
how to obtain probabilities for the system entering a certain region
in configuration space. This is in the context of quantum cosmological
and related reparametrisation invariant models. M. E. Guimaraes (Brazil):
String�s Current Induced by the Dilatonic Coupling of Gravity We investigate the nature of an ordinary cosmic string vortex in scalar-tensor extension of gravity. We find that, in this case, the extra scalar (dilaton) field can act as a time-like current travelling along the string, and localised into it, so that the corresponding string is in fact of the neutral limit superconducting kind. Such currents, leading to the formation of vorton states, might lead to an actual cosmological catastrophe from which one can derive strong constraints on the relevant theories. D. Birmingham
(Dublin): Choptuik Scaling and Quasi Normal Modes in the AdS/CFT
Correspondence We
establish an exact connection between the Choptuik scaling parameter
for the three-dimensional BTZ black hole, and the imaginary part of
the quasinormal frequencies for scalar perturbations. Via the AdS/CFT
correspondence, this leads to an interpretation of Choptuik
scaling in terms of the timescale for return to equilibrium of the
dual conformal field theory. E.
Winstanley (Sheffield): Is There Classical
Super-Radiance in Kerr-Newman-Anti-de Sitter Black Holes? By
studying the modes of a classical scalar field on a Kerr-Newman-Anti
de Sitter (KN-AdS) black hole, we ask whether super-radiance occurs.
The answer depends on the boundary conditions at infinity and our
definition of positive frequency. Alessandro
Fabbri (Bologna): 2D Black Holes and
Dimensional Reduction A
four dimensional massless and minimally coupled scalar field acquires,
after dimensional reduction under spherical symmetry, a nontrivial
coupling with the dilaton field. Within this theory and in the
background Schwarzschild space-time, we compare the results for the
stress tensor coming from canonical quantisation and those derived in
the effective action method. S.
Mignemi (Cagliari): Primary Scalar Hair of
Black Holes in String Theory Modifications
of the Einstein-Hilbert action induced by effective string theory
allow the presence of primary hair for non-minimally coupled scalar
fields. ----------------------------------------------------------------------------------------------------------- R.
Steinbauer (Vienna): Generalised Pseudo-Riemannian
Geometry for General Relativity The
study of singular space-times by distributional methods faces the
fundamental obstacle
of the inherent nonlinearity of the field equations. Staying strictly
within the distributional (in particular: linear) regime, as
determined in [1], excludes a number of physically interesting
examples (e.g., cosmic strings). In
recent years, several authors have therefore employed nonlinear
theories of generalized functions (Colombeau algebras, in particular)
to tackle general relativistic problems (cf. [2],[3] as well as [4]
for a survey). Under
the influence of these applications in general relativity the
nonlinear theory [1]
Geroch,R., Traschen,J., Phys.Rev.D, 36(1987),1017�1031. [2]
Clarke,C.J.S., Vickers,J.A., Wilson,J.P., Class. Quantum Grav.,
13(1996). [3]
Kunzinger,M., Steinbauer,R., Class. Quant. Grav.,16(1999),1255-1264. [4]
Vickers,J.A. �Nonlinear generalized functions in general
relativity� in Grosser,M., H�rmann,G., Kunzinger,M.,
Oberguggenberger,M. editors m Nonlinear Theory of Generalized
Functions, volume 401,CRC Research Notes, 275--290, Boca Raton,
1999. CRC Press [5]
Grosser,M., Farkas,E., Kunzinger,M., Steinbauer,R., Memoirs
Am.Math.Soc., 153(2001)(also http://arXiv.org/abs/math.FA/9912214,
9912215}). [6]
Grosser,M., Kunzinger,M., Steinbauer,R., Vickers,J., Adv. Math., to
appear (see also http://arXiv.org/abs/math. FA/9912216}). [7]
Kunzinger,M., Steinbauer,R., �distributional geometry�, Submitted,
math.FA/0102019, 2001. [8]
Kunzinger, M., Steinbauer, R., �Generalized pseudo-Riemannian
geometry�, Submitted, math.FA/0107057, 2001. R.
Garattini (Bergamo): Wormholes and
Space-Time Foam: the case with a cosmological constant Following
the subtraction procedure for manifolds with boundaries, we calculate
by variational methods, the energy difference between spaces having
the same asymptotic behavior. In particular, by looking at the
Schwarzschild-Anti-de Sitter, the Schwarzschild-de Sitter and the
Schwarzschild spaces, we compute the one loop approximation for TT
tensors and we discover the existence of an unstable mode at zero
temperature, which can be stabilized by the boundary reduction method.
Implications on different
scenarios of a foam-like space are discussed. J-.W.
van Holten (Amsterdam): World-Line
Deviations In
general relativity absolute accelerations have no meaning. In
contrast, relative accelerations produce well-defined obervable
effects. In pure gravity, it is a measure for the curvature of
space-time (tidal forces); in extensions of GR, like Einstein-Maxwell
theory, it is determined by both the space-time curvature as well as
the internal (Maxwell) two-form. In specific examples the resulting
world-line deviation rates can be computed, and we show how they can
be used as the first step in a systematic perturbation theory for the
calculation of orbits in (extended) general relativity. R.
Colistete (Paris): Higher-Order Geodesic
Deviations with the Kerr Metric Starting
with an exact and simple geodesic, we generate approximate geodesics
by summing up higher-order geodesic deviations in a fully relativistic
scheme. We apply this method to the problem of orbit motion of test
particles in Schwarzschild and Kerr metrics; from a simple circular
orbit as the initial geodesic we obtain finite eccentricity orbits as
a Taylor series with respect to the eccentricity. The explicit
expressions of these higher-order
geodesic deviations are derived using successive systems of linear
equations with constant coefficients, whose solutions are of harmonic
oscillator type. This scheme is best adapted for small eccentricities,
but arbitrary values of M/R. We also analyse the possible application
to the calculation of the emission of gravitational radiation from
non-circular orbits around a very massive body. V.
M. Villalba (Frankfurt): Creation of Scalar
and Dirac Particles in the Presence of a Time Varying Electric Field in
a Universe We
compute the density of scalar and Dirac particles created by a
cosmological anisotropic
Bianchi I universe in the presence of a time varying electric field. We show that the particle distribution
becomes thermal when one neglects the electric interaction. G.
Bergqvist(Sweden): Causal Tensors and
Simple Forms A
rank-r tensor on a Lorentzian manifold of dimension N is causal if the
contraction with r arbitrary causal future-directed vectors is
non-negative. General superenergy tensors, such as the Bel and Bel-Robinson
tensors, are examples of even ranked causal tensors, and may therefore
be useful when defining norms for geometric evolution equations. We
here show that any symmetric rank-2 causal tensor (energy-momentum
tensors satisfying the dominant energy condition) can be written as a
sum of at most N superenergy tensors of simple forms. If N=4 this can
be expressed in an elegant way as the sum of four spinors squared.
Since, for arbitrary N, the superenergy of any simple form is a
self-map of the cone (its square is proportional to the metric) this
leads to new representations and classifications of all conformal
Lorentz transformations and to generalisations of the
Rainich-Misner-Wheeler theory of determining the space-time physics
from its geometry. J.M.M. Senovilla (Bilbao):
Causal Tensors and Rainich Conditions We find the mathematical properties of the tensors satisfying the dominant property (generalisation of the dominant energy condition), including the case of the so-called superenergy tensors such as the Bel-Robinson tensor. We show that these are intimately related to conformally Lorentz transformations as they leave the null-cone invariant. This provides a wide generalisation of the algebraic Rainich conditions in arbitrary dimension and for many different fields. R.
Casadio (Bologna): Gamma-Ray Bursts from
Gravitational Collapse A
possible origin of gamma-ray bursts is the gravitational collapse of
compact objects. We study a self-gravitating shell of bosonic matter
coupled to a scalar radiation field in order to investigate a new
mechanism to extract energy from collapsing matter. We show that the
matter can form a condensate and the shell internal degrees of freedom
are excited during the collapse. The system then loses large amounts
of gravitational energy in the form of radiation. C.
Barrab�s (and P. A. Hogan) (Tours): Impulsive
Light-Like Signals A
general characterization of an impulsive light-like signal is given.
The signal may consist of a shell of null matter and/or an impulsive
gravitational wave. Several examples of impulsive light-like
signals are presented,
in particular those produced by recoil effects and by the
Aichelburg-Sexl boost of an isolated gravitating source. The detection
of these signals will also be mentioned. L.
Villain (Paris): Concerning r-Modes in
Neutron Stars Some
numerical results of non-viscous r-modes in a slowly rotating Neutron
Star within an elastic approximation are presented. This work dealt as
well with linear or non-linear Euler equations, taking into account
post-Newtonian radiation-reaction force and being built on a rigidly
or differentially rotating background. The numerical spectral methods
and the �evanescent viscosity� used are described. A
Yukawa coupling of fermions to the string forming Higgs field leads to
the existence of massless and massive fermionic bound states in the
vortex that can drastically modify the string dynamics. An exhaustive
study of these states is performed. In particular, it is shown that
there exists transitions between subsonic and supersonic regimes (i.e.
regimes in which the transverse perturbation propagation velocity is
less or greater than the longitudinal, sound-like one, respectively),
which appear as soon as the massless and massive modes are
respectively filled. This results in modifying the classical stability
of cosmic string loops. S.
Kaniel (Jerusalem): On The Derivation of the
Equations of Motion We
propose for the N-body problem of equations that are Lorentz invariant
a novel algorithm for the derivation of the equations of motion from
the field equations. It is: (1)
Compute
a static, spherically symmetric solution of the field equation. It
will be singular at the origin. This will be taken to be the field
generated by a single particle. (2)
Move
the solution on a trajectory P and apply the instantaneous Lorentz
transformation based on instantaneous velocity. (3)
Take,
as first approximation, the field generated by N particles to be the
superposition of the fields generated by the single particles. (4)
Compute
the leading part of the equation. Hopefully, only terms that involve
the acceleration will be dominant. This is the �inertial� part. (5)
Compute
the quadratic part of the equation. This is the agent of the
�force�. (6)
Equate
for each singularity, the highest order terms of the singularities
that came from the linear part and the quadratic parts, respectively.
This is an equation between the inertial part and the force. The
algorithm was applied to Einstein equations. The approximate evolution
of the scalar curvature leads, in turn, to an invariant scalar
equation. The algorithm for it did produce Newton�s law of
gravitation. This is, also, the starting point for the embedding of
the trajectories in a common field. B.
C. Nolan (Dublin): Weak Solutions for Weak
Singularities We
revisit the problem of the development of singularities in the
gravitational collapse of an inhomogeneous dust sphere. As shown in [Yodzis,P.
et al.,Comm. Math.Phys. 34(1973),135], naked singularities may occur
at finite radius where shells of dust cross one another. These
singularities are gravitationally weak [Newman,R.P.A.C., Class.
Quantum Grav. 3(1986),527], and it has been claimed that at these
singularities, the metric may be written in continuous form [Newman,R.;Christodoulou,
D. Comm. Math. Phys. 93(1984),171], with locally L^infty connection
coefficients [Christodoulou,D]. We correct these claims, and show how
the field equations may be reformulated as a first order,
quasi-linear, non-conservative, non-strictly hyperbolic system. We
discuss existence and uniqueness of weak solutions of this system
using Le Floch�s bounded functions of bounded variation (BV) [Le
Floch,P. Comm. Partial Diff. Eqns. 13(1988),669], where the product of
a BV function and the derivative of another BV function may be
interpreted as a locally finite measure. We analyze consequences for
the physics of these singularities, in particular the question of
cosmic censorship, and discuss generalisations to other matter models
and geometries. J.
Vickers (Southampton): Weak Singularities in
General Relativity According
to the Cosmic Censorship hypothesis realistic singularities should be
hidden by an event horizon. However there are many examples of
physically realistic space-times which are geodesically incomplete,
and hence singular according to the usual definition, which are not
inside an event horizon. Many
of these counterexamples to the cosmic censorship conjecture have a
curvature tensor which is reasonably behaved (for example bounded or
integrable) as one approaches the singularity. We give a class of weak
singularities which may be described as having distributional
curvature [C.J.S.Clarke,J.A.G.Vickers,J.P.Wilson,Class. Quantum Grav.
13 (1996),2485-2498]. Because of the non-linear nature of Einstein's
equations such distributional geometries are described using a
diffeomorphism invariant theory of non-linear generalised functions [M.Grosser,
M.Kunzinger, R.Steinbauer, H.Urbanke, J.Vickers, Ann. der Physik, 9
(1999), S173-75]. We
also investigate the propagation of test fields on space-times with
weak singularities. We give a class of singularities [J.
Vickers,J.P.Wilson, Class. Quantum Grav. 17(200)),
1333-1360;J.Vickers, J.P.Wilson,�Generalised
hyperbolicity:hypersurface singularities�,gr-qc/0101018] which do
not disrupt the Cauchy development of test fields and result in
space-times which satisfy Clarke's criterion of `generalised
hyperbolicity'. We consider that points which are well behaved in this way,
and where Einstein's equations make sense distributionally, should be
regarded as interior points of the space-time rather than
counterexamples to cosmic censorship. B. Boisseau
(Tours): Perturbations of a Cylindrical Vortex in a
Relativistic Perfect Isentropic Fluid and Nambu-Goto Dynamics By
a weak deformation of the cylindrical symmetry of a potential vortex
in relativistic perfect isentropic fluid we study the possible
dynamics of the central line of this vortex. In the stiff material the
Nambu-Goto equations are obtained. J.
Melanson (and P. Gravel) (New Brunswick): Energy
Conditions for Primordial Warp Drives We
find new lower bounds for the quantities of energy required to warp
drive transport objects at the speed of light or faster. We use an
idea of Van Den Broeck and consider a warp bubble of small surface
area and large spatial volume. The new bounds are obtained by working
on parameters whose latitude has never been considered. Warp bubbles
of three different radii are considered in details. If the time
permits, we shall mention how warp bubbles of very small radius could
act at the early stage of the universe to take charge of a part of the
role usually assigned to inflation. Aroon
Beesham (and S.G. Gosh)(Zululand): Higher
Dimensional Inhomogeneous Dust Collapse and Cosmic Censorship The
occurrence of central naked singularities are investigated in a
spherically symmetric self-similar higher dimensional inhomogeneous
dust collapse. The bound and unbound collapse scenarios are analysed.
The singularities are strong in the Tipler sense and generic in the
sense that they form from a nonzero set of regular initial data.
Implications of this result for the cosmic censorship hypothesis are
discussed. D.
Puetzfeld (Cologne): A Cosmological Model
in Weyl-Cartan Space-Time After
a short survey on the more general framework of the metric-affine
gravity (MAG) [F.W.Hehl, J.D.McCrea, E.W.Milke, Y. Ne�eman,
Phys.Rep.258(1995),1-171] we will introduce the Weyl-Cartan space-time
as one of its subcases. Within this space-time we will present a
cosmological model for early stages of the universe [D. Puetzfeld,
R.Tresguerres, Class. Quantum Grav.
18(2001),677-693(gr/qc0101050);R.Tresguerres, Proc.Relativity in
General (1993) 407-413, Salas, Asturias (Spain),Sept.7-10]. In this
model torsion and non-metricity are proportional to the Weyl 1-form.
We are going to discuss the bejavior of the cosmic scale factor and
the non-Riemannian quantities in detail. Additionally, we will present
an extension of the model, which was found recently, and give a short
outlook on possible future developments.
Y.
Itin (Jerusalem): Conserved Currents for General
Teleparallel Models The
obstruction for the existence of an energy-momentum tensor for the
gravitational field is connected with differential-geometric features
of the Riemannian manifold. It has not to be valid for alternative
geometrical structures. A
teleparallel manifold is defined as a parallelizable differentiable
4D-manifold endowed with a class of smooth coframe fields related by
global Lorentz, i.e. SO(1,3), transformations. A general 3-parameter
class of teleparallel models is considered. It includes a 1-parameter
subclass of models with the Schwarzschild coframe solution (generalised
teleparallel equivalent of gravity). A
new form of the coframe field equation is derived here from the
general teleparallel Lagrangian by introducing the notion of a
3-parameter conjugate field strength F. The field equation turns out
to have a form completely similar to the Maxwell field equation d*F=T.
By applying the Noether procedure, the source 3-form T is shown to be
connected with the diffeomorphism invariance of the Lagrangian. Thus
the source T of the coframe field is interpreted as the total
conserved energy-momentum current. A
reduction of the conserved current to the Noether current and the
Noether charge for the coframe is provided. The energy-momentum tensor
is defined as a map of the module of current 3-forms into the module
of vector fields. Thus an energy-momentum tensor for the coframe is
defined in a diffeomorphism invariant and a translational covariant
way. The
total energy-momentum current of a system is conserved. Thus a
redistribution of the energy-momentum current between material and
coframe (gravity) field is possible in principle, unlike as in the
standard GR. G.
A. Alekseev (Moscow): Characteristic Initial
Value Problems for Integrable Symmetry Reductions of Einstein�s
Equations A
new development of the �monodromy transform� method for solution
of integrable (1+1)-dimensional symmetry reductions of Einstein
equations (in particular, of vacuum and electrovacuum hyperbolic Ernst
equations) is presented. A set of linear (quasi-Fredholm) integral
equations equivalent to the dynamical parts of the symmetry reduced
Einstein equations is derived. The scalar kernels of these equations
contain a set of functional parameters (the �monodromy data�)
which characterise every analytical local solution and which are
determined completely by the characteristic initial data. In terms of
the solution of the derived integral equations the solution of the
characteristic initial value problem can be expressed in quadratures.
A generalisation of this approach to a non-analytical case (found in
collaboration with J.B. Griffiths) with applications to the colliding
plane gravitational or gravitational and electromagnetic waves is also
discussed. Examples of evaluation procedure are given for construction
of exact solutions of the reduced Einstein�s equations starting from
the characteristic initial data for the fields. J.P.S.
Lemos (and V. Cardoso) (Lisbon): Radiation
Generated by the Infall of a Scalar Particle in a Schwarzschild-Anti-de
Sitter Background The
predicted BH production at the LHC in the brane world scenario makes
it important to investigate radiative processes associated with BH's
in asymptotically anti-de Sitter spaces. Here we compute the spectra, waveforms and total scalar
energy radiated during the radial infall of a small test particle
coupled to a scalar field into a Schwarzschild-anti-de Sitter black
hole. For large black holes, the spectra and waveforms are in general
not dominated by quasinormal ringing, as it was in asymptotically flat
space, and does not peak at the lowest quasinormal frequency. For
small black holes, the spectra is dominated by a resonance. V.
Cardoso (and J.P.S. Lemos) (Lisbon): Quasi
Normal Modes of Schwarzschild-Anti-de Sitter Black Holes: Electromagnetic and
Gravitational Perturbations We
study the quasi-normal modes (QNM) of electromagnetic and
gravitational perturbations of a Schwarzschild black hole in an
asymptotically Anti-de Sitter (AdS) space-time.
Some of the electromagnetic modes do not oscillate, they only
decay, since they
have pure imaginary frequencies.
The gravitational modes show peculiar features: the odd and
even gravitational perturbations no longer have the same
characteristic quasinormal frequencies. There is a special mode for
odd perturbations whose behavior differs completely from the usual one
in scalar and electromagnetic perturbation in an AdS
spacetime, but has a similar behavior to the Schwarzschild
black hole in an asymptotically flat spacetime: the imaginary part of
the frequency goes as 1/r, where r is the horizon radius. We also
investigate the small black hole limit showing that the imaginary part of the
frequency goes as r^2. These results are important to the AdS/CFT
conjecture since according to it the QNMs describe the approach to
equilibrium in the conformal field theory. M.
Carmeli (Beer Sheva): Cosmological Constant
and Dark Matter: Theory versus Experiment Most
of the calculations done to obtain the value of the cosmological
constant use methods of quantum gravity, a theory that has not been
established as yet, and a variety of results are usually obtained. The
numerical value of the cosmological constant is then supposed to be
inserted in the Einstein field equations, hence the evolution of the universe
will depend on the calculated value. Here we present a fundamental
approach to the problem. The theory presented here uses a Riemannian
four-dimensional presentation of gravitation in which the coordinates
are those of Hubble, i.e. distances and velocity rather than space and
time. We solve these field equations and show that there are three
possibilities for the universe to expand but only the accelerating
universe is possible. We extract from the theory the cosmological
constant and show that it equals 2.036x10^-35 s^-2. This value is in
excellent agreement with the measurements obtained by the High-Z
Supernova Team and the Supernova Cosmology Project. Finally it is
shown that the three-dimensional space of the universe is flat, as the
Boomerang experiment shows. V.
Pravda (and A. Pravdova) (Czech Republic):
On Boost-Rotation Symmetric Space-Times with (Non) Spinning
Sources Boost-rotation symmetric space-times correspond to the gravitational field of uniformly accelerated "particles". After a short introduction to the theory of boost-rotation symmetric space-times with non-spinning and spinning sources, two examples will be analysed: the C metric and the spinning C-metric, representing e.g. uniformly accelerated Schwarzschild and Kerr black holes, respectively. J.
C. Fabris (Brazil): Classical
Analogue of Quantum Cosmological Perfect Fluid Model The quantization of gravity coupled to a perfect fluid model leads to a Schr�dinger-like equation, where the matter variable plays the role of time. The wave function can be determined, for an arbitrary barotropic equation of state p = α ρ, and wave packets constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition to the ordinary classical model of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. Its existence permits us to study the stability of those singularity-free models. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of α , while the radiative non-flat case is equivalent to the harmonic oscillator. The classical repulsive fluid needed to reproduce the quantum results is the same in both cases. |
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