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Davide Batic

Publications and source records attributed to Davide Batic.

At least 37 records · Page 2Linked to original sources
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 Schrödinger 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

Quasinormal Modes in Noncommutative Schwarzschild Black Holes: A Spectral Analysis

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous claims in the literature regarding the instability of these black holes but also reveal remarkable stability for both non-extreme and extreme Schwarzschild black holes under various perturbations.

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

The Tomimatsu-Sato metric reloaded

In this work, we derive exact analytic formulae for the inner and outer surfaces representing the boundary of the ergoregion appearing in the Tomimatsu-Sato (TS) metric. Exact expressions for the radii of the ergoregion in prolate spheroidal coordinates and in Boyer-Lindquist coordinates are obtained. We also found that in addition to the ring-shaped naked singularity there is an event horizon placed in the inner region inside the aforementioned curvature singularity. In comparing our results with previous studies, we also uncovered and corrected several errors in the literature. Finally, we provide tables of numerical values for the inner and outer boundaries of the ergoregion for different values of the rotational parameter. We hope this study will be a useful resource for all researchers interested in the Tomimatsu-Sato metric.

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↗
arXiv2018

Einstein-Cartan Cosmologies

Cosmologies based on General Relativity encompassing an anti-symmetric connection (torsion) can display nice desirable features as the absence of the initial singularity and the possibility of inflation in the early stage of the universe. After briefly reviewing the standard approach to the cosmology with torsion, we generalize it to demonstrate that several theories of torsion gravity are possible using different choices of the diffeomorphic invariants in the Lagrangians. As a result, distinct cosmologies emerge. In all of them it is possible that the universe avoids the initial singularity and passes through an initial accelerated expansion. Differences between these theories are highlighted.

gr-qc↗