arXiv subjects

Tomasz Pawłowski

Publications and source records attributed to Tomasz Pawłowski.

At least 19 recordsLinked to original sources

arXiv2026

Integral Hilbert spaces and the dynamics of loop quantum cosmos

Polymer quantization program applied in Loop Quantum Gravity/Cosmology leads to nonseparable Hilbert spaces. Commonly, one sidesteps this problem by singling out and working with a separable superselection sector. This is however often no longer accessible in more involved models beyond isotropic ones. In an alternative approach one builds a separable Hilbert space as an integral over all available sectors. Here we test the dynamics following from the latter on the example of a flat isotropic Universe admitting negative cosmological constant and a massless scalar field. There, numerical evolution of (initially) semiclassical states shows that there is no relevant difference in their long term semiclassicality properties in comparison to those in a single sector approach. Further, the older (problem-specific) numerical methods are compared against an application of more common and more efficient standard tools (eigen library).

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arXiv2026

Asymmetric Quantum Oppenheimer-Snyder Collapse

We study black hole formation resulting from the collapse of a homogeneous and isotropic dust ball within a framework built upon loop quantum cosmology. Using loop dynamics formulated for Lemaitre-Tolman-Bondi spacetimes---which reduce to the asymmetric loop quantum cosmological bounce scenario---we analyze the dust ball undergoing power-law contraction followed by a de Sitter-like expansion. We discover an emergence of a physical shock at the dust ball surface, characterized by a continuous induced metric and a discontinuous extrinsic curvature arising from a dynamical mismatch between the expanding interior and the contracting exterior vacuum shells. Furthermore, we explicitly derive two variants of Schwarzschild-like line elements for the vacuum sector, and we demonstrate that the resulting spacetime is geodesically complete featuring a rich causal structure. This establishes, for the first time, fully dynamical regular black hole formation within a framework consistent with loop quantum cosmology.

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arXiv2026

Prism Effect in Quantum Gravity

Modifications to the dispersion relation of electromagnetic (EM) waves are a central probe in the search for quantum gravitational effects. In this work, we construct a general framework for the interaction between the EM field and a quantum background geometry, employing an extended Born-Oppenheimer approximation. This leads to a quasi-phenomenological model for EM wave propagation in curved spacetime. Unlike previous semi-classical approaches for mode-dependent dispersion relations, our framework naturally reproduces chromatic dispersion effects analogous to those observed in light-matter interactions in nonlinear optics. As a concrete application, we analyze EM wave propagation on a flat quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) background, combining analytical techniques with numerical simulations to extract observable signatures of the prism-like behavior induced by quantum light-geometry interactions. Crucially, it remains valid across all energy regimes, enabling access to quantum gravitational corrections beyond the semi-classical limit.

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arXiv2026

Revisiting light propagation over (loop) quantum Universe

We investigate the propagation of electromagnetic waves over a quantum cosmological background, aiming to uncover potential signatures of quantum gravity through modifications to the dynamics of the field. Building on symmetry-reduced approaches to spacetime quantization, specifically loop quantum cosmology and geometrodynamics, and extending the Born-Oppenheimer approximation for interacting fields, we construct a quasi-phenomenological framework capable of probing all energy regimes. Unlike previous semi-classical treatments confined to low-energy limits, our analysis employs both analytical and numerical methods to study wave dynamics in a flat quantum Friedmann-Lemaitre-Robertson-Walker Universe. Our results confirm consistency with general relativity at low energies, reveal quantum geometric corrections at higher energies, and demonstrate that loop quantum effects suppress modifications relative to those predicted by geometrodynamics-based quantization.

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arXiv2025

Causal structure of nonhomogeneous dust collapse in effective loop quantum gravity

We study the causal structure for spherically symmetric dust collapse within a model of effective loop quantum gravity in midisuperspace framework. We develop a general strategy (working beyond the dynamical model of our consideration) for constructing double null coordinates, allowing the extraction of conformal diagrams within single coordinate charts. With the methods introduced, we confirm that the homogeneous Oppenheimer-Snyder collapse scenario resembles the Reissner-Nordström-like picture. For the nonhomogenous collapse scenario, we construct the conformal diagrams, subsequently, we study its relevant properties, in particular, dust particles' trajectories, apparent horizons and shell-crossing singularities. We conclude that a significant region of spacetime remains inaccessible to the model's dynamics due to the formation of the shell-crossing singularities. The question of whether a timelike singularity, similar to that in the homogeneous dust ball collapse scenario, arises in the nonhomogeneous case remains unresolved. Furthermore, we find that phenomena such as black hole explosions or gravitational shock waves cannot be witnessed by an external observer who does not cross any horizon. Indeed, the collapse cannot take place within single asymptotic region.

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arXiv2025

Quantum dust collapse with cosmological constant and methods for constructing conformal diagrams

The loop quantum gravitational collapse of the dust ball in presence of positive cosmological constant is investigated within the Oppenheimer-Snyder collapse scenario. The dust ball interior is described within the framework of loop quantum cosmology, while its exterior geometry is determined by the differentiability of the spacetime metric at the dust ball surface and the assumption of the (vacuum) exterior to be stationary. In order to determine the global causal structure of the investigated spacetime a robust (numerical) method of constructing Penrose-Carter diagrams is built. Unfortunately the presence of cosmological constant does not cure the problems already present in the case of it vanishing -- the exterior geometry resembles that of Reissner-Nordström-de Sitter black hole, in particular featuring timelike singularities.

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arXiv2025

Revisiting semiclassical effective dynamics for quantum cosmology

We revise the technique of semiclassical effective dynamics, in particular reexamining the evaluation of Poisson structure of the so-called central moments capturing quantum corrections, providing a systematic, pedagogical, and efficient algorithm for evaluation of said structure. The resulting closed formulae for Poisson brackets involve less summatios than recent results in the literature, thus being more optimal for applications. Found formulae are then applied to a general class of isotropic cosmological models with locally observable configuration variables for the admitted matter fields. In particular, this allowed to formulate a consistent and nontrivial limit or fiducial cell (infrared regulator) removal for models describing spatially noncompact spacetimes.

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arXiv2025

Primodial power spectrum in loop quantum cosmology for different regularizations

In Loop Quantum Cosmology, the quantization of the Hamiltonian constraint involves a regularization procedure which is affected by certain ambiguities. Moreover, different regularizations lead to distinct mathematical formulations and, consequently, to different physical predictions. In this work, we explore the impact of this regularization on the primordial power spectrum of cosmological perturbations. More specifically, we study this power spectrum for the conventional regularization used in Loop Quantum Cosmology and for two alternative prescriptions suggested in the literature. We set initial conditions for the perturbations at the bounce corresponding to a recently proposed vacuum state, optimally adapted to the background dynamics. This choice of vacuum is based on an asymptotic Hamiltonian diagonalization in the ultraviolet sector of the perturbations which provides a non-oscillating power spectrum. Employing a suitable approximation to the propagation equations of the perturbations around the bounce, we are able to obtain an analytic expression for the primordial power spectrum of this vacuum for all the discussed regularizations. We compare the results and prove that the main relevant distinction between the corresponding spectra is the scale where power suppression occurs. The associated wavenumber scale is proportional to the square root of the critical density in Loop Quantum Cosmology, density which is different for each of the studied regularizations.

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arXiv2023

Rainbow Oppenheimer-Snyder collapse and the entanglement entropy production

The dust ball collapse is studied in the context of the "rainbow metric" approach (where the matter content is supplemented with a scalar field perturbation) to the Oppenheimer-Snyder collapse scenario within the framework of loop quantum cosmology. The global spacetime structure is determined for this scenario and subsequently used to evaluate the entanglement entropy via a slight adaptation of existing formulas. The resulting model is shown to qualitatively resemble the Reissner-Nordström black hole spacetime, in particular, it still contains singularities, which allows us to define the entropy only for portions of the null infinity. The consequence of these results for the black hole information loss paradox is discussed. Furthermore, the results in presence of the scalar field are used in discussion regarding the viability of the selected scenario, in particular, the assumption of stationarity used to determine the exterior metric.

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arXiv2022

Regularizations and quantum dynamics in loop quantum cosmology

One of critical components of Loop Quantum Gravity (LQG) and Cosmology (LQC) -- Thiemann regularization procedure is non-unique. Different choices of particular prescriptions lead to models which differ in both mathematical structure and physical predictions. Here we briefly recall a set of such prescriptions proposed in the literature in context of isotropic LQC on the example of a flat universe with massless scalar matter content. For the one least investigated so far, further called Yang-Ding-Ma prescription, a detailed analysis of its mathematical structure and resulting quantum dynamics is performed, confirming and extending the results obtained so far by phenomenological methods. In order to probe the dynamics, a relatively robust method (working in the approximation of the macroscopic universe) of evaluating quantum trajectories is devised. Said method is a variant of a semiclassical treatment that allows to express the trajectories analytically as function of internal clock and a set of certain central moments -- constants of motion encoding quantum corrections up to arbitrary order in systematic manner. As a test of method's robustness analogous evaluation of the quantum trajectory in volume is performed for those of other prescriptions, for which it is applicable. The limitations of the treatment are further briefly discussed.

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arXiv2022

Rainbow Black Hole From Quantum Gravitational Collapse

Quantum evolution of a scalar field's modes propagating on quantum spacetime of a collapsing homogeneous dust ball is written effectively, as an evolution of the same quantum modes on a (semiclassical) dressed geometry. When the backreaction of the field is discarded, the classical spacetime singularity is resolved due to quantum gravity effects and is replaced by a quantum bounce on the dressed collapse background. In the presence of backreaction, the emergent (interior) dressed geometry becomes mode dependent and the energy density associated with the backreaction of each mode scales as a radiation fluid. Semiclassical dynamics of this so-called {\em rainbow} dressed background is analyzed. It turns out that the backreaction effects speed up the occurrence of the bounce in comparison to the case where only a dust fluid is present. By matching the interior and exterior regions at the boundary of dust, a mode-dependent black hole geometry emerges as the exterior spacetime. Properties of such a rainbow black hole are discussed. That mode dependence causes, in particular, a chromatic aberration in the gravitational lensing process of which maximal magnitude is estimated via calculation of the so-called Einstein angle.

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arXiv2019

Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of LQG in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and graph-preserving Hamiltonian is central, result in the formulation of a set of no-go statements, severely limiting the possibility of recovering a physically consistent effective dynamics this way.

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arXiv2018

Emergent de Sitter epoch of the quantum Cosmos

The quantum nature of the Big Bang is reexamined in the framework of Loop Quantum Cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a flat expanding Universe.

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arXiv2018

Local version of the no-hair theorem

Non-extremal isolated horizons embeddable in 4-dimensional spacetimes satisfying the vacuum Einstein equations with cosmological constant are studied. The horizons are assumed to be stationary to the second order. The Weyl tensor at the horizon is assumed to be of the Petrov type D. The corresponding equation on the intrinsic horizon geometry is solved in the axisymmetric case. The family of the solutions is $2$-dimensional, it is parametrized by the area and the angular momentum. The embeddability in the Kerr - de Sitter, the Kerr - anti de Sitter and the Near extremal Horizon spacetimes obtained by the Horowitz limit from the extremal Kerr - de Sitter and extremal Kerr - anti de Sitter is discussed. This uniqueness of the axisymmetric type D isolated horizons is a generalization of the similar earlier result valid in the cosmological constant free case.

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arXiv2018

The Petrov type D isolated null surfaces

Generic black holes in vacuum-de Sitter / Anti-de Sitter spacetimes are studied in quasi-local framework, where the relevant properties are captured in the intrinsic geometry of the null surface (the horizon). Imposing the quasi-local notion of stationarity (null symmetry of the metric up to second order at the horizon only) we perform the complete classification of all the so called special Petrov types of these surfaces defined by the properties (structure of principal null direction) of the Weyl tensor at the surface. The only possible types are: II, D and O. In particular all the geometries of type O are identified. The condition distinguishing type D horizons, taking the form of a second order differential equation on certain complex invariant constructed from the Gaussian curvature and the rotation scalar, is shown to be an integrability condition for the so called near horizon geometry equation. The emergence of the near horizon geometry in this context is equivalent to the hyper-suface orthogonality of both double principal null directions. We further formulate a no-hair theorem for the Petrov type D axisymmetric null surfaces of topologically spherical sections, showing that the space of solutions is uniquely parametrized by the horizon area and angular momentum.

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arXiv2017

Local rotational symmetry Gowdy model in Loop Quantum Gravity

We provide a complete quantization for the Gowdy model with local rotational symmetry in vacuum. We start with a redefinition of the classical constraint algebra such that the Hamiltonian constraint has a vanishing Poisson bracket with itself. We apply a canonical quantization within loop quantum gravity and an improved dynamics scheme. We construct the exact solutions to the constraints and the physical Hilbert space, together with the physical observables. The quantization provides a physical picture without singularities. Besides, a genuine discretization of the spatial geometry emerges by means of a new quantum observable without classical analogue.

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arXiv2017

Loop quantization of the Gowdy model with local rotational symmetry

We provide a full quantization of the vacuum Gowdy model with local rotational symmetry. We consider a redefinition of the constraints where the Hamiltonian Poisson-commutes with itself. We then apply the canonical quantization program of loop quantum gravity within an improved dynamics scheme. We identify the exact solutions of the constraints and the physical observables, and we construct the physical Hilbert space. It is remarkable that quantum spacetimes are free of singularities. New quantum observables naturally arising in the treatment partially codify the discretization of the geometry. The preliminary analysis of the asymptotic future/past of the evolution indicates that the existing Abelianization technique needs further refinement.

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arXiv2016

Universe's memory and spontaneous coherence in loop quantum cosmology

The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology. This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large Universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.

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