Seminář se koná v úterý ve 13:10 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičkách 2, Praha 8
Is the lack of perturbative renormalizability in Einstein’s general relativity a failure of the perturbative QFT framework to describe quantum aspects of gravity at the fundamental level? My answer is NO. In fact, the addition of quadratic curvature invariants to the Einstein-Hilbert action makes it possible to achieve “strict” renormalizability in four dimensions. In this talk I show that strict renormalizability is still a very powerful criterion for selecting unique and predictive theories in sub-Planckian regimes, even when gravity is taken into account. After describing some aspects of Quadratic Gravity, I will compare it with other approaches and argue that it is the most predictive as it can explain new physics in the sub-Planckian regime, for example, it offers a natural explanation for the inflationary phase in the early Universe. Finally, I will make some comments on the (super-)Planckian regime.
Boundary counterterms are required to cancel the divergences in the bulk action of asymptotically AdS gravity. These boundary terms are prescribed by a systematic procedure known as Holographic Renormalization, developed in the context of AdS/CFT correspondence. In this seminar, we show that, in four and six bulk dimensions, these counterterms can also be obtained from a proper embedding of Einstein in Conformal gravity (Conformal Renormalization).
Geometric optics limit is known to be a good-enough approximation for the calculation of distances and image distortions in the Universe. In cosmology, we usually assume a point source that emits spherical waves and only a small section of the wavefront is accessible to the observer. In the geometric optics limit, this section is represented by a thin bundle of rays. Accordingly, the intensity profile on the transverse, observational screen is homogeneous. In this talk, I will outline the analogies between the paraxial ray optics of the Newtonian theory and the thin bundles in general relativity. I then propose a method adopted from the paraxial wave optics in order to study the wave-like effects of light propagation in general relativity. This method is sometimes referred to as ``wavization'' due to its resemblance to the semi-classical quantization techniques. The idea is to use certain phase space methods and symplectic symmetries to superpose two bundles initiated from a small yet finite size source. With this, we explore the possibility of obtaining inhomogeneous intensity profiles on the transverse plane associated with the fundamental Gaussian mode. The Gaussianity of the intensity profiles of such light beams is sourced by the spacetime curvature and not necessarily by random processes. We observe that their form is preserved throughout the propagation in curved spacetime on account of the symplectic symmetries of the underlying phase space. Finally, we show that the caustics can be avoided with this method. In addition, the extended source effect can be studied on account of Gaussian beam decomposition techniques.
We will review the classical double copy, which maps exact solutions of classical gauge theories like electromagnetism, to solutions of general relativity. We will cover both the Kerr-Schild and Weyl formulations of this map. Following a survey of known exact solutions, we will review why a position-space classical solution double copy is even feasible. We will briefly discuss some perturbative approaches, and then close by relating several gravitational objects (including horizons and Penrose limits) to their gauge theory analogues.
The reduction of gravitational Lagrangians by a specified symmetry group can sometimes result in field equations that are fully equivalent to the reduced ones—if this holds for all Lagrangians, it is known as the principle of symmetric criticality (PSC), which is a property of the infinitesimal group action only. In this talk, I will explain the rigorous process of symmetry reduction of Lagrangians and present all infinitesimal group actions that satisfy PSC. I will identify the corresponding invariant metrics (and l-chains), discuss their interrelations, and analyze the simplifications allowed by the residual diffeomorphism group and Noether identities, both before and after the variation of the reduced Lagrangian.
In this second presentation the case with a positive cosmological constant will be presented and the main differences with the case without cosmological constant will be enumerated. The entire idea is based on a couple of vector fields, defined at infinity, that describe the energy-momentum properties of the tidal gravitational field: the asymptotic super-momentum and the asymptotic super-Poynting vectors. They will be shown to lead to a criterion on the existence/absence of gravitational radiation at infinity. The necessity of going to the tidal level will be explained. The problem of incoming radiation will be analysed under the viewpoint of the so-called asymptotic radiant super-momenta. Application to specific spacetimes -and in particular to the general Einstein-Maxwell solution with type-D black holes- will be given showing the validity of the criterion. Time permitting, some discussion on conserved charges and symmetries will also be presented.
This is the first of two seminars on gravitational radiation at conformal infinity. In this one, the case with vanishing cosmological constant is addressed. After giving some brief historical context, the framework and tools are presented, namely: conformal completions à la Penrose and the Bel-Robinson tensor. The asymptotic version of the latter is used to characterise gravitational radiation in a new covariant, geometric and invariant way. This result is compared with the traditional condition based on the news tensor and showed to be equivalent to it. The advantages of the new criterium are stressed: in particular, its tidal nature allows one to apply it when the cosmological constant is positive - this matter is treated in the second talk of this series.
I will discuss cosmological domain walls with a review of their evolution and how they produce gravitational waves. Particular attention will be devoted to melting domain walls which are described by tension red-shifting with the expansion of the Universe, so that this network eventually fades away completely. These melting domain walls emit gravitational waves with the low-frequency spectral shape favoured by the recent NANOGrav 15 yrs data. This scenario involves a feebly coupled scalar field, which can serve as a promising dark matter candidate. This ultra-light dark matter has mass below 0.01 neV which is accessible through planned observations thanks to the effects of superradiance of rotating black holes. This talk is based on recent works: arXiv:2104.13722, arXiv:2112.12608, arXiv:2307.04582 and arXiv: 2406.17053 and arXiv: 2410.21971.
The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. At this order, both of the spin vectors as well as the angular momentum vector precess in an intricate pattern. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. Fortunately, Hamiltonian mechanics allows to define action variables by an invariant geometric construction. I will present closed formulas for the actions and frequencies for the motion of spinning test particles near Kerr black holes. I will then use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows to match the actions across both systems, providing a new dictionary for interpolation between the two limits.
In 1935, Einstein and Rosen (ER), in their seminal paper "Particle Problem in General Relativity" proposed that "a particle in the physical Universe has to be described by mathematical bridges connecting two sheets of spacetime" in order to achieve a consistent understanding of quantum fields in curved spacetime. We discuss similar conclusions independently arrived at by Schrodinger in 1956 and 't Hooft in 2016 in the context of cosmological and black hole spacetimes. Quantum effects at gravitational horizons involve inverse harmonic oscillators. We demonstrate that an analogous ER proposal of a mathematical bridge is envisioned by Berry and Keating for the description of a quantum inverse harmonic oscillator that has horizons in its phase space. Recently proposed direct-sum quantum theory reconciles the ER's vision by expressing a single quantum state in the physical space as a direct-sum of two components in the parity conjugate regions with opposite arrows of time. We discuss the implications of this framework for offering a new understanding of the ER bridges, promising a unitarity description of quantum fields in curved spacetime along with observer complementarity. Furthermore, we present compelling evidence for our new understanding of ER bridges in the form of large-scale parity asymmetric features in the cosmic microwave background. We finally discuss the implications of this new understanding for our endeavors in combining gravity and quantum mechanics.
Higher-derivative terms are relevant in several approaches to quantum gravity; they occur in the perturbative quantization of Einstein gravity and can be used to construct (super-)renormalizable quantum gravity models. In this talk, we present spherically symmetric static solutions of the most general six-derivative gravity using series expansions. It turns out that the only solutions of the complete theory, i.e., with generic coupling constants, that possess a Frobenius expansion around the origin (r=0) are necessarily regular. These results reveal a significant difference between higher-derivative gravity models with 4 and 6 derivatives in what concerns the space of classical solutions and their potential to resolve black hole singularities.
The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. In this talk I show that separability of the equations of motion can be recovered to linear order in spin by a shift of the worldline derived with the use of the hidden symmetry of Kerr space-time. Consequently, the closed-form solution of the motion is expressed in a way closely analogous to the solution for spinless particles. This finding enriches the understanding of separability and integrability properties of the dynamics of test particles and fields in Kerr space-time, and is particularly valuable for modeling inspirals of rotating compact objects into massive black holes.
Superintegrable systems are Hamiltonian systems with more integrals than are required for Liouville integrability, with the maximal number of functionally independent integrals being 2n-1. Second-order maximally superintegrable systems have been the most studied because of their connection with separation of variables and special functions. Of these, the non-degenerate second-order superintegrable systems in two- and three-dimensional conformally flat spaces were shown by Kalnins et al to be to be parameterised by an algebraic variety. All known non-degenerate systems in fact possess n(n+1)/2 linearly independent quadratic in the momenta integrals, and this property is termed "abundance". In this talk I will describe some recent work with Konrad Schobel and Andreas Vollmer describing the algebraic variety of abundant superintegrable systems in n dimensions and the interesting connections between superintegrable systems and other seemly unrelated fields that have followed.
The information loss paradox is usually stated as an incompatibility between general relativity and quantum mechanics. However, the assumptions leading to the problem are often overlooked and, in fact, a careful inspection of the main hypotheses suggests a radical reformulation of the problem. Indeed, I will present a thought experiment that leads to a more sharp formulation of the problem.
David Kubizňák Oldřich Semerák