8-11 April 2014
Department of Mathematical Analysis
S22, lecture room A, Galglaan 2, 9000 Gent,
Belgium
Tuesday 8
9:00-9:30 |
coffee |
9:30-10:30 |
Marcello Ortaggio:
Asymptotic
properties of gravitational and electromagnetic fields in higher dimensions |
10:45-11:45 |
Alan Barnes: Einstein Spacetimes with Constant Weyl Eigenvalues |
12:00-14:00 |
lunch |
14:00-15:00 |
Vladimir Manko: A novel approach to extending the Kerr solution |
15:15-16:15 |
Radu Slobodeanu: Shear-free fluids with linear EoS in general relativity |
17:00-18:00 |
reception |
Wednesday 9
9:00-9:30 |
coffee |
9:30-10:30 |
Raül Vera: Perturbed
matching theory to second order |
10:45-11:45 |
Borja Reina: Revisiting Hartle's perturbative model for
slowly rotating stars |
12:00-12:30 |
lunch |
12:30-21:30 |
excursion |
Thursday 10
9:00-9:30 |
coffee |
9:30-10:30 |
Timothy Clifton: The Initial Value Problem in Discrete Cosmological Models |
10:45-11:45 |
Kjell Rosquist: The Evolution of Discrete Cosmological Models |
12:00-14:00 |
lunch |
14:00-15:00 |
José Natário: Gravito-electromagnetic
analogies, physical significance of the curvature invariants and all that |
15:15-16:15 |
Filipe Costa: Dynamics of extended test bodies in General Relativity --- the problem
of the representative worldline |
Friday 11
9:00-9:30 |
coffee |
9:30-10:30 |
José Senovilla: Spacetimes with linear differential conditions on the curvature |
10:45-11:45 |
Michael Bradley: The quadrupole moment of rotating fluid balls |
12:00-14:00 |
lunch |
14:00-15:00 |
Lode Wylleman: Five dimensional Petrov type D spacetimes |
15:15-16:15 |
t.b.a. |
Abstracts and
reading material
Alan Barnes Einstein Spacetimes with Constant Weyl
Eigenvalues
Einstein spacetimes (that is vacuum spacetimes
possibly with a non-zero cosmological constant Λ) with a constant non-zero Weyl eigenvalue are considered. For type II & D this
assumption alone is sufficient to allow one to prove that the non-repeated
eigenvalue necessarily has the value 2Λ/3 and it turns out that the only
possible spacetimes are some Kundt-waves
considered by Lewandowski which are type II and a Robinson-Bertotti
solution of type D. For Petrov type I the only
solution in which all three Weyl eigenvalues are
constant turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl
eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al.
who proved their result for general spacetimes under
the assumption that all scalar invariants constructed from the curvature tensor
and all its derivatives were constant. Some preliminary results are also
presented for Petrov Type I vacua
in which either only one of the Weyl eigenvalues is
constant or in which the ratios of the Weyl
eigenvalues are constants. In particular in each case there is a simple
algebraic relation between the Newman-Penrose Weyl
tensor component Ψ2 and the ’cross-ratio’ of the optical scalars κν − σλ of the associated
principal null tetrad of the Weyl tensor.
(a
provisory manuscript can be obtained from the author or from the organizers)
Michael Bradley The quadrupole moment of
rotating fluid balls
Timothy Clifton: The Initial Value
Problem in Discrete Cosmological Models
In this talk I will
present recent results on the application of geometrostatics
to cosmological models. This technique allows one to find vacuum solutions to
the initial value problem that describe an arbitrary number of black holes. We
arrange these black holes in regular configurations on a 3-sphere, and compare
the resulting geometry to that of a Friedmann-Lemaitre-Robertson-Walker
solution with the same total mass. This process allows new cosmological models
to be constructed that are (in some sense) approximately homogeneous and
isotropic on large scales, while being highly inhomogeneous on small scales.
Suggested
references:
Dynamics of a lattice universe by the Schwarzschild-cell method (http://adsabs.harvard.edu/abs/1957RvMP...29..432L)
The method of images in geometrostatics (http://adsabs.harvard.edu/abs/1963AnPhy..24..102M)
Interaction energy in geometrostatics (http://adsabs.harvard.edu/abs/1963PhRv..131..471B)
An exact quantification of backreaction
in relativistic cosmology (http://arxiv.org/abs/1203.6478)
Backreaction and continuum limit in a closed universe
filled with black holes (http://arxiv.org/abs/1312.0494)
Vladimir Manko A novel approach to extending the Kerr solution
Filipe Costa Dynamics
of extended test bodies in General Relativity --- the problem of the
representative worldline
José Natário Gravito-electromagnetic analogies,
physical significance of the curvature invariants and all that
Gravito-electromagnetic analogies
Marcello Ortaggio Asymptotic
properties of gravitational and electromagnetic fields in higher dimensions
http://arxiv.org/abs/1403.7559
Borja Reina Revisiting Hartle's perturbative model for
slowly rotating stars
We explore
the perturbative stationary and axisymmetric matching
around a spherically symmetric background static matched configuration to
second order between a rotating perfect fluid interior and an asymptotically
flat vacuum exterior. To do that we provide a consistent analysis using modern perturbative theory, and, in particular, the theory of perturbative matchings to second
order [1]. The paticularisation to Hartle's setting, i.e. the explicit assumptions used in
[1], thus provides a firm ground where to study the importance (or lack
thereof) of the implicit assumptions made to construct the original model in
[1] and further developments.
Previous related material can be found in the paper by Michael Bradley et al.
"Slowly rotating fluid balls of Petrov type
D" Phys.Rev.D75:024013,2007
Kjell Rosquist
The Evolution of Discrete Cosmological Models
In this talk I will
report on general relativistic cosmological models in which the sources are
discrete. The distribution of the sources is assumed to be homogeneous and
isotropic on large scales. Such models belong to the class of locally
inhomogeneous models. One motivation for
considering this kind of models is to obtain a closer correspondence with the
actual universe as compared to models in which the matter is a fluid. The
relation between the evolution of exactly homogeneous
vs locally inhomogeneous models is a nontrivial and difficult problem because
of the nonlinear nature of the Einstein equations. In the talk I will give
examples of discrete models in which the evolution is tracked by analytical and
semi-analytical methods. Their relation to exactly homogeneous and isotropic
(FLRW) models will also be discussed.
José Senovilla Spacetimes with linear
differential conditions on the curvature.
In Lorentzian geometry, the traditional locally symmetric spacetimes, and the recurent spacetimes, can be generalized to involve higher order
derivatives of the Riemann tensor. In particular, we have recently studied and
identified the "2nd-order symmetric" spacetimes
---those with a vanishing second covariant derivative of the Riemann tensor.
This opens up a new entire world of interesting spacetimes,
by assuming linear differential conditions on the Riemann tensor. Some
properties of these spacetimes and their interest
will be analyzed. In particular, their intimate relationship with plane-wave spacetimes and thereby with Penrose limits will be
considered".
Radu Slobodeanu Shear-free fluids
with linear EoS in general relativity
Shear-free perfect fluids with linear equation of state
Raul Vera Perturbed matching
theory to second order
The aim of this talk
is to present the tools needed to revisit, from a consistent and rigorous point
of view, Hartle's perturbative
model of slowly rotating stars in GR [1]. Hartle's
model consists essentially of the perturbative
matching of a perfect fluid interior with an asymptotically flat vacuum
exterior, up to second order in a rotation parameter. The plan for this talk is
to review the general theory of perturbative matchings to second order, constructed by Marc Mars in 2005
[2].
References
[1] James B. Hartle The Astrophysical Journal 150
(1967) 1005-1029
[2] Marc Mars "First- and second-order perturbations of hypersurfaces" CQG 22 (2005) 3325–3347
Lode Wylleman
Last update:
5.3.2014