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
V nejbližší budoucnosti nejsou plánované žádné semináře.
We study the relationship between symmetries, boundary conditions, and conservation or flux-balance laws in General Relativity with the covariant phase space formalism. Non-trivial symmetries occur in arbitrary spacetimes if they admit a boundary, and the nature of the symmetries and of the charges one can construct depends on the chosen boundary conditions. These charges offer a refined solution to the issue of quasi-local observables in general relativity, although one must resolve potential ambiguities in their definitions. We consider both asymptotic and charges at finite distances, supported on both time-like and null boundaries. For time-like ones, we examined the dependency of the expression for the energy on boundary conditions, and proposed new Brown-York-type charges for Neumann and York’s boundary conditions. A comparison with canonical treatments confirmed a perfect agreement. For null boundaries, it is possible to consider leaky boundary conditions in a non-ambiguous way. We study the most general phase space permitting arbitrary metric variations, identify a one-parameter family of covariant symplectic potentials, and explain how restricting some of the variations is necessary for the symplectic potential to satisfy physical requirements of stationarity. This allows us to not only recover previous charge expressions, but introduce a new set of charges that extends the stationarity property to flat light-cones, with promising implications for dynamical entropies.
Analytical solution of a rotating black hole surrounded by accretion disc in full GR is, so far, unknown. The Ernst equation is nonlinear. In this talk we will provide a framework in which the solutions of linearised Ernst equations can be obtained from the linear perturbations of Kerr black hole treated in the formalism of the Debye potentials. In this way we recover all the metric perturbations in term of a single complex scalar function (which solves the Laplace equation).
Rotating bodies in curved space-time are coupled to the background by the so-called spin-curvature force. The spin vector of the body represents a new degree of freedom as compared to geodesic motion, thus making the dynamical system more complex and possibly even chaotic. At the same time, treating the spin of the lighter secondary in extreme mass ratio binaries at least to linear order is important for precise waveforms from these systems. In this talk I will show the integrability of generic motion of spinning particles in static, spherically symmetric space-times to linear order in spin. Then, I will present the closed-form solution of motion of spinning test particles near a Schwarzschild black hole in the form of elliptic integrals. I will also comment on how this relates to the generic Kerr problem and the way this result will be used in gravitational-wave modelling.
Black holes contain, deep in their interior, theoretical evidence of the failure of general relativity. A series of fundamental results, starting from the 1965 Penrose singularity theorem, proved that physically realistic initial conditions will inevitably produce a singular black hole spacetime. It is generally expected that a full theory of quantum gravity should remove the singularities that appear in general relativity. However, the lack of proper understanding of the dynamical laws dictating the evolution of spacetime and matter in these extreme situations hinders the extraction of predictions in specific models. I will discuss, in a model-independent manner, the different possibilities that singularity regularization may open, focus on fundamental open issues that need to be addressed to obtain viable nonsingular black hole candidates, and finally discuss observational signatures.
If relativistic gravitation has a quantum description, it must be meaningful to consider a spacetime metric in a genuine quantum superposition. But how might such a superposition be described, and how could observers detect it? I will present a new operational framework for studying "superpositions of spacetimes" via model particle detectors. After presenting the general approach, I show how it can be applied to describe a spacetime generated that is a superposition of two expanding spacetimes. I will then move on to show how black holes in two spatial dimensions can be placed in a superposition of masses and how such detectors would respond. The response exhibits signatures of quantum-gravitational effects reminiscent of Bekenstein’s seminal conjecture concerning the quantized mass spectrum of black holes in quantum gravity. I will provide further remarks concerning the meaning of the spacetime metric, and on distinguishing spacetime superpositions that are genuinely quantum-gravitational, notably with reference to recent proposals to test gravitationally-induced entanglement.
The current theory of gravity admits space-times with non-trivial topology. It turns out that a change in topology, even with a minimal change in geometry, can have observable consequences on local physics. We will consider the simplest model of a wormhole connecting two Euclidean spaces and investigate the consequences for electrical phenomena. We will show that charged particles remember, in a sense, which side of the wormhole they came from and that they are sensitive to the wormhole. The wormhole will glow in the presence of moving charges, and the magnetostatics will not be as static as we are used to without the wormhole.
Suitable as an exercise in Classical Electrodynamics placed in exotic destinations.
We begin by formulating an analytic model of a non-singular bouncing cosmology, the bounce phase of which receives a correction inspired by loop quantum cosmology. We then study the semi-classical particle production associated with the spacetime within the Unruh-DeWitt particle detector framework, analysing the rate of particle detection with the aim of (a) understanding quantum effects at early times; (b) identifying relics of pre-bounce physics; and (c) highlighting signatures of non-singular theories.
Fast quasi-periodic oscillations (QPOs) give us a tool to probe strong gravity and dense matter equation of state in X-ray binaries with a neutron star as one of the components. Nevertheless, the QPO modulation mechanism remains an unresolved puzzle. To this end, oscillations of an inner accretion torus can modulate the accretion rate and induce the variations of the flux from the boundary layer.
After reviewing the basic properties of theories of non-linear electrodynamics, I will focus on two particular examples of recently studied models: i) ModMax theory which is the most general theory that shares all symmetries of Maxwell's electrodynamics and ii) MadMax theory which is the unique theory (that depends only on the field invariant F^2) whose radiative solutions can be found in the Robinson-Trautman class and admits the Maxwell-like C-metric solutions. I will also discuss a generalization of the MadMax theory to an arbitrary number of dimensions and its special features in d=3.
Jiří Bičák Oldřich Semerák