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Marek Nowakowski

Publications and source records attributed to Marek Nowakowski.

At least 19 recordsLinked to original sources
arXiv2026

Roadmap Towards Quantum Entanglement Positron Emission Tomography (QE-PET)

Annihilation photons are quantum entangled in their polarization, a property that is not accessible in state-of-the-art clinical Positron Emission Tomography (PET). This roadmap describes the current status of research in the emerging field of quantum entanglement applications involving these photons for medical diagnosis. It outlines the underlying physics phenomena and the development of detector systems that can serve as a foundation for future Quantum Entanglement PET (QE-PET) scanners. These scanners will be capable of utilizing the entanglement between annihilation photons by measuring their Compton scattering on electrons. This roadmap comprises up-to-date experimental results on the study of quantum entanglement and the decoherence of annihilation photons, alongside the current theoretical understanding of these phenomena. The methods and detector technologies described herein are being developed (i) in order to enhance standard PET imaging by suppressing random coincidences in the reconstruction of annihilation site density distributions, (ii) in order to establish the degree of quantum entanglement as a diagnostic biomarker for tissue pathology and oxygenation, and (iii) in order to elaborate a method for pH imaging. Whether entanglement-based imaging and pH mapping can be successfully translated into clinical practice remains an open question and a subject of exciting ongoing research. This roadmap serves as an invitation to the scientific community to join this burgeoning field.

physics.med-ph↗
arXiv2024

The Universe according to DESI results

The recent fit of cosmological parameters by the Dark Energy Spectroscopic Instrument (DESI) collaboration will have a significant impact on our understanding of the universe. Given its importance, we conduct several consistency checks and draw conclusions from the fit. Specifically, we focus on the following key issues relevant to cosmology: (i) the acceleration of the universe's expansion, which, according to the fit, differs over cosmological time compared to the standard cosmological model; (ii) the age of the universe, which appears slightly shorter than the age of the oldest stars; and (iii) the solution of the scale factor, both numerically and in an approximate analytical form.

gr-qc↗
arXiv2024

Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario

We set up the Wheeler-DeWitt (WDW) equation for late gravitational collapse. The fact that the gravitational collapse and the expanding/ collapsing universe can be described within the realm of the Robertson-Walker metric renders the corresponding WDW equation for collapsing matter a timeless Schr\"odinger equation. We explore the consequences of such an equation and find the density to be quantized in terms of the Planck density. Apart from that, the wave function as a solution of the WDW equation shows that the initial singularity is avoided. We concentrate on different factor orderings in the kinetic term of the equation and show how after splitting off an exponential ansatz, new polynomials entering the solution can be constructed. This enables us to conclude that the factor ordering changes the details of the solution and interpretation, but overall on a qualitative level the results remain the same. We also probe into the effects of a positive cosmological constant. It offers the possibility of a tunneling scenario at the cosmological horizon.

gr-qc↗
arXiv2024

Gravitational Collapse via Wheeler-DeWitt Equation

We analyze the Wheeler-DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Roberston-Walker metric in which the WDW equation takes the form of a times-less Schrödinger equation. We set up the corresponding WDW potential for the collapse and study the solutions of the wave function. The results show that the central singularity appearing in classical general relativity is avoided, the density is quantized in terms of the Planck density and the expectation value of the scale factor exhibits a discrete behavior.

gr-qc↗
arXiv2023

New vistas on the Laplace-Runge-Lenz vector

Scalar, vector and tensor conserved quantities are essential tools in solving different problems in physics and complex, nonlinear differential equations in mathematics. In many guises they enter our understanding of nature: charge, lepton, baryon numbers conservation accompanied with constant energy, linear or angular total momenta and the conservation of energy-momentum/angular momentum tensors in field theories due to Noether theorem which is based on the translational and Lorentz symmetry of the Lagrangians. One of the oldest discovered conserved quantities is the Laplace-Runge-Lenz vector for the $1/r$-potential. Its different aspects have been discussed many times in the literature. But explicit generalisations to other spherically symmetric potentials are still rare. Here, we attempt to fill this gap by constructing explicit examples of a conserved vector perpendicular to the angular momentum for a class of phenomenologically relevant potentials. Hereby, we maintain the nomenclature and keep calling these constant vectors Laplace-Runge-Lenz vectors.

math-ph↗
arXiv2023

The mathematical foundations of the asymptotic iteration method

We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the approximants. With the help of this alternative termination condition and certain properties of continuous fractions, we derive a closed formula for the asymptotic function $α$ of the AIM technique in terms of an infinite series. Furthermore, we show that such a series converges pointwise to $α$ which, in turn, can be interpreted as a specific term of the minimal solution of a certain recurrence relation. We also investigate some conditions ensuring the existence of a minimal solution and hence, of the function $α$ itself.

math.CA↗
arXiv2023

In-Stabilities of massive white dwarfs in modified gravity

Super-Chandrasekhar white dwarfs are a timely topic in the last years in the scientific community due to its connection to supernovae type Ia (SN Ia). Some early studies tackled the possibility of white dwarfs surpassing the Chandrasekhar limit by means of a magnetic field. More recently, modified gravity has been highlighted as the reason for these stars to surpass the Chandrasekhar limit and becoming a supernova progenitor. However, in general simple assumptions are considered for the stellar structure and equation of state (EoS), which can lead to unreliable conclusions. In this work, we want to be rigorous and consider a realistic EoS to describe the white dwarfs in general relativity and modified gravity, taking into account nuclear instabilities that limit the maximum mass.

gr-qc↗
arXiv2022

Possible Connection between Dark Matter and Supermassive Black Holes

Dark Matter (DM) is usually studied in connection with rotational curves in the outskirts of the galaxies. However, the role of DM might be different in the galactic bulges and centers where Supermassive Black Holes (SMBHs) dominate the gravitational interaction. Indeed, given the fact that DM is the dominant matter species in the Universe, it is natural to assume a close connection between DM and SMBHs. Here we probe into this possibility by constructing stable objects with fuzzy mass distributions based on standard DM profiles. These astrophysical objects come out in three types: a fuzzy droplet without horizon and fuzzy Black Holes (BHs) with one or two horizons. We emphasize that all objects are solutions of Einstein equations. Their effective potentials which govern the motion of a test body, can display a reasonable similarity to the effective potential of a Schwarzschild BH at the galactic center. Therefore, some of our solutions could, in principle, replace the standard BH-picture of the galactic center and, at the same time, have the advantage that they have been composed of the main matter ingredient of the Universe.

gr-qc↗
arXiv2022

On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric

In view of a result recently published in the context of deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated to the angular equation arising after the separation of the Dirac equation in the Kerr metric and we show how efficiently a quasi-linear first order PDE for the angular eigenvalues can be derived. We also prove that it is not possible to obtain an ordinary differential equation for the eigenvalues where the role of the independent variable is played by the particle energy or the black hole mass. Finally, we construct new perturbative expansions for the eigenvalues in the Kerr case and obtain an asymptotic formula for the eigenvalues in the case of a Kerr naked singularity.

gr-qc↗
arXiv2022

Rings of light caused by gravitational waves

We reconsider the case of the geodesic motion of a massive and massless beam of test particles in a gravitational wave. In particular, we use a direct Lagrangian approach which simplifies the calculation. Our findings differ partly from previously performed calculations The final result can be interpreted as rings of light seen by the observer. We give a new interpretation to this picture and show that over large distances the effect, albeit rare, could in principle be observable.

gr-qc↗
arXiv2021

Non-singular non-flat universes

The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein-Cartan cosmology, the Milne-McCrea universe with quantum corrections and a non-flat universe with bulk viscosity. Within these models, we probe into the initial singularity by using different techniques. Several nonsingular universes emerge, one of the possibilities being a static non-expanding and stable Einstein universe.

gr-qc↗
arXiv2021

Relevant scales for the $C$-metric with positive cosmological constant

In this work, we study the weak and strong gravitational lensing in the presence of an accelerating black hole in a universe with positive cosmological constant $Λ$. First of all, we derive new perturbative formulae for the event and cosmological horizons in terms of the Schwarzschild, cosmological and acceleration scales. In agreement with previous results in the literature, we find that null circular orbits for certain families of orbital cones originating from a saddle point of the effective potential are allowed and they do not exhibit any dependence on the cosmological constant. They turn out to be Jacobi unstable. We also show that it is impossible to distinguish a $C$-black hole from a $C$-black hole with $Λ$ if we limit us to probe only into effects associated to the Sachs optical scalars. This motivates us to analyze the weak and strong gravitational lensing when both the observer and the light ray belong to the aforementioned family of invariant cones. In particular, we derive analytical formulae for the deflection angle in the weak and strong gravitational lensing regimes.

gr-qc↗
arXiv2021

Fuzzy dark matter black holes and droplets

We consider the possibility of having Dark Matter (DM) black holes motivated by the Einasto density profile. This generalizes both the noncommutative mini black hole model and allows DM to enter as the matter constituent which makes up the black hole. We show that it is possible to construct a black hole solution for each value of the Einasto index and for different values of the mass parameter, provided that the we work with the energy-momentum tensor of an anisotropic fluid. In particular, we achieve that by first considering the equation of state (EOS) $p_r=-ρ$. It turns out that the corresponding black hole solution exhibits a horizon structure similar to that of a Reissner-Nordström black hole and the central singularity is replaced by a regular de Sitter core. We also show that if the previous EOS is replaced by a nonlocal one, it is possible to construct a self-gravitating fuzzy DM droplet but also in this case, the radial pressure is negative. Finally, we contemplate scenarios of different dark matter black holes with moderate mass values which could have formed in galaxies. In particular, we probe the possibility whether such black holes could also be the central galactic objects.

gr-qc↗
arXiv2020

Classical dynamics from a unitary representation of the Galilei group

We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of classical mechanics, particularly the absence of an uncertainty principle between the position and momentum of a particle. It is shown that the theory exposed in the article contains the Koopman-von Neumann formalism of classical mechanics as a particular case.

math-ph↗
arXiv2019

Viscous Cosmologies

We probe into universes filled with Quark Gluon Plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the Quark Gluon Plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor $R(t)$ which goes to zero only asymptotically. We further extend the model of bulk viscosity to include a Cosmological Constant. We contrast the previous results with the cosmology of universes with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann-Lamaître-Robertson-Walker metric. To this end we use a version of the energy-momentum tensor from the Müller-Isreal-Stewart theory which leads to causal Navier-Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges non-singular.

gr-qc↗
arXiv2019

Perturbing microscopic black holes inspired by noncommutativity

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel-Kramers-Brillouin (WKB) approximation we show that the widely used WKB method does not converge in the critical cases where instabilities show up at the third order. By employing the inverted potential method, we demonstrate that the instabilities are an artifact of the WKB method. Finally, we discuss the usefulness of the asymptotic iteration method to find the QNMs.

gr-qc↗