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
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.
Future space-based gravitational-wave detectors like LISA will require highly accurate gravitational wave templates for detecting systems like extreme mass ratio inspirals and estimating their parameters. In our previous work, we considered orbits of a spinning body around a Schwarzschild black hole and numerically calculated contribution of the spin to the gravitational-wave fluxes of energy and angular momentum fluxes from these orbits. Because the spin is small, its contribution to the fluxes can be calculated with much lower precision than the precision of the leading nonspinning part of the fluxes. Therefore, in this work, we expand the linear-in-spin part of the GW fluxes in a post-Newtonian parameter and eccentricity and obtain an approximative analytic solution which is valid for low eccentricities and high separations. We compare the results with the numerical data and, using the approximative fluxes, calculate extreme mass ratio inspirals and their waveforms. Through the mismatch between our approximated inspirals and fully relativistic inspirals we assess the validity of our approximation for expected signals detected by LISA.
Although there are explicit examples of numerical and perturbative solutions of charged rotating black hole solutions in higher dimensional Einstein-Maxwell theory, an explicit exact solution in closed form is unknown. In their famous paper "Black holes in higher dimensional spacetimes," Myers and Perry attempted to obtain a charged version of their black hole solution with one rotation parameter, analogous to Kerr-Newman. The attempt did not result in a charged-black hole but in a weak "no-go" result. Motivated partly by this and recent developments in Kerr-Schild double copy, we study the Kerr-Schild class of spacetimes in higher dimensional Einstein-Maxwell theory, including an arbitrary cosmological constant. Assuming an expanding Kerr-Schild (K-S) vector k and a vector potential aligned along it, we restrict our study to the charged solutions that can be generated by a K-S transformation of a vacuum K-S solution. In the case of twisting k, we show that a charged solution can exist only when k is shear-free, thereby extending Myers-Perry's previous "no-go" result. We show that the general twisting-shearfree solutions are charged (A)dS-Taub-NUT solutions with a base space of constant holomorphic sectional curvature. In the non-twisting case, we obtain an example of a shearing Vaidya-like solution with a null electromagnetic field in five dimensions.
By using a new perturbative approach we derive a fully covariant and gauge invariant theory of adiabatic, radial perturbations of perfect fluid stars within the theory of general relativity, which is equivalent to (but more powerful than) the Chandrasekhar pulsation equation. We discuss how the choice of frame in which perturbations are described can significantly simplify the mathematical analysis of the problem, and we single out two different relevant frames: comoving and static. The properties of the perturbation equations in both frames are discussed, and we show that on the one hand, it is possible to find analytical solutions for the perturbation equations if the background is sufficiently regular, and on the other hand the system is also suitable for numerical implementation. Exploiting the new formalism, we derive an upper bound for the maximum compactness of stable, perfect fluid stars, which is equation-of-state-agnostic and significantly smaller than the Buchdahl bound. Finally, the covariance of the theory allows us to draw some insights into the thermodynamics of perturbative non-equilibrium systems.
4-Dimensional Einstein-Gauss-Bonnet (4DEGB) gravity has garnered significant attention in the last few years as a phenomenological competitor to general relativity. We consider the theoretical and observational implications of this theory in both the early and late universe, (re-)deriving background and perturbation equations and constraining its characteristic parameters with data from cosmological probes. Our investigation surpasses the scope of previous studies by incorporating non-flat spatial sections. We explore consequences of 4DEGB on the sound and particle horizons in the very early universe, and demonstrate that 4DEGB can provide an independent solution to the horizon problem for some values of its characteristic parameter alpha. Finally, we constrain an unexplored regime of this theory in the limit of small coupling alpha (empirically supported in the post-Big Bang Nucleosynthesis era by prior constraints). This version of 4DEGB includes a geometric term that resembles dark radiation at the background level, but whose influence on the perturbed equations is qualitatively distinct from that of standard forms of dark radiation. In this limit, only one beyond-LambdaCDM degree of freedom persists, which we denote as alphaC. Our analysis yields the estimate alphaC = (-9 ± 6) × 10-6 thereby providing a new constraint of a previously untested sector of 4DEGB.
Time: 13-15
Speakers: Ondřej Zelenka, David Trestini, Tomáš Ledvinka, Debora Lančová
We shall discuss static solutions of scalar tensor theories that acquire primary scalar hair. The solutions are asymptotically flat and are continuously related to the Schwarzschild metric. They depend on two independent parameters mass and scalar charge and can have quite rich horizon structure. The scalar field is found to be regular on the horizon. The black holes can become regular at the origin for a specific relation in between the charges.
The Kerr-Sen black hole is a rotating charged black hole solution arising from heterotic string theory with a U(1) gauge field, a dilaton and an axion appearing through the Kalb-Ramond 3-form tensor. The Kerr-Sen metric depends on three parameters identified with the mass, the charge and the angular momentum. We will show how it can fit in a Kerr-Schild form.
Gravitational memory effect is the permanent displacement in the relative separation between freely falling particles resulting from the passage of gravitational wave train. We obtain a closed form expression for the linearized perturbation up to quadrupolar order around de Sitter space-times generated by spatially compact sources. We demonstrate that such a source causes a displacement memory effect close to future infinity. We also discuss a correspondence between memory effect and asymptotic symmetries of de Sitter.
I will discuss a Monte Carlo method designed to compute stationary solutions of the general-relativistic Vlasov equation describing a gas of non-colliding particles. Our method consists of three elements: 1) selecting a set of parameters of individual trajectories, which correspond to assumed properties of the distribution function (e.g., initial, asymptotic or boundary conditions), 2) solving geodesic equations for the selected sample of parameters, 3) implementing a suitable coarse-graining scheme, which yields approximations to observable quantities (particle current density, energy momentum tensor). I will discuss difficulties associated with problems 1) and 3), providing a collection of examples related with stationary accretion models in the Schwarzschild spacetime. In the second part I will also show an application to accretion of the collisionless gas onto moving black holes.
Jiří Bičák Oldřich Semerák