arXiv subjects

Tiberiu Harko

Publications and source records attributed to Tiberiu Harko.

At least 91 records · Page 5Linked to original sources

arXiv2021

Cosmic strings in generalized hybrid metric-Palatini gravity

We consider the possible existence of gravitationally bound stringlike objects in the framework of the generalized hybrid metric-Palatini gravity theory, in which the gravitational action is represented by an arbitrary function of the Ricci and of the Palatini scalars, respectively. The theory admits an equivalent scalar-tensor representation in terms of two independent scalar fields. Assuming cylindrical symmetry, and the boost invariance of the metric, we obtain the gravitational field equations that describe cosmic stringlike structures in the theory. The physical and geometrical properties of the cosmic strings are determined by the two scalar fields, as well by an effective field potential, functionally dependent on both scalar fields. The field equations can be exactly solved for a vanishing, and a constant potential, respectively, with the corresponding string tension taking both negative and positive values. Furthermore, for more general classes of potentials, having an additive and a multiplicative algebraic structure in the two scalar fields, the gravitational field equations are solved numerically. For each potential we investigate the effects of the variations of the potential parameters and of the boundary conditions on the structure of the cosmic string. In this way, we obtain a large class of stable stringlike astrophysical configurations, whose basic parameters (string tension and radius) depend essentially on the effective field potential, and on the boundary conditions.

gr-qc↗

arXiv2021

Cosmological evolution and dark energy in osculating Barthel-Randers geometry

We consider the cosmological evolution in an osculating point Barthel-Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe the physical properties of the gravitational field, as well as the cosmological dynamics. For the Barthel-Randers geometry the connection is given by the Levi-Civita connection of the associated Riemann metric. The generalized Friedmann equations in the Barthel-Randers geometry are obtained by considering that the background Riemannian metric in the Randers line element is of Friedmann-Lemaitre-Robertson-Walker type. The matter energy balance equation is derived, and it is interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. The cosmological properties of the model are investigated in detail, and it is shown that the model admits a de Sitter type solution, and that an effective cosmological constant can also be generated. Several exact cosmological solutions are also obtained. A comparison of three specific models with the observational data and with the standard $Λ$CDM model is also performed by fitting the observed values of the Hubble parameter, with the models giving a satisfactory description of the observations.

gr-qc↗

arXiv2021

Gravitationally Induced Particle Production through a Nonminimal Torsion-Matter Coupling

We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion--matter coupling. An intriguing feature of this theory is that the divergence of the matter energy--momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy--momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard $Λ$CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy--momentum tensor. We consider specific models, and we show that cosmology with a torsion--matter coupling can almost perfectly reproduce the $Λ$CDM scenario, while it additionally gives rise to particle creation rates, creation pressures, and entropy generation through gravitational matter production in both low and high redshift limits.

gr-qc↗

arXiv2021

Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity

We generalize and unify the $f(R,T)$ and $f(R,L_m)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$, of the trace of the energy-momentum tensor $T$, and of the matter Lagrangian $L_m$, so that $L_{grav}=f(R,L_m,T)$. We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy-momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov-Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $f(R,L_m,T)$ of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

gr-qc↗

arXiv2021

Jacobi stability analysis of the classical restricted three body problem

The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a very useful model for investigating the behavior of real astronomical objects in the Solar System. In such a system, there are five Lagrangian equilibrium points, and one important characteristic of the motion is the existence of linearly stable equilibria at the two equilibrium points that form equilateral triangles with the primaries, in the plane of the primaries' orbit. We analyze the stability of motion in the restricted three body problem by using the concept of Jacobi stability, as introduced and developed in the Kosambi-Cartan-Chern (KCC) theory. The KCC theory is a differential geometric approach to the variational equations describing the deviation of the whole trajectory of a dynamical system with respect to the nearby ones. We obtain the general result that, from the point of view of the KCC theory and of Jacobi stability, all five Lagrangian equilibrium points of the restricted three body problem are unstable.

astro-ph.IM↗

arXiv2021

Static spherically symmetric three-form stars

We consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert-Einstein action with a Lagrangian constructed from a three-form field $A_{αβγ}$, which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff fluid, radiation-like, bag model and the Bose-Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application of the obtained results, we suggest that the 2.5$M_{\odot}$ mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form field gravity theory.

gr-qc↗

arXiv2021

Analytical solutions of the one-dimensional Schrödinger equation with position-dependent mass

The study of the Schrödinger equation with the position-dependent effective mass has attracted a lot of attention, due to its applications in many fields of physics, including the properties of the semiconductors, semiconductor heterostructures, graded alloys, quantum liquids, Helium-3 clusters, quantum wells, wires and dots etc. In the present work we obtain several classes of solutions of the one-dimensional Schrödinger equation with position-dependent particle mass. As a first step the single particle Schrödinger equation with position-dependent mass is transformed into an equivalent Riccati type equation. By considering some integrability cases of the Riccati equation, seven classes of exact analytical solutions of the Schrödinger equation are obtained, with the particle mass function and the external potential satisfying some consistency conditions.

quant-ph↗

arXiv2021

A Brief Introduction to the Adomian Decomposition Method, with Applications in Astronomy and Astrophysics

The Adomian Decomposition Method (ADM) is a very effective approach for solving broad classes of nonlinear partial and ordinary differential equations, with important applications in different fields of applied mathematics, engineering, physics and biology. It is the goal of the present paper to provide a clear and pedagogical introduction to the Adomian Decomposition Method and to some of its applications. In particular, we focus our attention to a number of standard first-order ordinary differential equations (the linear, Bernoulli, Riccati, and Abel) with arbitrary coefficients, and present in detail the Adomian method for obtaining their solutions. In each case we compare the Adomian solution with the exact solution of some particular differential equations, and we show their complete equivalence. The second order and the fifth order ordinary differential equations are also considered. An important extension of the standard ADM, the Laplace-Adomian Decomposition Method is also introduced through the investigation of the solutions of a specific second order nonlinear differential equation. We also present the applications of the method to the Fisher-Kolmogorov second order partial nonlinear differential equation, which plays an important role in the description of many physical processes, as well as three important applications in astronomy and astrophysics, related to the determination of the solutions of the Kepler equation, of the Lane-Emden equation, and of the general relativistic equation describing the motion of massive particles in the spherically symmetric and static Schwarzschild geometry.

astro-ph.IM↗

arXiv2021

Warm inflation with non-comoving scalar field and radiation fluid

We consider a warm inflationary scenario in which the two dominant matter components present in the early Universe, the scalar field, and the radiation fluid, evolve with different four-velocities. This cosmological system is mathematically equivalent to a single anisotropic fluid, evolving with a four-velocity that is a function of the two independent fluid four-velocities. Due to the presence of the anisotropic physical parameters, the overall cosmological evolution is also anisotropic. We derive the gravitational field equations of the noncomoving scalar field-radiation mixture for a Bianchi type I geometry. By considering that the decay of the scalar field is accompanied by a corresponding radiation generation, we formulate the basic equations of the warm inflationary model in the presence of two noncomoving components. By adopting the slow roll approximation, we perform a detailed comparison of the theoretical predictions of the warm inflationary scenario with noncomoving scalar field and radiation fluid with the observational data obtained by the Planck satellite, by investigating both the weak dissipation and strong dissipation limits. Constraints on the free parameters of the model are obtained in both cases. The functional forms of the scalar field potentials compatible with the noncomoving nature of warm inflation are also derived.

gr-qc↗

arXiv2021

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity

We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl type $f(Q,T)$ gravity, in which the nonmetricity $Q$ is represented in the standard Weyl form, fully determined by the Weyl vector, while $T$ represents the trace of the matter energy-momentum tensor. The effects of the Weyl geometry and of the extra force induced by the nonmetricity-matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the nonmetricity-matter coupling, are obtained in the weak field approximation. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl type $f(Q,T)$ gravity.

gr-qc↗

arXiv2020

The effects of the dark energy on the static Schrödinger-Newton system -- an Adomian Decomposition Method and Padé approximants based approach

The Schrödinger-Newton system is a nonlinear system obtained by coupling together the linear Schrödinger equation of quantum mechanics with the Poisson equation of Newtonian mechanics. In the present work we will investigate the effects of a cosmological constant (dark energy or vacuum fluctuation) on the Schrödinger-Newton system, by modifying the Poisson equation through the addition of a new term. The corresponding Schrödinger-Newton-$Λ$ system cannot be solved exactly, and therefore for its study one must resort to either numerical or semianalytical methods. In order to obtain a semianalytical solution of the system we apply the Adomian Decomposition Method, a very powerful method used for solving a large class of nonlinear ordinary and partial differential equations. Moreover, the Adomian series are transformed into rational functions by using the Padé approximants. The semianalytical approximation is compared with the full numerical solution, and the effects of the dark energy on the structure of the Newtonian quantum system are investigated in detail.

gr-qc↗

arXiv2020

Black hole solutions in modified gravity induced by quantum metric fluctuations

The inclusion of the quantum fluctuations of the metric in the geometric action is a promising avenue for the understanding of the quantum properties of gravity. In this approach the metric is decomposed in the sum of a classical and of a fluctuating part, of quantum origin, which can be generally expressed in terms of an arbitrary second order tensor, constructed from the metric, and from the thermodynamic quantities describing matter fields. In the present paper we investigate the effects of the quantum fluctuations on the spherically symmetric static black hole solutions of the modified field equations, obtained from a variational principle, by assuming that the quantum correction tensor is given by the coupling of a scalar field to the metric tensor. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, we obtain their solutions numerically. We detect the formation of a black hole from the presence of a singularity in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential, are considered. The thermodynamic properties of the black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated.

gr-qc↗

arXiv2020

Series solution of the Susceptible-Infected-Recovered (SIR) epidemic model with vital dynamics via the Adomian and Laplace-Adomian Decomposition Methods

The Susceptible-Infected-Recovered (SIR) epidemic model as well as its generalizations are extensively used for the study of the spread of infectious diseases, and for the understanding of the dynamical evolution of epidemics. From SIR type models only the model without vital dynamics has an exact analytic solution, which can be obtained in an exact parametric form. The SIR model with vital dynamics, the simplest extension of the basic SIR model, does not admit a closed form representation of the solution. However, in order to perform the comparison with the epidemiological data accurate representations of the time evolution of the SIR model with vital dynamics would be very useful. In the present paper, we obtain first the basic evolution equation of the SIR model with vital dynamics, which is given by a strongly nonlinear second order differential equation. Then we obtain a series representation of the solution of the model, by using the Adomian and Laplace-Adomian Decomposition Methods to solve the dynamical evolution equation of the model. The solutions are expressed in the form of infinite series. The series representations of the time evolution of the SIR model with vital dynamics are compared with the exact numerical solutions of the model, and we find that, at least for a specific range of parameters, there is a good agreement between the Adomian and Laplace-Adomian semianalytical solutions, containing only a small number of terms, and the numerical results.

q-bio.PE↗

arXiv2020

Testing Bose-Einstein Condensate dark matter models with the SPARC galactic rotation curves data

The nature of one of the fundamental components of the Universe, the dark matter, is still unknown. One interesting possibility is that dark matter could exist in the form of a self-interacting Bose-Einstein Condensate (BEC). The fundamental properties of the dark matter in this model are determined by two parameters only, the mass and the scattering length of the particle. In the present study we investigate the properties of the galactic rotation curves in the BEC dark matter model, with quadratic self-interaction, by using 173 galaxies from the recently published Spitzer Photomery \& Accurate Rotation Curves (SPARC) data. We fit the theoretical predictions of the rotation curves in the slowly rotating BEC models with the SPARC data by using genetic algorithms. We provide an extensive set of figures of the rotation curves, and we obtain estimates of the relevant astrophysical parameters of the BEC dark matter halos (central density, angular velocity and static radius). The density profiles of the dark matter distribution are also obtained. It turns out that the BEC model gives a good description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core/cusp problem.

gr-qc↗

arXiv2020

Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings

Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing. However, the discovery of the late-time cosmic acceleration, which represents a new imbalance in the governing gravitational field equations, has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation, and has spurred much research in modified gravity, where extensions of the Hilbert-Einstein action describe the gravitational field. In this review, we perform a detailed theoretical and phenomenological analysis of two largely explored extensions of $f(R)$ gravity, namely: (i) the hybrid metric-Palatini theory; (ii) and modified gravity with curvature-matter couplings. Relative to the former, it has been established that both metric and Palatini versions of $f(R)$ gravity possess interesting features but also manifest severe drawbacks. A hybrid combination, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and avoids some drawbacks of the original approaches. Relative to the curvature-matter coupling theories, these offer interesting extensions of $f(R)$ gravity, where the explicit nonminimal couplings between an arbitrary function of the scalar curvature $R$ and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor. We extensively explore both theories in a plethora of applications, namely, the weak-field limit, galactic and extragalactic dynamics, cosmology, stellar-type compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvature-matter coupling theory.

gr-qc↗

arXiv2020

Cosmic stringlike objects in hybrid metric-Palatini gravity

We consider static and cylindrically symmetric interior string type solutions in the scalar-tensor representation of the hybrid metric-Palatini modified theory of gravity. As a first step in our study, we obtain the gravitational field equations and further simplify the analysis by imposing Lorentz invariance along the $t$ and $z$ axes, which reduces the number of unknown metric tensor components to a single function $W^2(r)$. In this case, the general solution of the field equations can be obtained, for an arbitrary form of the scalar field potential, in an exact closed parametric form, with the scalar field $ϕ$ taken as a parameter. We consider in detail several exact solutions of the field equations, corresponding to a null and constant potential, and to a power-law potential of the form $V(ϕ)=V_0ϕ^{3/4}$, in which the behaviors of the scalar field, of the metric tensor components and of the string tension can be described in a simple mathematical form. We also investigate the string models with exponential and Higgs type scalar field potentials by using numerical methods. In this way we obtain a large class of novel stable string-like solutions in the context of hybrid metric-Palatini gravity, in which the basic parameters, such as the scalar field, metric tensor components, and string tension, depend essentially on the initial values of the scalar field, and of its derivative, on the $r=0$ circular axis.

gr-qc↗

arXiv2020

Black hole and naked singularity geometries supported by three-form fields

We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert-Einstein action with a Lagrangian constructed from a three-form field $A_{αβγ}$, which is related to the field strength and a potential term. The field equations are derived from a variational principle and are obtained explicitly for a static and spherically symmetric geometry in vacuum. For the case of the vanishing three-form field potential the gravitational field equations can be solved exactly. However, for arbitrary potentials, due to their mathematical complexity, numerical approaches are adopted in studying the behavior of the metric functions and the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the time-like Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are also investigated in detail.

gr-qc↗

arXiv2020

A simple computational approach to the Susceptible-Infected-Recovered (SIR) epidemic model via the Laplace-Adomian Decomposition Method

The Susceptible-Infected-Recovered (SIR) epidemic model is extensively used for the study of the spread of infectious diseases. Even that the exact solution of the model can be obtained in an exact parametric form, in order to perform the comparison with the epidemiological data a simple but highly accurate representation of the time evolution of the SIR compartments would be very useful. In the present paper we obtain a series representation of the solution of the SIR model by using the Laplace-Adomian Decomposition Method to solve the basic evolution equation of the model. The solutions are expressed in the form of infinite series. The series representations of the time evolution of the SIR compartments are compared with the exact numerical solutions of the model. We find that there is a good agreement between the Laplace-Adomian semianalytical solutions containing only three terms, and the numerical results.

q-bio.PE↗