Seminar is held on Tuesdays at 13:10 pm in the lecture room of the Institute
on the 10th floor of the department building at Trója, V Holešovičkách 2, Prague 8
I will discuss spacetime symmetries that enable consistent symmetry reductions of gravitational Lagrangians, fully recovering the reduced field equations for any four-dimensional metric theory of gravity. After reviewing the principle of symmetric criticality (PSC), I will present the PSC-compatible symmetries, symmetry-invariant metrics and l-chains; analyze mutual relations of symmetries and examples of known GR solutions; and address simplifications of the reduced Lagrangians allowed by residual diffeomorphisms (via Noether identities). As an application, I will show how symmetry reduction can be used to construct non-polynomial quasi-topological theories exhibiting GR-like integrability of the field equations across a broad class of symmetries, including those of spherical, hyperbolic, and planar Schwarzschild and Taub–NUT, B-metrics, near-horizon extreme Kerr, and the swirling universe, and which admit exact closed-form solutions in these cases.
The motion of spinning test particles in curved space-time is a classical relativistic problem. Astrophysically, the model captures the leading spin-orbital coupling influencing the motion of rotating compact objects. Consequently, solving the equations of motion of spinning particles in black hole space-times to linear order in spin provides information used in the modelling of extreme mass ratio inspirals. To leading order, the spin of the particle is parallel transported, and this feeds into the equations of motion of the particle. Thus, it was already known that separable parallel transport made the problem much more tractable, even though we struggled to incorporate this usefully in the Hamiltonian formalism. Here we end those struggles and end up proving the following theorem: if parallel transport in a space-time is separable, then so is the motion of spinning test particles to linear order in spin.
I will describe a new construction of Ricci flat metrics using gauged linear sigma models satisfying the Calabi-Yau condition. The approach will be introductory using elementary examples to illustrate the main points and to underline the connection between physical and mathematical concepts.
TBA
The Vaidya spacetime is a spherically symmetric solution of the Einstein equations with a null dust source. This can be used to model the gravitational collapse of a thick shell of radiation: a flat interior region is matched at an inner boundary to the null dust filled region, which is then matched at an outer boundary to Schwazschild spacetime. A central singularity inevitably forms, and depending on the profile of the energy density of the null dust, this singularity can be globally naked. Motivated by the cosmic censorship hypothesis, we consider perturbations of this configuration. We review previous work, and describe recent work where the perturbation of the inner boundary - the past null cone of the central singularity - is analysed using a framework for studying perturbations of general hypersurfaces. This sets boundary conditions for perturbations at the past null cone, and we then consider the evolutionary problem, focussing on the question of the stability of the Cauchy horizon of the naked singularity.
This talk is based on our recent paper e-Print: 2511.04650. Scalar fields with a global U(1) symmetry often appear in cosmology and astrophysics. We study the spherically-symmetric, stationary accretion of such a classical field onto a Schwarzschild black hole in the test-field approximation. Thus, we consider the relativistic Bondi accretion beyond a simplified perfect-fluid setup. We focus on the complex scalar field with canonical kinetic term and with a generic quartic potential which either preserves the U(1) symmetry or exhibits spontaneous symmetry breaking. It is well known that in the lowest order in gradient expansion the dynamics of such a scalar field is well approximated by a perfect (super)fluid; we demonstrate that going beyond this approximation systematically reduces the accretion rate with respect to the perfect fluid case. Hence, black holes can provide a way to distinguish a perfect fluid from its ultraviolet completion in the form of the complex scalar field.
Taub–NUT spacetimes are related by double Wick rotations to the near-horizon extreme Kerr geometry and to the swirling universe. Similarly, the planar Reissner-Nordström solution can be mapped to the Melvin spacetime. We show that this is not a peculiarity of individual solutions in general relativity. Rather, double Wick rotations establish mappings between entire classes of spacetime symmetries, independently of the underlying geometric theory of gravity. This provides a systematic way of generating new solutions in a given theory from known ones by exploiting the correspondence between these symmetry classes.
I will show a complete classification of D-dimensional Kundt spacetimes of Weyl type N and traceless Ricci type N in (anti-)de Sitter. Using a coordinate system with almost-Killing normalization, I will provide invariant subfamilies (generalzed Siklos, pp-, and Kundt waves) and present their canonical forms.
I will discuss the current understanding of the landscape of bosonic stars in simple GR models, the hairy black holes that are associated with them, and the corresponding dynamics. Some applications to phenomenological questions will be addressed.
Scalar-tensor theories with derivative interactions form backgrounds which spontaneously break Lorentz invariance (e.g. cosmology during inflation or the dark energy era). The dynamics of small scalar fluctuations on general anisotropic backgrounds -- phonons -- can be described as geodesic motion in an effective "acoustic" space time, with the acoustic metric providing the relativistic description of general media. This acoustic metric and its inverse give the dispersion relation, rays and phase velocities and construct two dual sound cones.
I will discuss how to read off true instabilities -- ghosts and gradient instabilities -- from the invariant properties of the acoustic metric, but also discuss false instabilities that may appear for some observers, relating this to Cherenkov radiation and the ill-posedness of the Cauchy problem. I will show that the geometric discussion of the sound cones is equivalent to the usual Hamiltonian description for an energy related to an conserved acoustic energy-momentum tensor for the fluctuations, distinct from the usual space-time one.
As full quantum gravity still remains elusive, we can gain at least limited insight into the quantum features of black holes through apt approximations, semi-classical gravity being one of them. While finding solutions even to this simplified theory is still difficult task to do, thanks to the techniques of AdS/CFT correspondence and holography, quantum-corrected black holes in all orders of backreaction with both rotation and Maxwell electromagnetic charges have been discovered. In my talk, I would like to show you how we can apply this computational framework to gravity coupled to non-linear electrodynamics and present you with resulting novel charged quantum-corrected black holes and their thermodynamics.
In this talk, I will present new rotating black hole solutions of the low-energy effective action of string theory in any dimension. These geometries are asymptotically flat with a linear dilaton vacuum and exhibit unusual thermodynamic properties, including a mass-independent Hawking temperature. I will also discuss charged extensions in 3 and 4 dimensions, which lead to closed time-like curves inside the inner horizon. Finally, I will demonstrate that these solutions can be derived via the large-d limit of the Myers-Perry black holes.
Isolated horizons provide a local generalization of the black hole horizon adapted to dynamical settings. Their intrinsic geometry is described by a Riemannian 2-metric and a rotation 1-form. Curiously, if the horizon is extremal or of Petrov Type D, the induced Einstein Equations may be expressed as local geometry constraints, namely the Petrov Type D and the Near Horizon Geometry Equations. I will present the full family of solutions for spherical, axially symmetric horizons, possibly with a conical singularity. I will discuss their embeddings into the Plebański-Demiański spacetimes with the NUT parameter, either in the periodic-time interpretation by Misner or in the presence of space-time conical singularities.
A series of works by Belinskii, Khalatnikov and Lifshitz (BKL) conjectured that spacetime near a generic spacelike singularity locally behaves in a chaotic way. Since BKL conjecture concerns very strong gravity regimes, it is natural to ask how quantum gravity influences it. We tackle this question by looking at perturbative quantum corrections to Bianchi I and II metrics approximating the relevant features of BKL conjecture. We argue that even such perturbative effects can completely change the nature of BKL dynamics. While we work in the framework of thermodynamic gravity, our findings also apply to the effective dynamics of loop quantum cosmology.
Oldřich Semerák