Proceedings Series


Vol. 16 (2023), No. 6, 28 Articles

The 8\(^\mathrm {th}\) Conference of the Polish Society on Relativity

Warsaw, Poland; 19–23 September, 2022

Front Matter


List of Participants


Gravitational Wave Astronomy — Avant le Déluge

abstract

The era of gravitational-wave (GW) astronomy is now well under way, with nearly 100 compact binary coalescences (CBCs) confidently detected in the first three observing runs of LIGO and Virgo. With the fourth observing run of LIGO, Virgo, and KAGRA starting in early 2023, it is timely to review what has been learned so far, both from the CBC events and from the absence of other types of GW detections, particularly continuous radiation. Prospects for making such new discoveries soon will be discussed, along with the potential insights to be gained from the deluge of CBC events expected in the coming years and decades.


Strong Lensing of Gravitational Waves — New Opportunities for Multimessenger Astronomy

abstract

We have entered the era of gravitational wave astronomy with routine detections of GW signals by the LIGO–Virgo–KAGRA interferometric detectors. Future perspectives are bright with the new generations of GW detectors: ground-based — Einstein Telescope and Cosmic Explorer or space-borne — LISA, DECIGO, BBO. Gravitational waves travelling along null geodesics can undergo strong gravitational lensing like electromagnetic waves do. Hence, strong lensing of gravitational waves is becoming a popular research topic. In this contribution, I concisely review the state-of-the-art in this subject and present new opportunities opening for the multimessenger astronomy from detections of lensed GW signals.


Beyond Geometric Optics Limit of Gravitational Wave Lensing in Palatini \(f(\hat {R})\) Gravity

abstract

The planned next generation of detectors such as Einstein Telescope, Cosmic Explorer, and space-based detectors such as LISA are likely detect gravitational waves signals more frequently than the current generation LIGO detectors. With such an increased frequency of detection, we expect some of the signals to be gravitationally lensed. An opportunity that lensing opens up is to test different theories of gravity. In this work, we study gravitational lensing in the context of Palatini \(f(\hat {R})\) gravity using the WKB approximation in the geometric optics limit and beyond.


Average Zero-expansion Regions of the Universe

abstract

Persistent tensions in the \(\Lambda \)CDM cosmological model underline the importance of tests of its basic assumptions. One such potential test arises from the fact that the surface of zero expansion around the collapsing object with spherical symmetry is strictly related to the object’s mass and the value of the cosmological constant. We propose a complementary probe relating the averaged zero-expansion volume to the mass and the background cosmological Hubble parameter. Using the relativistic Zel’dovich approximation, we are able to relax the spherical symmetry assumption and hence obtain a more general test of cosmological dynamics. Alternatively, our method can serve as a test of compatibility of relativistic \(N\)-body simulations and the scalar, averaged Einstein’s equations with the relativistic Zel’dovich approximation serving as a closure condition.


The General Relativistic Two-body Problem at 5PN

abstract

The general relativistic conservative compact binary dynamics is given through the fifth post-Newtonian (5PN) order. Through the 4PN order, the well-established methods and results get summarized. At the 5PN order, a recently completed computation is presented including comparisons with the literature. Three rational numbers are still under discussion. Terms not yet calculated at the 6PN order get pointed out.


Neutrino Cooled Disk in Post-merger System Studied via Numerical GR MHD Simulation with a Composition-dependent Equation of State

abstract

The code HARM-COOL, a conservative scheme for relativistic magnetohydrodynamics, is being developed in our group and works with a tabulated equation of state of dense matter. This EOS can be chosen and used during dynamical simulation, instead of the simple ideal gas one. In this case, the inversion scheme between the conserved and primitive variables is not a trivial task. In principle, the code needs to solve numerically five coupled non-linear equations at every time-step. The 5D recovery schemes were originally implemented in HARM and worked accurately for a simple polytropic EOS which has an analytic form. Our current simulations support the composition-dependent EOS, formulated in terms of rest-mass density, temperature, and electron fraction. In this contribution, I discuss and compare several recovery schemes that have been included in our code. I also present and discuss their convergence tests. Finally, I show a set of preliminary results of a numerical simulation, addressed to the post-merger system formed after the binary neutron stars (BNS) coalescence.


Stiffness, Complexity, Cracking and Stability of Relativistic Compacts Stars

abstract

The compactness of a relativistic compact star provides an essential clue to the matter composition of the star. In this paper, we explore many versions of the Tolman VII solution to analyse the maximum compactness of a relativistic star in the context of a given equation of state (EOS). For an EOS specified by the model parameters in the Tolman VII solution, we evaluate the critical bound on compactness above which the stellar composition becomes unstable against radial oscillations. We also outline the possible link between stellar stability, ‘complexity’, and ‘cracking’ of an anisotropic stellar configuration.


Maximum Mass and Stability of Differentially Rotating Neutrons Stars

abstract

We present our study on stability of differentially rotating, axisymmetric neutron stars described by a polytropic equation of state with \({\mit \Gamma } = 2\). We focus on quasi-toroidal solutions with a degree of differential rotation \(\widetilde A=1\). Our results show that for a wide range of parameters, hypermassive, quasi-toroidal neutron stars are dynamically stable against quasi-radial perturbations, which may have implications for newly born neutron stars and binary neutron stars mergers.


Complex and Real Para-Kähler Einstein Spaces

abstract

Complex and real neutral, 4-dimensional, para-Kähler Einstein spaces are considered. Metrics of all para-Kähler Einstein spaces which are algebraically degenerate are found.


Timelike and Null Geodesics in the Schwarzschild Space-time: Analytical Solutions

abstract

The theory of Schwarzschild geodesics is revisited. Using a theorem due to Weierstrass and Biermann, we derive concise formulas describing all timelike and null trajectories in terms of Weierstrass elliptic functions. The formulation given in this note uses an analogue of the so-called Mino time.


Resonant Enlargements of the Poincaré/AdS (Super)Algebras from Pattern-based Analysis

abstract

Applying an efficient pattern-based computational method of generating the so-called ‘resonating’ algebraic structures results in a broad class of the new Lie (super)algebras. Those structures inherit the AdS base (anti) commutation pattern and can be treated as the enlargements of the Poincaré or Anti-de-Sitter (super)algebras. Obtained superalgebras are rooted in the Semigroup expansion method and Maxwell and Soroka–Soroka algebras, spanned by the Lorentz generator \(J_{ab}\), translations \(P_{a}\), and additional Lorentz-like generator \(Z_{ab}\). Considered configurations include cases up to two fermionic supercharges \(Q_{\alpha }\) and offer interesting modifications to the gauge (super)gravity theories.


Critical Relaxation in AdS/CFT

abstract

It is not only known that hairy black holes can exist in asymptotically Anti-de Sitter (AdS) spaces, but also that in the context of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, such black holes can be interpreted as holographic duals of superfluids. After a perturbation, these black holes usually exhibit an exponentially damped ringing down described by quasi-normal modes, however, we will show that for perturbations around the exact critical point that characterizes the onset of the formation of scalar hair, this relaxation will exhibit a power law behaviour at late times. We will also explain how this can be interpreted through the lens of the AdS/CFT correspondence.


Equatorial Accretion on the Kerr Black Hole

abstract

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. At infinity, the gas obeys the Maxwell–Jüttner distribution, restricted to the equatorial plane. In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The accretion slows down the rotation of the black hole. We present preliminary results for the Vlasov gas accretion onto the Kerr black hole moving with a velocity parallel to the equatorial plane.


Spherical and Non-spherical Collapse of a Finite Two-layer Body — Initial Conditions

abstract

It is well-known that a collapsing single-layer sphere with spatially constant mass density leads to the Schwarzschild black hole, but the outcome is less clear when one considers the simplest multi-layer generalization of this: That of a homogeneous core surrounded by a homogeneous envelope of lower mass density, where both are joined at their common interface using the Darmois matching conditions. In this exploration, we set up the appropriate static initial conditions for the subsequent collapse of this two-layer sphere, and find that it is necessary to approximate the relative mass densities. We then go on to discuss how our setup could also be applied in the corresponding non-spherical case, where the ultimate goal is to determine at an analytical level how multiple layers may lead to the formation of something different to the Kerr black hole during a rotating collapse.


EFT Approach to Black Hole Scalarization and Its Compatibility with Cosmic Evolution

abstract

We address the issue of black hole scalarization and its compatibility with cosmic inflation and Big Bang cosmology from an effective field theory (EFT) point of view. In practice, using a well-defined and healthy toy model which (in part) has been broadly considered in the literature, we consider how higher-order theories of gravity, up to cubic operators in Riemann curvature, fit within this context. Interestingly enough, we find that already at this minimal level, there is a non-trivial interplay between the Wilson coefficients which are otherwise completely independent, constraining the parameter space where scalarization may actually occur. Conclusively, we claim that the EFT does exhibit black hole scalarization, remaining compatible with the inflationary paradigm, and admitting General Relativity as a cosmological attractor.


Examining Quasinormal Mode Instability with the Pseudospectrum

abstract

The gravitational waves emitted by compact objects such as neutron stars or black holes are characterized by quasinormal modes (QNMs). The QNM frequencies encode information about the relic object, and — in the most energetic cases — are sensitive to higher-curvature corrections to General Relativity. Their stability depends on how the frequencies change in response to perturbations, and the pseudospectrum allows us to quantify these changes. In this work, we review how the pseudospectrum is used to examine the stability of the gravitational modes of Schwarzschild black holes. We then discuss ongoing work into applying these methods to the quasinormal modes of a Yang–Mills soliton.


Analysis of Topologically Non-trivial Solutions of Maxwell Equations in de Sitter Spacetime

abstract

Construction of a generalization of electromagnetic Hopfions for de Sitter spacetime is briefly presented. We analyze non-trivial properties of field lines of the solution.


Scalar Curvature Operator for Loop Quantum Gravity on a Cubical Graph

abstract

We introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. The operator is constructed by writing the Ricci scalar classically as a function of the Ashtekar variables and regularizing the resulting expression on a cubical spin network graph. While our construction does not apply to the entire Hilbert space of loop quantum gravity, the proposed operator can be applied to concrete calculations in various approaches which are derived from the framework of full loop quantum gravity using states defined on cubical graphs.


3D Gravity, Point Particles, and Deformed Symmetries

abstract

It is well known that gravity in 2+1 dimensions can be recast as the Chern–Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into spacetime as (spinning) conical defects. Then, in principle, one may integrate out the gravitational degrees of freedom to obtain the effective particle action; the most interesting consequence is that the momentum space of a particle turns out to be curved. This is still not completely understood in the case of a non-zero cosmological constant.


Mixmaster Universe: Semiclassical Dynamics and Inflation from Bouncing

abstract

In this work, we explore the quantum Bianchi type IX model, its semi-classical features, and its relevance in early cosmology to tentatively explain inflation and production of primordial structures. We specially focus on the analytical and numerical exploration of the dynamical system derived from the phase-space portraits. Afterwards we investigate the reliability of our results with regard to inflation and post inflation scenarios commonly accepted nowadays.


Quantum Chaos of the Belinski–Khalatnikov–Lifshitz Scenario

abstract

We quantize the solution to the massive model of the Belinski–Khalatnikov–Lifshitz (BKL) scenario using the integral quantization method. Classical deterministic chaotic behavior of the BKL scenario turns under quantization into stochastic chaos.


Integral Quantization and Quantum Time

abstract

Integral quantization and time treated on the same footing as other quantum observables are considered. They allow to construct quantum gravity models in a more natural way because an idea of time as a quantum observable is consistent with General Relativity, contrary to time treated as a parameter. The projection evolution formalism is shortly presented. A semiquantal approximation is defined.


Ascribing Quantum System to Schwarzschild Spacetime with Naked Singularity — ACS Quantization Method

abstract

The quantization of the Schwarzschild black hole by using the affine coherent state (ACS) quantization method is presented. I introduce quantization of both temporal and spatial coordinates. I propose the method of quantum analysis of the gravitational singularity. In the presented model, the quantum effects smear the gravitational singularity indicated by the Kretschmann invariant avoiding its localization in the configuration space.


Quantum Dynamics of Relativistic Systems

abstract

We discuss the time problem in quantum gravity. We illustrate the problem with a model of gravitational waves in a quantum Friedmann universe. We propose a possible prescription for dealing with the unitarily inequivalent quantum dynamical descriptions based on different internal clocks. Our prescription permits unambiguous clock-independent physical predictions.


Complex Scalar Field in \(\kappa \)-Minkowski Spacetime

abstract

It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation from the classical behaviour, one of which is the noncommutativity of spacetime coordinates. In this context, the non-commutativity scale is seen as an observer-independent length scale. Of course, such a scale imposes a modification of ordinary relativistic symmetries, which now need to be deformed to accommodate this fundamental scale. The \(\kappa \)-Poincaré algebra is an example of this deformation. In what follows, I will briefly describe a construction of a \(\kappa \)-deformed complex scalar field theory, while at the same time shedding light on the behaviour of discrete and continuous symmetries in this formalism. This in turn will open the way to the study of the application of this formalism to actual physical processes. I will then conclude with some comments and prospects for the future.


The Gauge Issue and the Hamiltonian Theory of Cosmological Perturbations

abstract

We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological perturbations. This approach includes a discussion of the gauge-invariant dynamics of perturbations as well as an analysis of gauge transformations, gauge-fixing, partial gauge-fixing, and spacetime reconstruction. We will introduce the Kuchař parametrization of the kinematical phase space as a convenient tool for studying the gauge transformations. The key element of this approach is the reconstruction of spacetime based on gauge-fixing conditions.


Structure Forming Plane Symmetric Dust Inhomogeneous Cosmological Model

abstract

We present a special case of the plane symmetric model from the G3/S2-symmetric space-times solving the Einstein equations for a dust source which exhibits a controlled form of the growth of finite matter density inhomogeneities.


Challenging \(\Lambda \)CDM with Scalar-tensor \(f(R,T)\) Gravity and Thermodynamics of Irreversible Matter Creation

abstract

We investigate gravitationally-induced particle production in the equivalent scalar-tensor representation of \(f(R,T)\) gravity. In this theory, the matter energy-momentum tensor may not be conserved due to a non-minimal curvature–matter coupling. As such, we explore the consequences of such a non-conservation within the scope of particle production by using the formalism of irreversible thermodynamics of open systems. Accordingly, we obtain the expressions for the particle creation rate and for the creation pressure. Finally, we explore the de Sitter solution with a constant and non-constant matter energy density and determine the explicit expressions for the two scalar fields and both creation rate and pressure.


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