## Seminars

### Summer term 2019

### Black-hole evolution from stellar collapse

Abstract: We present a local approach towards black-hole evaporation, which relies on the absence of quantum phase transition across the stellar surface. We show that this approach augmented with Bekenstein’s black-hole entropy gives the Hawking effect if the null energy condition is violated in the initial quantum-field vacuum. If otherwise, an astrophysical black hole may then be expanding, that corresponds to the anti-Hawking effect, i.e. a positive-energy radiation flows into the black hole, taking its origin far away from the event horizon. This quantum process is reverse to the Hawking effect, as the latter is described by a negative-energy influx nearby the horizon, which goes over to a positive-energy outflux in the far-horizon region. We also provide examples of quantum vacua well-known in the literature, which give rise to both quantum effects from stellar collapse.

### Canonical quantization of minisuperspace models with variational symmetries

Abstract: In this talk I will describe how the symmetries of the minisuperspace action are used to integrate the system at the classical and quantum level. For the latter case, we use the canonical quantisation and impose the symmetries as operators on the wave function together with the constraints. This leads to a selection rule which prevents their simultaneous imposition on the wave function and consequently to the choice of subalgebras. Some of them lead to the classical solution but there are cases where we obtain quantum corrections. These, in the Bohmian interpretation we used, are indicated when the quantum potential in the quantum Hamilton–Jacobi equation does not vanish. I will discuss some examples of physical interest.

### The Cosmological Constant and the mass of the Local Group

Abstract: The two-body problem of M31 and the Milky Way (MW) galaxies with a cosmological constant background is studied, with emphasis on the possibility that they experienced past encounters. By implementing the initial conditions of the big bang and the last measured relative distance and velocities (i.e. the Timing Argument), it is shown that if M31 and the MW had more than one encounter then the mass of the Local Group (LG) would be a few times higher than if there had been no encounters. Past encounters are possible only for non-zero transverse velocity, and their viability is subject to observations of the imprints of such near collisions. While it has been previously shown that the presence of the cosmological constant requires a higher mass for the LG, here, using a recent Gaia - based measurement of the transverse velocity the derived LG mass is (3.36 +1.14 -0.7) · 10^(12) M☉ with no cosmological constant or (4.54 +1.2 -0.75) · 10^(12)M☉ with a cosmological constant background. If the LG has had one past encounter, LG mass is (9.70 +2.19 -1.55) · 10^(12) M☉ or (9.99 +2.22 -1.58) · 10^(12) M☉ with a cosmological constant background. Modified Newtonian Dynamics (MOND) is also studied, as the accelerations of the Local Group are fully in the deep MOND regime. MOND yields the order of magnitude for the expected baryonic mass only after one past encounter, assuming MOND does not include dark matter. While we only consider the LG as two point masses, our calculations provide a benchmark for future work with simulations to test the effect of the finite size of galaxies and tidal fields due to the neighbouring structures. This model can be also used to test screening mechanisms and alternative theories of gravity.

### On surface terms and double layers in quadratic gravity

Abstract:
The talk consists of three parts.

In the first part it is demonstrated using the simple example of the spherically
symmetric Weyl + Einstein gravity, that the junction conditions in the presence of
the double layer admit the appearance of the arbitrary function determined by
the bulk solutions and, on the other hand, the very stringent requirements are
imposed on the structure of the matching surface, namely, its extrinsic curvature
tensor has to be zero.

In the second part the junction conditions on the singular hypersurface (Israel
equations) are derived from the least action principle.

And, in the third part, the same procedure is applied for the case of the quadratic
gravity. It is shown how the abovementioned “unusual” features can be
implemented quite naturally in the least action principle.

### How to construct wave packets with complete classical–quantum correspondence in quantum cosmology

Abstract: I discuss “canonical” wave packets in quantum cosmology which exhibit complete classical-quantum correspondence. I will present a prescription for initial conditions that leads to the classical description. I also study the situation from de-Broglie Bohm interpretation of quantum mechanics and show that the corresponding Bohmian trajectories are in complete agreement with the classical counterparts. As an interesting application, I will apply this method to the Schrödinger equation and obtain wave functions with complete classical-quantum correspondence for a large class of one-dimensional potentials.

### A covariant treatment of Lorentzian spacetimes in the Einstein–Hilbert truncation

Abstract: The perturbative non-renormalizability of pure Quantum Einstein Gravity at a 2-loop level signifies the need of a new treatment for the theory. Asymptotically Safe Gravity is a newly developed field of study where one using non-perturbative methods tries to prove the Ultraviolet completion of the theory within the framework of Quantum Field Theory. Such a completion is shown with the existence of a non-Gaussian fixed point at high energies, during the study of the renormalization group trajectories. Here, the tools essential to generate such trajectories for causal (Lorentzian) spacetimes are established. Furthermore, a careful treatment of the gravitational partition functional over foliatable spacetimes in a covariant manner takes place. Finally, employing a specific approximation (Einstein–Hilbert truncation) we bring the Functional Renormalization Group Equation in a solvable form, which provides evidence for the existence of the non-Gaussian fixed point.

### Affine Coherent State Quantization: A Brief Introduction and Some Applications

Abstract: Loop quantum gravity (LQG) is a background-independent approach to the unification of general relativity and quantum theory. While LQG has many desirable properties, the independence of a fixed metric makes it difficult to discuss the renormalisation group, since there is no way of defining an a priori notion of scale (such as a maximum energy or lattice length), since that would depend on space-time geometry, which is fully fluctuating in the theory. In this talk I will present recent progress in developing a background-independent notion of RG flow for the path-integral formulation of LQG. I will show first numerical explorations of the RG flow, and discuss the relation to standard notions of renormalisation.

### Affine Coherent State Quantization: A Brief Introduction and Some Applications

Abstract: I will go through the basics of affine coherent state quantization (ACSQ), and illustrate the advantages and drawbacks of ACSQ by discussing some examples, including the Lemaître–Tolman–Bondi model.

### Dynamical symmetries of the Bianchi models

Abstract:
In the first part of this talk we will focus on the derivation of the following statement concerning the general relativistic dynamics of the Bianchi models:

*The special automorphism group* 𝑆Aut(𝔤) *is the symmetry group of the equations of motion, satisfied by the metric ℎ _{𝑖𝑗}, in the absence of matter sources.*

In the second part we will employ the notion of homogeneity preserving diffeomorphisms in order to shed light onto this statement from a spacetime point of view.

### Non-local "ghost-free" gravity

Abstract:
Singularities are a well known problem of Einstein's General Theory
of Relativity. It is believed that any consistent theory of gravity
should resolve them. In this talk, we will explore such an avenue in
the context of classical non-local gravity.

In particular, I will present the model of so-called "ghost-free
gravity" (at the linearized level). This can be thought of as a
generalization of Fierz--Pauli theory with infinitely many
derivatives. These derivatives, unlike in Pauli–Villars
regularization schemes, are combined in such a way that there appear
no unphysical ghost modes in the propagator at tree level. I will
demonstrate that the Newtonian potential is regularized in this
theory, and comment on steps towards exploring ghost-free gravity in
the strong field regime of black holes.

If time permits I will also comment on non-local gravity formulated
via a non-local constitutive law. At the linear level, this
formalism is closely related to ghost-free gravity, even though the
origin of non-locality might be of an entirely different nature.

### Quantum Geometrodynamics of Higher Derivative Theories with and without Conformal Symmetry

Abstract:
This thesis concerns with a framework of canonical quantization of gravity based on the Einstein–Hilbert action extended by terms quadratic in curvature. The aim is to investigate the semiclassical limit of such a theory and compare it with the semiclassical limit of the canonical quantization of the Einstein–Hilbert action alone, the latter of which is the usual approach in this framework.

General Relativity has passed the tests from the length scales of micrometers up to the cosmological scales. The classical evolution of our Universe seems to be described by the so-called $\Lambda$CDM model, which was recently tested by the Planck satelite with success. The recent discovery of gravitational waves seems to confirm also the linearized, long-range behavior of vacuum General Relativity. However, the behavior of gravity at short scales and relatively high energies, i.e. in the regimes where quantum effects of matter fields and spacetime become relevant, remains so far within the many possible theoretical approaches to its understanding. It is expected that near the initial singularity of our Universe — the Big Bang — the description of gravity drastically deviates from General Relativity and a theory of quantum gravity is necessary. But already near the theoretical limit of the highest observable energy scale (energy per excitation of a quantum field) — the Planck energy scale — it is expected that the effects of quantum field-theoretical description of matter propagating on classical curved spacetimes play a significant role. Because of this, General Relativity changes in two ways. First, the energy-momentum tensor is replaced by the expectation value of the energy-momentum tensor operator. Second, since the latter diverges, the regularization of these divergences has shown that it is necessary to modify General Relativity by adding to the Einstein–Hilbert action, among others, terms quadratic in curvature such as the square of the Ricci scalar and the square of the Weyl tensor. Since these terms generate fourth order derivatives in the modified Einstein equations, the doors were opened for investigating modified classical theories of gravity, in order to provide alternative interpretations of dark matter and the accelerated expansion of the Universe. However, an often neglected fact in these classical approaches is that these terms are suppressed at the present, classical scales. This is also reflected in the fact that the respective coupling constants of these new terms are proportional to the Planck constant and are thus of perturbative nature. Therefore they are only relevant at high energy/strong curvature regimes, typical for the very early universe. At extremely high energy scales, i.e. near and above the Planck energy scale, it is expected that the perturbative description breaks down and that a full quantum theory of gravity — which assumes that the spacetime itself is quantized as well — is necessary.

The main goal of this thesis is to quantize the Einstein–Hilbert action extended by the quadratic curvature terms is within the canonical quantization approach, thus formulating quantum geometrodynamics of the higher derivative theories. The motivation is to provide an alternative to the standard canonical quantization based on the Einstein–Hilbert action alone, because the latter does not generate the quadratic curvature terms in the semiclassical limit. A particular formulation of a semiclassical approximation scheme is employed which ensures that the effects of the quadratic curvature terms become perturbative in the semiclassical limit. This leaves the classical General Relativity intact, while naturally giving rise to its first semiclassical corrections.

Another topic of interest is a classical theory where the quadratic Ricci scalar and the Einstein–Hilbert term are absent from the action, which then enjoys the symmetry with respect to the conformal transformation of fields (local Weyl rescaling). We pay a special attention to this case, because near and beyond Planck scales it is expected that conformal symmetry plays a
very important role, since it provides a natural setting for the absence of the notion of a physical length scale. Certain useful model-independent tools are also constructed in this thesis. Firstly, it is shown that if coordinates are treated as dimensionless and if a set of variables based on the unimodular decomposition of the metric is introduced, the only conformally variant degree of freedom becomes apparent. This makes the geometrical origin of the physical length scale apparent as well, which is especially important in the interpretations of conformally invariant quantum theories of gravity. With such an approach several earlier results become much more transparent. Secondly — which naturally follows from the application of the set of these new variables — a model-independent generator of conformal field transformations is constructed in terms of which a reformulation of the definition of conformal invariance is given. Thirdly, it is argued that a canonical quantization scheme makes more sense to be based on the quantization of generators of relevant transformations, than on the first class constraints.

The thesis thus attempts to combine several minor but important aspects of a theoretical approach and use them to pursue the main goal.

Date | Time | Speaker | Topic | Room |
---|---|---|---|---|

April 2, 2019 | 12:00 |
Viacheslav Emelyanov (KIT, Karlsruhe) |
Black-hole evolution from stellar collapse | Konferenzraum 1 (Neubau) |

April 9 | 12:00 |
Adamantia Zampeli (Charles University, Prague) |
Canonical quantization of minisuperspace models with variational symmetries | Konferenzraum 1 (Neubau) |

April 23 | 12:00 |
Yi-Fan Wang (Uni Cologne) |
Dynamically assisted Schwinger effect | Konferenzraum 1 (Neubau) |

April 30 | 12:00 |
Tatevik Vardanyan (Uni Bonn) |
Wheeler–DeWitt quantum cosmology of Bianchi II model | Konferenzraum 1 (Neubau) |

May 14 | 12:00 |
David Chay Benisty (BGU Negev / GU Frankfurt) |
The Cosmological Constant and the mass of the Local Group | Konferenzraum 1 (Neubau) |

May 21 | 12:00 |
Victor Berezin (INR RAS, Moscow) |
On surface terms and double layers in quadratic gravity | Konferenzraum 1 (Neubau) |

June 4 | 12:00 |
Pouria Pedram (IAU, Tehran) |
How to construct wave packets with complete classical–quantum correspondence in quantum cosmology | Konferenzraum 1 (Neubau) |

June 6 | 10:00 (c.t.) | Dimitrios Gkiatas (Uni Bonn; Master Colloquium) |
A covariant treatment of Lorentzian spacetimes in the Einstein–Hilbert truncation | Seminarraum 1, BCTP |

June 25 | 12:00 |
Benjamin Bahr (Uni Hamburg) |
Background–independent renormalization in spin foam quantum gravity | Konferenzraum 1 (Neubau) |

July 2 | 12:00 |
Tim Schmitz (Uni Cologne) |
Affine Coherent State Quantization: A Brief Introduction and Some Applications | Konferenzraum 1 (Neubau) |

July 9 | 12:00 |
Nick Kwidzinski (Uni Cologne) |
Dynamical symmetries of the Bianchi models | Konferenzraum 1 (Neubau) |

August 20 | 16:00 |
Jens Boos (UAlberta, Edmonton) |
Non-local "ghost-free" gravity | Neubau |

September 16 | 14:00 |
Branislav Nikolic (Uni Cologne; disputation) |
Quantum Geometrodynamics of Higher Derivative Theories with and without Conformal Symmetry | Seminarraum II (II. Physikalische Institut) |

## Past seminars

Winter term 2018/19

Summer term 2018

Winter term 2017/18

Summer term 2017

Winter term 2016/17

Summer term 2016

Winter term 2015/16

Summer term 2015

Winter term 2014/15

Summer term 2014

Winter term 2013/14

Summer term 2013

Winter term 2012/13

Summer term 2012

Winter term 2011/12

Summer term 2011

Winter term 2010/11

Summer term 2010

Winter term 2009/10

Summer term 2009

Winter term 2008/09

Summer term 2008

Winter term 2007/08

Summer term 2007

Winter term 2006/07

Summer term 2006

Summer term 2005

Winter term 2004/05

Summer term 2004

Winter term 2003/04

Summer term 2003