Proceedings Series

Vol. 13 (2020), No. 2, pp. 159 – 338

The 6\(^\mathrm {th}\) Conference of the Polish Society on Relativity



Space-based Gravitational Wave Observations in the Mid-band Frequency Region

Acta Phys. Pol. B Proc. Suppl. 13, 167 (2020)

page 167 •


The intermediate Gravitation Wave (GW) frequency detection band, i.e. the frequency region that is in between those accessible by space-based interferometers with million-kilometer armlengths and ground-based detectors, could be unveiled relatively soon. A space-based GW interferometer of arm-length equal to about 100,000 km would achieve an optimal sensitivity within an observational frequency band that is “blue-shifted” with respect to those of the LISA and TaiJi missions by about a factor 30. By opening the mid-band GW frequency region, such a mission would complement the scientific capabilities of both ground- and million-kilometer arm-length detectors and provide an enhanced scientific return over those obtainable by each detector operated as stand-alone.

A Few Numbers from the Turnaround Epoch of Collapse

Acta Phys. Pol. B Proc. Suppl. 13, 177 (2020)

page 177 •


The turnaround epoch of gravitational collapse is examined by means of the relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid’s evolution reveal some scale-independent universality of parameters for a wide variety of initial conditions. In particular, the density contrast of the collapsing domain at the turnaround is shown to be significantly smaller than the value provided by the Eulerian perturbative (homogeneous and spherical) model. Combined curvature and kinematical backreaction are shown to be of the order of the energy density. Possible improvements of our treatment are put into perspective.

full authors' list

B. Cuadros-Melgar, E. Abdalla, R.D.B. Fontana, J. de Oliveira, E. Papantonopoulos, A.B. Pavan

Instability of a Reissner–Nordström–AdS Black Hole from a Derivative Coupling Perturbation

Acta Phys. Pol. B Proc. Suppl. 13, 181 (2020)

page 181 •


We consider massive scalar perturbations coupled to the Einstein tensor, the so-called derivative coupling term, in the background of a Reissner–Nordström–AdS black hole. By studying the scalar potential, we identify the possible existence of instabilities due to the appearance of a negative well. This suspicion is confirmed through the calculation of the corresponding quasinormal modes. We show that there is a critical value of the derivative coupling that triggers this instability and that this critical value also depends on the black hole charge.

Asymptotically Conserved Quantities of the Gravitational Charges Associated with (3+1) Decomposition of CYK Tensors

Acta Phys. Pol. B Proc. Suppl. 13, 187 (2020)

page 187 •


The conformal Yano–Killing (CYK) tensor enables one to construct a conserved quantity (charge) as a two-dimensional surface integral in four-dimensional spacetime. The aim of the paper is to present a (3+1) decomposition of CYK tensor and discuss the splitting of CYK charge on Cauchy surface.

On Some Solutions of the Type [D] Self-dual Spaces

Acta Phys. Pol. B Proc. Suppl. 13, 193 (2020)

page 193 •


Complex, 4-dimensional, self-dual spaces which are two-sided conformally recurrent are considered. The explicit metrics of the spaces of the type [D] \(\otimes \ [-]\) are presented.

Fermion Condensation Under Rotation on Anti-de Sitter Space

Acta Phys. Pol. B Proc. Suppl. 13, 199 (2020)

page 199 •


Due to the local curvature, the fermion condensate (FC) for a free Dirac field on anti-de Sitter (adS) space becomes finite, even in the massless limit. Employing the point splitting method using an exact expression for the Feynman two-point function, an expression for the local FC is derived. Integrating this expression, we report the total FC in the adS volume and on its boundary.

Fierz Theory Versus Linear Gravity

Acta Phys. Pol. B Proc. Suppl. 13, 203 (2020)

page 203 •


One of the most popular points of view on linearized gravity is massless spin-2 particle theory. This theory is often used as a starting point to formulate a quantum version of gravity theory. The spin-2 field has the well-defined local density of energy equal to \(\frac 12(E^2+B^2)\) in analogy to Maxwell electrodynamics. However, energy in linearized gravity is non-local. The relations and differences between linearized gravity and the spin-2 field theory will be discussed in this paper.

Top-down Approach to the Curved Spacetime Effective Field Theory (cEFT) — Theory and Examples

Acta Phys. Pol. B Proc. Suppl. 13, 209 (2020)

page 209 •


The effective field theory (EFT) turns out to be an instrument of an immense value in all aspects of modern particle physics being theory, phenomenology or experiment. In the paper, I will show how to extend the systematic top-down approach to construction of the EFT proposed by Hitoshi Murayama (LBL, Berkeley) and separately by John Ellis (King’s College London) groups to the curved spacetime. To this end, I will take advantage of the heat kernel method so far extensively used in obtaining the one-loop effective action in curved spacetime. After an introduction of the formalism, I will discuss its application to the problem of an influence of gravity on the stability of the Higgs effective potential.

On the Relation Between the Canonical Hamilton–Jacobi Equation and the De Donder–Weyl Hamilton–Jacobi Formulation in General Relativity

Acta Phys. Pol. B Proc. Suppl. 13, 213 (2020)

page 213 •


A relation between the canonical Hamilton–Jacobi (HJ) theory and the De Donder–Weyl Hamilton–Jacobi (DWHJ) theory in the calculus of variations is studied. In the case of a scalar field in curved space-time and in general relativity in Gaussian coordinates, we show how the functional derivative canonical HJ equation is derived from the partial derivative DWHJ equation. The derivation is based on the split between space and time and the Ansatz which relates the HJ functional eikonal on the infinite dimensional space of initial data with the DWHJ eikonal functions on the finite dimensional space of field variables and space-time coordinates.

Quantum Gravity on a Torus

Acta Phys. Pol. B Proc. Suppl. 13, 223 (2020)

page 223 •


We analyze four-dimensional quantum gravity model defined by Causal Dynamical Triangulations (CDT). One of the key features of CDT is that the geometry of quantum space-time can be globally foliated into spatial slices with fixed three-dimensional topology. We show that CDT with toroidal spatial topology (\(T^3\)) has rich phase structure, including the semiclassical phase \(C\) consistent with Einstein’s general relativity. Some of the phase transitions are also found to be second (or higher) order which makes a possibility of taking continuum limit viable. These findings are consistent with earlier results obtained in CDT with spherical spatial topology (\(S^3\)).

Massline and Other Recent Results of CDT Quantum Gravity

Acta Phys. Pol. B Proc. Suppl. 13, 227 (2020)

page 227 •


With the basis of CDT quantum gravity, we implemented a dynamical particle in the form of a massline, which is minimally coupled to the geometry via the action \(S_m=m \, L\), where \(m\) is the bare mass and \(L\) is the length of the line. During our simulations, we measured the radial distribution of the volume and curvature around the line, which resulted in nontrivial findings. Furthermore, we measured the length of the line in the function of the mass and found agreement with the expected theoretical value.

Version corrected according to Erratum Acta Phys. Pol. B Proc. Suppl. 13, 575 (2020)

A Note on Brane Inflation

Acta Phys. Pol. B Proc. Suppl. 13, 231 (2020)

page 231 •


This short note emphasises a potential tension between string models of inflation based on systems of branes and antibranes and the spectrum of strings in curved space, in particular the requirement that the leading Regge trajectory extends to the Planck scale allowing for the conventional string theory UV completion of gravity.

The Origin of Merging Black Holes

Acta Phys. Pol. B Proc. Suppl. 13, 237 (2020)

page 237 •


LIGO’s discovery of gravitational waves from massive merging black hole binaries posed the fundamental question — what is the origin of these black holes? Two models have been proposed: field stellar binaries and capture. In the former, the binary was born as two massive stars. In this case, some level of alignment of the black holes spins with the orbital angular momentum is expected. In the latter, the two black holes evolve individually and were dynamically captured. The black holes’ spins and the orbital angular momentum are not correlated and hence they are expected to be isotropically distributed. The effective spin, \(\chi _{\mathrm {eff}}\), is probably the best parameter that can distinguish between the models. Recently, independent analysis of the LVC O1–O2 sample revealed, in addition to the original ten identified by LVC, eight new mergers. We present here a concise model for the spin evolution of field binaries and use it to estimate the expected \(\chi _{\mathrm {eff}}\) distribution. We compare this distribution as well as several isotropic distributions, reflecting capture scenarios, to the observations. While the current data slightly prefers field binaries, isotropic distributions or a combination of both origins are possible. Future detection in O3 and O4 of a few dozens to few hundred mergers will enable us to distinguish with sufficient statistical significance between the different models.

Stability of Polytropic Stars in Palatini Gravity

Acta Phys. Pol. B Proc. Suppl. 13, 249 (2020)

page 249 •


We will briefly discuss the necessary conditions for stability of polytropies in \(f(\hat R)\) Palatini gravity and the differences with the GR ones.

Solar System Constraints on Analytic Palatini \(f(R)\) Gravity

Acta Phys. Pol. B Proc. Suppl. 13, 255 (2020)

page 255 •


The post-Newtonian equations-of-motion corrections to finite volume massive bodies and light rays for an arbitrary analytical Palatini \(f(R)\) theory are derived. It is shown that, apart from a mass-energy redefinition that is explicitly found here, which cannot be constrained by solar system tests, the predictions are the same as in general relativity.

Effects of Self-gravity of the Accretion Disk Around Rapidly Rotating Black Hole in Long Gamma Ray Bursts

Acta Phys. Pol. B Proc. Suppl. 13, 261 (2020)

page 261 •


We prescribe a method to study the effects of self-gravity of accretion disk around a black hole associated with long Gamma Ray Bursts (GRBs) in an evolving background Kerr metric. This is an extension to our previous work where we presented possible constraints for the final masses and spins of these astrophysical black holes. Incorporating the self-force of the accreting cloud around the black hole is a very important aspect due to the transient nature of the event, in which a huge amount of mass is accreted and changes the fundamental black hole parameters i.e. its mass and spin, during the process. Understanding of the GRBs engine is important because they are possible sources of high-energy particles and gravitational waves as most of the energy released from the dynamical evolution is in the form of gravitational radiation. Here, we describe the analytical framework we developed to employ in our numerical model. The numerical studies are planned for the future work.

Discrete Scale Invariance in Holography and an Argument Against the Complexity = Action Proposal

Acta Phys. Pol. B Proc. Suppl. 13, 267 (2020)

page 267 •


The AdS/CFT correspondence often motivates research on questions in gravitational physics whose relevance might not be immediately clear from a purely GR perspective, but which are nevertheless interesting. In these proceedings, we summarise two such results recently obtained by the author. One concerns, broadly speaking, the possible isometry groups of a spacetime sourced by physical matter. The other one provides a possible argument against the recently proposed complexity = action conjecture.

Cosmographic Reconstruction to Discriminate Between Modified Gravity and Dark Energy

Acta Phys. Pol. B Proc. Suppl. 13, 271 (2020)

page 271 •


Cosmography represents a model-independent approach potentially useful to discriminate among concurring cosmological scenarios. After reviewing the main features and shortcomings of standard cosmography, we highlight how to overcome the convergence issue jeopardizing current low redshift-cosmographic distances. To do so, we give particular attention to the use of cosmographic rational approximations, among them the Padé and Chebyshev polynomials. We thus focus on dark energy models and concurring extended and modified gravity models, in view of present cosmographic findings. We stress that current (and above all) future cosmographic constraints will be able to disentangle dark energy from alternative gravity, showing which model can be effectively reliable to describe the today observed accelerating universe.

Quantum Big Bounce Scenario and Primordial Gravitational Waves

Acta Phys. Pol. B Proc. Suppl. 13, 279 (2020)

page 279 •


The evolution of the quantum Friedmann–Lemaitre–Robertson–Walker model filled with radiation is studied. From the coherent states quantisation procedure, the non-singular behaviour of the very early universe is obtained. The model is expanded to the first order in tensor perturbations. Quantum perturbations evolving on a quantum spacetime produce primordial gravitational waves via parametric amplification mechanism. The spectrum of the primordial gravitational waves is presented.

Signatures of Extended Theories of Gravity in Black Hole Oscillations

Acta Phys. Pol. B Proc. Suppl. 13, 283 (2020)

page 283 •


In general relativity, the Kerr metric uniquely represents the geometry surrounding an isolated, rotating black hole. An identification of significant non-Kerr features in some astrophysical source would then provide a ‘smoking-gun’ for the break-down of general relativity in the strong-field regime. On the other hand, Kerr black holes are common to many other theories of gravity, and thus a validation of the Kerr metric does not necessarily favour general relativity amongst all possibilities. The nature of gravitational perturbations will however differ between different theories of gravity. Future precision tests involving gravitational waves from oscillating black holes, such as identifications of the quasi-normal mode spectrum from ring-down, will thus be able to probe the underlying theory, even if the object is Kerr. Here, we write down the equations governing metric perturbations of a Kerr black hole in \(f(R)\) gravity in a form that is more conducive to numerical study.

On Universal Black Holes

Acta Phys. Pol. B Proc. Suppl. 13, 291 (2020)

page 291 •


Recent results on universal black holes in \(d\) dimensions are summarized. These are static metrics with an isotropy-irreducible homogeneous base space which can be consistently employed to construct solutions to virtually any metric theory of gravity in vacuum.

Covariant Formulation of Light Propagation in Cosmological Models

Acta Phys. Pol. B Proc. Suppl. 13, 297 (2020)

page 297 •


We present a covariant approach to the problem of light beam propagation in cosmological models within the framework of classical geometric optics in general relativity. Using the concept of screen surface orthogonal to the observer’s world-line and to the bundle of geodesics, we introduce covariant four-dimensional definitions and derive propagation equations for Sachs and Jacobi optical fields and for the area distance.

Graviton and Massive Symmetric Rank-two Tensor in String Theory

Acta Phys. Pol. B Proc. Suppl. 13, 303 (2020)

page 303 •


Spin-two particles appear in the spectra of both open and closed string theories. We studied a graviton and massive symmetric rank-two tensor in string theory both of which carry spin two. A graviton is a massless spin-two particle in closed string theory, while a symmetric rank-two tensor is a massive particle with spin two in open string theory. Using Polyakov’s string path integral formulation of string scattering amplitudes, we calculated cubic interactions of both spin-two particles explicitly, including \(\alpha ^\prime \)-corrections (string corrections). We observed that the cubic interactions of the massive spin-two particle differed from those of the graviton. The massive symmetric rank-two tensor in open string theory becomes massless in the high-energy limit, where \(\alpha ^\prime \rightarrow \infty \) and \(\alpha ^\prime \)-correction terms, containing higher derivatives, dominate: In this limit, the local cubic action of the symmetric rank-two tensor of open string theory coincides with that of the graviton in closed string theory.

On the Precanonical Structure of the Schrödinger Wave Functional in Curved Space-time

Acta Phys. Pol. B Proc. Suppl. 13, 313 (2020)

page 313 •


The functional Schrödinger equation in curved space-time is derived from the precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional product integral of precanonical wave function restricted to a field configuration. The functional Schrödinger representation of QFT in curved space-time appears as a singular limiting case of a formulation based on precanonical quantization, which leads to a hypercomplex generalization of quantum formalism in field theory.

Quantum Creation of a Universe–Antiuniverse Pair

Acta Phys. Pol. B Proc. Suppl. 13, 325 (2020)

page 325 •


If one analyses the quantum creation of the universe, it turns out that the most natural way in which the universes can be created is in pairs of universes whose time flow is reversely related. It means that the matter that propagates in one of the universes can be seen, from the point of view of the other universe, as antimatter, and vice versa. They thus form a universe–antiuniverse pair. From a global point of view, i.e. from the point of view of the whole multiverse ensemble, the creation of universes in universe–antiuniverse pairs restores the matter–antimatter asymmetry observed in each individual universe and it might provide us with distinguishable imprints of the whole multiverse proposal.

List of Participants



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