Quasi-normal modes of the BTZ black hole with torsion

Jens Boos (Köln)

The basic structures of the Mielke–Baekler model of topologically massive gravity in (2+1) dimensions [1, 2] are reviewed, and its Bañados–Teitelboim–Zanelli(BTZ)-like black hole solution [3, 4] is briefly presented.

We then present quasi-normal modes as applied to asymptotically anti de Sitter black hole spacetimes: they are solutions to scalar, electromagnetic, spinorial or tensorial wave equations with specific boundary conditions.

The associated frequency to each mode is called quasi-normal frequency, and their imaginary part is relevant for the stability question of the black hole under consideration. They turn out to be negative for the BTZ black hole [5, 6], making it stable against perturbations. It remains to be seen how tensorial modes affect the stability issue.

References:

1. E. W. Mielke and P. Baekler, “Topological gauge model of gravity with torsion,” Phys. Lett. A 156 (1991) 399, inspire.
2. P. Baekler, E. W. Mielke and F. W. Hehl, “Dynamical symmetries in topological 3-D gravity with torsion,” Nuovo Cim. B 107 (1992) 91, inspire.
3. M. Bañados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69 (1992) 1849, [hep-th/9204099].
4. A. A. García, F. W. Hehl, C. Heinicke and A. Macías, “Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion,” Phys. Rev. D 67 (2003) 124016, [gr-qc/0302097].
5. D. Birmingham, “Choptuik scaling and quasinormal modes in the AdS / CFT correspondence,” Phys. Rev. D 64 (2001) 064024, [hep-th/0101194].
6. R. Becar, P. A. Gonzalez and Y. Vasquez, “Dirac quasinormal modes of Chern-Simons and BTZ black holes with torsion,” Phys. Rev. D 89 (2014) 2, [arXiv:1306.5974 [gr-qc]].

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Physical appearances and interpretations of the Barbero-Immirzi parameter

Patrick J. Wong (Köln)

The Barbero-Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose physical significance is as-of-yet unknown. It is an inherent characteristic of the quantum theory as it appears in the spectra of geometric operators and appears classically in the coupling of fermions and gravity. The parameter’s appearance in the area and volume spectra imply that it plays a role in determining the fundamental length scale of space. This relationship with length scales motivates a possible conformal interpretation.

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Status of inflation with the most recent observational data and future perspectives

Alexei Starobinsky (Landau Institute)

Present knowledge about physical properties of an inflationary stage in the early Universe (curvature, its rate of change, inflaton mass, etc.) which follows from the most recent observational data including the Planck 2014 ones is reviewed and possibilities to find out anything new about it are discussed. In particular, features in the CMB temperature anisotropy power spectrum in the multipole range l=20-40 are of interest in this respect and may point to some new physics during inflation.

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On the Reduction of General Relativity to Newtonian Gravitation

Sam Fletcher (München)

Limiting relations between physical theories should aspire to be both perfectly general and to be explanatory: they should relate or otherwise account for as many features of the two theories as possible, and endeavor to explain why the older, simpler theory to which the other reduces continues to be as successful as it is. Despite often being introduced as straightforward, candidateaccounts of the reduction of general relativity (GR) to Newtonian gravitation (NG) have either been insufficiently general, or have not clearly been able to explain the empirical success of NG, such as it is.

Building on work by Ehlers and others, I propose a different account of the reduction relation that is perfectly general and meets the explanatory demand one would make of it. In doing so, I highlight the role that a topology on the collection of all spacetimes plays in defining the relation, and how the choice of topology corresponds with broader or narrower classes of observables that one demands be well-approximated in the limit.

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Some benefits and problems of c and α varying theories

Mariusz Dąbrowski (Szczecin)

I will discuss the basic framework of varying physical constants theories. In particular, I will show some benefits of varying speed of light c theories and try to point out problems in their proper formulation. I will also present some observational aspects of varying fine structure constant α theories as related to varying c theories and its observational verification.

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Chameleonic strings and the cosmological constant problem

Andrea Zanzi (Ferrara)

Chameleon fields are quantum fields (typically scalar) where the mass depends on the matter density of the environment. A chameleonic solution to the cosmological constant problem is presented. To a certain extent the lagrangian of the model can be obtained from string theory. The correct Dark Energy scale is recovered in the Einstein frame without fine-tuning of the parameters. In this model different conformal frames are non-equivalent at the quantum level (the Einstein frame is the physical one) and, moreover, a chameleonic equivalence principle for quantum gravity can be formulated (quantum gravitation is equivalent to a conformal anomaly). A detailed phenomenological analysis of this proposal is necessary. The stringy origin of the lagrangian should be further explored.

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Physics after the discovery of the Higgs boson

Jochum Johan van der Bij (Freiburg)

The discovery of the Higgs boson at the Large Hadron Collider in CERN opens a new era of physics. The study of its properties can lead to new insights in fundamental physics. Already with the presently known properties one has indications for the existence and form that new physics can take. I present two extensions, one in the scalar sector and one in the neutrino sector, that are indicated by present data. The results have important implications in cosmology. They can be tested by existing and new colliders.

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More on "Little Lambda" in Hořava-Lifshitz gravity

Luis Pires (Nijmegen)

While motivated as a putative theory of quantum gravity, the classical limit of Hořava-Lifshitz gravity is an interesting model in itself. The main difference between this classical theory and general relativity lies in the presence of a new dimensionless coupling in the kinetic term of the action, the so-called ?little lambda? whose role is still up for debate.

As a starting point for our work, we look at two apparently contradictory statements about its effect on the theory and show that they actually refer to two different versions of the theory, distinguishable by the way the lapse function is defined. We then focus on the so-called non-projectable theory, where the lapse is a function of spacetime, and show how the presence of lambda gives rise to a non-trivial constraint algebra, reminiscent of the conditions present in the CMC gauge of GR.

Gravity in higher dimensions à la Lovelock

Naresh Dadhich (Pune, India)

The Lovelock generalization of GR is the most natural as it retains the second order character of the equation of motion. However higher order terms make non-zero contribution only in dimensions >4. We define the N-th order Lovelock Riemann analogue, then the equation of motion follows from the trace of its Bianchi derivative that vanishes.

In particular we consider pure Lovelock gravity that includes only one N-th order term and then show that it has the universal property that Lovelock vacuum is Lovelock flat in all odd, d=2N+1, dimensions. We will argue that pure Lovelock is the right gravitational equation in higher dimensions.

Mass and center of mass in Newtonian gravity and general relativity

Carla Cederbaum (Tübingen)

Isolated gravitating systems such as stars, black holes, and galaxies play an important role both in Newton's theory of gravity and in Einstein's theory of general relativity. While the definition of mass and center of mass via the mass density is straightforward in Newtonian gravity, there is no definitive corresponding notion in general relativity. Instead, there are several alternative approaches in general relativity to defining the center of mass of an isolated system. We will discuss these different approaches and present some explicit examples. Moreover, we will introduce the notion of Newtonian limit and use it to relate the Newtonian and the relativistic centers in the case of static systems.

Second order curvature invariants for the Plebański–Demiański solution

Jens Boos (Köln)

The Plebański–Demiański (PD) solution is a seven parameter type D solution of the Einstein–Maxwell equations [1]. It can be used to describe a uniformly accelerating Kerr–Newman black hole in a de Sitter spacetime with an additional NUT parameter.

Recently, Griffiths & Podolský introduced new coordinates to recover the well-known Boyer–Lindquist coordinates from the polynomial PD coordinates [2]. The necessary coordinate transformations will be sketched briefly.

In the following, I will present a computer algebra-based calculation (Reduce with Excalc [3, 4]) yielding second order curvature (pseudo-)invariants for this spacetime. The result will be of remarkably simple structure very similar to electrodynamics.

References:

1. J. F. Plebański and M. Demiański, “Rotating, charged, and uniformly accelerating mass in general relativity,” Annals Phys. 98 (1976) 98, DOI: 10.1016/0003-4916(76)90240-2.
2. J. B. Griffiths and J. Podolský, “A New look at the Plebański-Demiański family of solutions,” Int. J. Mod. Phys. D 15 (2006) 335 [arXiv:gr-qc/0511091].
3. A. C. Hearn, REDUCE User’s Manual, Version 3.5 RAND Publication CP78 (Rev. 10/93). The RAND Corporation, Santa Monica, CA 90407-2138, USA (1993). Nowadays Reduce is freely available for download; for details see [reduce-algebra.com] and [sourceforge.net].
4. J. Socorro, A. Macias and F. W. Hehl, “Computer algebra in gravity: Programs for (non-)Riemannian space-times. 1,” Comput. Phys. Commun. 115 (1998) 264 [arXiv:gr-qc/9804068].

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Quantum Geometrodynamics of Conformal Gravity

Branislav Nikolić (Köln/Bonn)

In order to study the role of the conformal symmetry (symmetry under local Weyl rescaling) at the level of quantum gravity, a toy model of conformally invariant gravitational action described with squared Weyl tensor is quantized canonically, with and without coupled scalar field. An analog to the Wheeler-DeWitt equation has been proposed, leading to the formulation of quantum geometrodynamics of the conformally invariant gravity.

From this, the semiclassical expansion in terms of coupling constant is performed and it has been shown that in the highest order one obtains the proposed Hamilton-Jacobi equation and that in the next order one obtains functional Schroedinger equation, analogously as in the case of quantum geometrodynamics of General Relativity. Furthermore, the conformal action is extended to the more physically justified action containing additional Einstein-Hilbert term, that breaks the conformal invariance. Upon performing the semiclassical expansion with respect to the relative couplings of the two terms, the Einstein-Hamilton-Jacobi equation is derived in the highest order. Here, some possible issues regarding the quantization of the second class constraints are also discussed.

The outcome of this thesis is that, apart from the deeper insight into the conformal symmetry and the first class constraints both at the classical and quantum level, the first steps towards the formulation of quantum geometrodynamics of the higher derivative theories has been made. This constructs a concrete ground for the introduction of quantum cosmology in higher derivative theories, and opens the door for investigation of the relation between problem of time, arrow of time and the conformal symmetry, both on quantum and classical level, from a new perspective.

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The static metric extension problem in axisymmetry

Markus Strehlau (AEI Potsdam/Köln)

Motivated by the problem of defining a quasi local mass, Robert Bartnik formulated the static metric extension conjecture. This can be interpreted as an open boundary problem, where the metric on the inner boundary surface of the extension and its mean curvature are the prescribed conditions. To gain further insight into this problem, we use axisymmetric extensions to simplify it. Here we show how to construct a geometric flow, based on a mean curvature flow, to approach the inner boundary of the extension. It will be implemented numerically using a pseudo-spectral method.