Relativity Seminar
of the Institute of Theoretical Physics

spring 2023

Given seminars:

February 28, 2023
Axially symmetric stationary perturbations of a Kerr black hole: Debye superpotential for charged ring or circular current, and further generalizations
Dr. David Kofroň
We provide an explicit, closed and compact expression for the Debye superpotential of a circular EM source in a stationary axisymmetric spacetime. It is obtained by integrating the Green function of Teukolsky Master Equation (TME). The Debye potential itself is then, for a particular configuration, calculated in the same manner as the phi_0 field component is calculated from the Green function of the TME - by convolution of the Green function with sources. In such a way we provide an exact field of charged ring and circular current on the Kerr background, finalizing thus the work of Linet. We will also shortly discuss the recent progress (and complications) in extending these results to gravitational perturbations.

March 7, 2023
Zoom talk:
Accretion disk structure around a uniformly accelerating black hole
Dr. Shokoufe Faraji
ZARM Institute, University of Bremen
Generalisation of the relativistic accretion thick disc model is considered to the background of a spinning charged accelerating black hole described by the C-metric to study the effects of this background on the disc model. In this talk, a review of this metric will be presented and the main properties of the accretion disc model and its dependence on the initial parameters of the underlying spacetime will be discussed.

March 14, 2023
Monarch migration of Carrollian particles on the black hole horizon
doc. David Kubizňák
After discussing the basics of Carrollian physics, we shall revisit the motion of massless particles with anyonic spin in the black hole horizons. As recently shown, such particles can move within the horizon of the black hole due to the coupling of charges associated with a 2-parametric central extension of the 2-dimensional Carroll group to the magnetic field around black holes -- the so called "anyonic spin-Hall effect". We shall study several examples of such motions. Of these, the most interesting is the motion in a misaligned (asymptotically uniform) magnetic field around Kerr, which results in a time dependent motion of Carrollian particles that is reminiscent of "monarch migration".

March 21, 2023
Gravitational self-force in a highly regular gauge
Dr. Samuel Upton
Astronomical Institute of the Czech Academy of Sciences
Extreme-mass-ratio inspirals (EMRIs) will be an important gravitational-wave source for the Laser Interferometer Space Antenna (LISA), a future space-based gravitational-wave detector. In an EMRI, a stellar mass compact object, such as a black hole or neutron star, slowly spirals into a supermassive black hole while continually emitting gravitational waves. The primary way of modelling these systems is through a perturbative method known as gravitational self-force. To accurately model EMRI systems requires us to go to second order in perturbation theory, which creates a number of issues. In this talk, I will present an overview and current status of the field of gravitational self-force research and present work done to develop a class of highly regular gauges to ameliorate the strong divergences one finds near the worldline of the small object that hinder rapid numerical calculations.

March 28, 2023
Relativistic positioning systems and automatic differentiation
Dr. Justin C. Feng
Center for Astrophysics and Gravitation @ Instituto Superior Técnico, University of Lisbon
I discuss the framework of relativistic positioning systems for satellite navigation. I then discuss a new approach to the relativistic location problem (i.e. the determination of the position of a user from satellite data) in a generic spacetime geometry. This approach makes use of automatic differentiation. Time permitting, I will discuss in detail the potential applications of this powerful new tool in computational physics.

March 28, 2023
!!! 10:40, within Seminar of the ITP !!!
Efficient trajectory calculations for extreme mass ratio inspirals using near-identity (averaging) transformations
Dr. Philip Lynch
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Department of Astrophysical and Cosmological Relativity
Future space based gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA) will allow for the detection extreme mass ratio inspirals (EMRIs) which consist of a stellar mass compact object spiralling into a massive black hole (MBH) due to gravitational radiation reaction. These sources are of particular interest for their ability to accurately map the spacetime of the MBH, allowing for unprecedentedly accurate measurements of the MBH's mass and spin, and tests of general relativity in the strong field regime. To reach the science goals of the LISA mission, one requires waveform models that are (i) accurate to within a fraction of a radian, (ii) extensive in the source's parameter space and (iii) fast to compute, ideally in less than a second. We focus on the later criteria by utilising techniques that will speed up inspiral trajectory calculations as well as extending prior models to include the MBH's spin. We develop the first EMRI models that incorporate the spin of the MBH along with all effects of the gravitational self-force (GSF) to first order in the mass ratio. Our models are based on an action angle formulation of the method of osculating geodesics (OG) for generic inspirals in Kerr spacetime. For eccentric equatorial inspirals and spherical inspirals, the forcing terms are provided by an spectral interpolation of the first order GSF. For generic inspirals where sufficient GSF data is not available, we construct a toy model from the previous two models. However, the OG method is slow to evaluate due to the dependence of the equations of motion (EOM) on the orbital phases. Therefore, we apply a near-identity (averaging) transformation (NIT) to eliminate all dependence of EOM on the orbital phases while maintaining all secular effects to post-adiabatic order. This inspiral model can be evaluated in less than a second for any mass-ratio as we no longer have to resolve all ~105 orbit cycles of a typical EMRI.
April 4, 2023
Exact solutions in 2+1 dimensional gravity
Mgr. Matúš Papajčík
Exact solutions in the lower dimensional theory of gravity have found their use in many areas of theoretical physics from string theory and AdS/CFT correspondence to quantum gravity. They play an important role as toy models, therefore, their study is highly desirable. Keeping in mind that within 3D gravity virtually all spacetimes must belong to either the expanding Robinson-Trautman class or the non-expanding Kundt class of geometries, we investigate the exact solutions of the coupled system of Einstein-Maxwell equations for these geometries, allowing also for a non-vanishing cosmological constant. We discuss the found electrovacuum solutions and identify the special subclass of charged black hole spacetimes in 2+1 gravity.

April 18, 2023
Zoom talk:
Toroidal structures in astrophysical objects: gravitational properties
Prof. Elena Bannikova
INAF Capodimonte Astronomical Observatory (Naples) / V. N. Karazin Kharkiv National University / Radio Astronomy Institute of NAS of Ukraine
There are astrophysical objects possessing toroidal (ring) structures, for example, ring galaxies and dusty tori in active galactic nuclei. The masses of such toroidal-ring structures are substantial, which requires accounting of its gravitational properties. In my talk I will give a review of our results about the gravitational properties of a torus starting from its gravitational potential for the circular and elliptical cross-sections. I will consider the dynamics in a gravitational field of a central mass and a gravitating ring where there is a region of unstable equilibrium —the "Lagrangian circle" (LC). The closed circular orbits exist only to a certain radius corresponding to the "outermost stable circular orbit" (OSCO). In this case there is analogy with the ISCO in the relativistic case. The existence of region with non-circular orbits between LC and OSCO can explain the observed gap in the distribution of stellar density in ring galaxies. The effects of gravitational lensing show that in this lens system the formation of three Einstein rings is possible.

April 25, 2023
Non-local scalar fields in static spacetimes
Dr. Ivan Kolář
Non-local exponential operators with an infinite number of derivatives appear in modern physics in various contexts. They arise naturally in the effective models of string theories but they also play an important role in ghost-free UV completions of GR. In this talk, I will discuss the methods for solving linear non-local scalar field equations in (curved) static spacetimes. The methods are based on the heat kernels and their estimates in compact and non-compact manifolds. I will present several examples of static and time-dependent solutions and also discuss their regularity. The talk is based on arXiv:2201.09908.

May 2, 2023
Comparing effective-one-body and gravitational self-force results as tools for third-generation gravitational wave detectors
Angelica Albertini
Astronomical Institute, Czech Academy of Sciences
Gravitational self-force theory and the effective-one-body (EOB) formalism are two different approaches to the two-body problem in general relativity, both suited to describe black hole binary evolutions, but natively pertaining to different domains of validity. After briefly introducing the two formalisms, I will present a comparison between the related gravitational waveforms, both in the time domain and in the frequency domain, locating the region of largest agreement. I will then introduce some updates to the EOB model, paving the way for accurate waveform modeling for third-generation detectors.

May 9, 2023
No seminar. You may watch MTW anniversary instead.
May 16, 2023
Covariant relativistic stars
Dr. Sante Carloni
We apply the 1+1+2 covariant semi-tetrad approach to derive in covariant form the Tolman-Oppenheimer-Volkoff equations. These equations naturally include anisotropic pressures and are easily extended to the multifluid case. The covariant TOV equations are then used to obtain new exact solutions using direct resolution and reconstruction techniques. Finally, we show that the well-known generating theorems for the solutions of the TOV equations can be represented by simple deformations and that these theorems can be used also to derive multifluid solutions from single fluid ones.

May 23, 2023
Observers and flows in black hole space-times: The inside story
Prof. Oleg B. Zaslavskij
Department of Physics and Technology, V. N. Karazin Kharkiv National University
We consider general radially moving frames realized in the background of nonextremal black holes having causal structure similar to that of the Schwarzschild metric. In doing so, we generalize the Lemaitre approach, constructing free-falling frames which are built from the reference particles with an arbitrary specific energy e_0 including e0<0 and a special case e0=0. The general formula of 3-velocity of a freely falling particle with the specific energy e with respect to a frame with e_0 is presented. We point out the relation between the properties of considered frames near a horizon and the Banados-Silk-West effect of an indefinite growth of energy of particle collisions. Using our radially moving frames, we consider also nonradial motion of test particles including the regions near the horizon and singularity. We also point out the properties of the Lemaitre time at horizons depending on the frame and sign of particle energy.

May 30, 2023
!!! At 10:40 within the ITP Seminar !!!
Microscopics of de Sitter entropy from precision holography
Prof. Thomas Hertog
Department of Theoretical Physics, Faculty of Science, KU Leuven
I explain how quantum corrections to the entropy of four-dimensional de Sitter space can be computed using the AdS/CFT correspondence. Employing the intertwinement of Euclidean de Sitter and anti de Sitter saddles, I embed effective de Sitter gravity theories in M-theory and conjecture that the partition function of the ABJM CFT dual encodes all perturbative corrections to the de Sitter entropy in the static patch. This conjecture is checked for the first two subleading corrections to the area-law by studying four-derivative terms and one-loop effects in de Sitter gravity. Finally I comment on the extension of this framework to compute more tangible cosmological observables.

June 13, 2023
!!! At 10:40 !!!
Dancing with Gargantua: gravitational waves from extreme-mass-ratio inspirals
Dr. Gabriel A. Piovano
University College Dublin, School of Mathematics and Statistics
Gravitational waves have revolutionized how we observe the Universe. However, current detectors are limited by the overwhelming seismic noise in the low-frequency range. Only space-borne observatories like the future LISA and Taiji missions can reach the rich gravitational wave spectrum in the milliHertz band. Among the sources detectable by space-borne interferometers, extreme-mass-ratio binaries are arguably the most interesting. These systems are composed of a massive black hole and a much smaller compact body. The latter falls into the heavier companion in a slow process called extreme-mass-ratio inspiral (EMRI), emitting gravitational waves with complex features. The properties of an EMRI binary could be recovered from a detected years-long signal with astounding precision, which might lead to exciting discoveries in astrophysics, gravitational, and particle physics. On the other hand, EMRIs are challenging sources to model, and there are still several open problems in data analysis for space detectors. This seminar aims to be an introduction to EMRIs, and is divided into three parts. In the first part, I will overview the theorical tools commonly employed to construct EMRI waveforms, focusing on black hole perturbation theory techniques. I will then introuduce Bayesian statistics applied to gravitational wave data analysis. Finally, I will talk about my current research on parameter estimation for spinning EMRI binaries.

June 13, 2023
Gyroscopes orbiting gargantuan black holes: Incorporating secondary spin into large mass-ratio inspirals
Lisa V. Drummond
MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology
Very large mass-ratio binary black hole systems are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). We hope to use these systems to probe the spacetime in exquisite detail and make precision measurements of the larger black hole’s properties. Accurate models using general relativistic perturbation theory will allow us to realize the potential of these large mass-ratio systems. Such models must include post-geodesic corrections, which account for forces driving the smaller black hole away from a geodesic trajectory. An important post-geodesic effect is gravitational self-force, which describes the small body's interaction with its own spacetime curvature. This effect includes the backreaction due to gravitational-wave emission that leads to the inspiral of the small body into the black hole. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime. This introduces a second post-geodesic correction called the spin-curvature force. In this talk, I will present our calculation of spinning-body inspirals and associated waveforms that include both spin-curvature forces and the leading backreaction of self forces. I will discuss what aspects of the self force have been neglected, and what must be done to include these aspects in the future. Finally, I will discuss how we use a near-identity transformation to eliminate dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies.

June 16, 2023
!!! Friday 11:00 !!!
How to kick a black hole
Prof. Jörg Frauendiener
Department of Mathematics and Statistics, University of Otago
It is well known that gravitational waves interact in a non-linear way. This makes it difficult to describe them rigourously. The cleanest description is based on a certain conformal invariance of the Einstein equations — a fact which was established by R. Penrose and was used by H. Friedrich to prove several important global results for general relativistic space-times. The so called conformal field equations implement this conformal invariance on the level of partial differential equations. They provide various well-posed initial (boundary) value problems for use in different situations. The talk will give a computational perspective on the non-linear interaction of gravitational waves with an initially static (and spherically symmetric) black hole. We will show how to kick it and possibly how to spin it up.

July 7, 2023
!!! Friday at 13:10 !!!
Transverse metric expansion at a general null hypersurface
Gabriel Sánchez Pérez
Department of Fundamental Physics, University of Salamanca

I will discuss a systematic procedure to obtain identities for the derivatives of the metric along a transverse direction on a general null hypersurface of arbitrary dimension. These identities are fully general and could be applied in many contexts of interest, such as degenerate and non-degenerate Killing horizons, homothetical Killing horizons, or even null infinity. In particular, one can establish at which order the obstruction to determine higher order derivatives appears on each case. This is joint work with my PhD supervisor Marc Mars.

July 18, 2023
!!! Tuesday 11:00 !!!
Perturbing the perturbed: Stability of the QNMs for asymptotically de Sitter black holes
Dr. Sumanta Chakraborty
School of Physical Sciences, Indian Association for the Cultivation of Science, Kolkata
I wish to address the question whether the quasi-normal modes, the characteristic frequencies associated with perturbed black hole spacetimes, central to the stability of these black holes, are themselves stable? For this purpose, we have provided a general method of transforming to the hyperboloidal coordinate system, for both asymptotically flat and asymptotically de Sitter spacetimes, which neatly captures the dissipative boundary conditions, and the differential operator becomes non-self-adjoint. Employing the pseudospectrum analysis and numerically implementing the same through Chebyshev's spectral method, we present how the quasi-normal modes will drift away from their unperturbed values under external perturbation of the scattering potential. We also discuss the implications of the instability of the fundamental quasi-normal mode on the strong cosmic censorship conjecture.

Zoom link

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