arXiv subjects

Tiberiu Harko

Publications and source records attributed to Tiberiu Harko.

At least 109 records · Page 6Linked to original sources

arXiv2020

Weyl type $f(Q,T)$ gravity, and its cosmological implications

We consider an $f(Q,T)$ type gravity model in which the scalar non-metricity $Q_{αμν}$ of the space-time is expressed in its standard Weyl form, and it is fully determined by a vector field $w_μ$. The field equations of the theory are obtained under the assumption of the vanishing of the total scalar curvature, a condition which is added into the gravitational action via a Lagrange multiplier. The gravitational field equations are obtained from a variational principle, and they explicitly depend on the scalar nonmetricity and on the Lagrange multiplier. The covariant divergence of the matter energy-momentum tensor is also determined, and it follows that the nonmetricity-matter coupling leads to the nonconservation of the energy and momentum. The energy and momentum balance equations are explicitly calculated, and the expressions of the energy source term and of the extra force are found. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of standard general relativity. We consider several cosmological models by imposing some simple functional forms of the function $f(Q,T)$, and we compare the predictions of the theory with the standard $Λ$CDM model.

gr-qc↗

arXiv2020

Comment on "Reexamining $f\left(R,T\right)$ gravity", Phys. Rev. D 100, 064059 (2019)

In a recent paper, "Reexamining $f\left(R,T\right)$ gravity", by S. B. Fisher and E. D. Carlson, Phys. Rev. D 100, 064059 (2019), the authors claim that for the particular $f(R,T)$ modified gravity model, with $f(R,T)=f_1(R)+f_2(T)$, the term $f_2(T)$ must be included in the matter Lagrangian and therefore it does not have any physical significance. We carefully reexamine the line of reasoning presented in the paper, and we show that there are several major conceptual problems related to the author's physical interpretations, as well as in the physical and mathematical approaches used to derive the energy-momentum tensor of the theory. These problems raise some serious concerns about the validity of most of the results presented in the paper.

gr-qc↗

arXiv2020

Vortex solutions in atomic Bose-Einstein condensates via the Adomian Decomposition Method

We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions of the vortex equation are expressed in the form of infinite power series. The power series representations are compared with the exact numerical solutions of the Gross-Pitaevskii equation for the uniform and the harmonic potential, respectively. We find that there is a good agreement between the analytical and the numerical results.

cond-mat.quant-gas↗

arXiv2020

Irreversible thermodynamical description of warm inflationary cosmological models

We investigate the interaction between scalar fields and radiation in the framework of warm inflationary models by using the irreversible thermodynamics of open systems with matter creation/annihilation. We consider the scalar fields and radiation as an interacting two component cosmological fluid in a homogeneous, spatially flat and isotropic Friedmann-Robertson-Walker (FRW) Universe. The thermodynamics of open systems as applied together with the gravitational field equations to the two component cosmological fluid leads to a generalization of the elementary scalar field-radiation interaction model, which is the theoretical basis of warm inflationary models, with the decay (creation) pressures explicitly considered as parts of the cosmological fluid energy-momentum tensor. Specific models describing coherently oscillating scalar waves, scalar fields with a constant potential, and scalar fields with a Higgs type potential are considered in detail. For each case exact and numerical solutions of the gravitational field equations with scalar field-radiation interaction are obtained, and they show the transition from an accelerating inflationary phase to a decelerating one. The theoretical predictions of the warm inflationary scenario with irreversible matter creation are also compared in detail with the Planck 2018 observational data, and constraints on the free parameters of the model are obtained.

gr-qc↗

arXiv2020

Distinguishing Brans-Dicke-Kerr type naked singularities and black holes with their thin disk electromagnetic radiation properties

The possible existence of naked singularities, hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon is still an open problem in present day astrophysics. From an observational point of view distinguishing between astrophysical black holes and naked singularities also represents a major challenge. One possible way of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around these different types of compact objects. In the present paper we continue the comparative investigation of accretion disk properties around axially-symmetric rotating geometries in Brans-Dicke theory in the presence of a massless scalar field. The solution of the field equations contains the Kerr metric as a particular case, and, depending on the numerical values of the model parameter $γ$, has also solutions corresponding to non-trivial black holes and naked singularities, respectively. Due to the differences in the exterior geometries between black holes and Brans-Dicke-Kerr naked singularities, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities.

gr-qc↗

arXiv2019

Finslerian geometrization of quantum mechanics in the hydrodynamical representation

We consider a Finslerian type geometrization of the non-relativistic quantum mechanics in its hydrodynamical (Madelung) formulation, by also taking into account the effects of the presence of the electromagnetic fields on the particle motion. In the Madelung representation the Schrödinger equation can be reformulated as the classical continuity and Euler equations of classical fluid mechanics in the presence of a quantum potential, representing the quantum hydrodynamical evolution equations. The equation of particle motion can then be obtained from a Lagrangian similar to its classical counterpart. After the reparametrization of the Lagrangian it turns out that the Finsler metric describing the geometric properties of quantum hydrodynamics is a Kropina metric. We present and discuss in detail the metric and the geodesic equations describing the geometric properties of the quantum motion in the presence of electromagnetic fields. As an application of the obtained formalism we consider the Zermelo navigation problem in a quantum hydrodynamical system, whose solution is given by a Kropina metric. The case of the Finsler geometrization of the quantum hydrodynamical motion of spinless particles in the absence of electromagnetic interactions is considered in detail, and the Zermelo navigation problem for this case is also discussed.

quant-ph↗

arXiv2019

Jeans instability and turbulent gravitational collapse of Bose-Einstein Condensate dark matter halos

We consider the Jeans instability and the gravitational collapse of the rotating Bose-Einstein Condensate dark matter halos, described by the zero temperature non-relativistic Gross-Pitaevskii equation, with repulsive inter-particle interactions. In the Madelung representation of the wave function, the dynamical evolution of the galactic halos is described by the continuity and the hydrodynamic Euler equations, with the condensed dark matter satisfying a polytropic equation of state with index $n=1$. By considering small perturbations of the quantum hydrodynamical equations we obtain the dispersion relation and the Jeans wave number, which includes the effects of the vortices (turbulence), of the quantum pressure and of the quantum potential, respectively. The critical scales above which condensate dark matter collapses (the Jeans radius and mass) are discussed in detail. We also investigate the collapse/expansion of rotating condensed dark matter halos, and we find a family of exact semi-analytical solutions of the hydrodynamic evolution equations, derived by using the method of separation of variables. An approximate first order solution of the fluid flow equations is also obtained. The radial coordinate dependent mass, density and velocity profiles of the collapsing/expanding condensate dark matter halos are obtained by using numerical methods.

gr-qc↗

arXiv2019

$f(Q,T)$ gravity

We propose an extension of the symmetric teleparallel gravity, in which the gravitational action $L$ is given by an arbitrary function $f$ of the nonmetricity $Q$ and of the trace of the matter energy-momentum tensor $T$, so that $L=f(Q,T)$. The field equations of the theory are obtained by varying the gravitational action with respect to both metric and connection. The covariant divergence of the field equations is obtained, with the geometry-matter coupling leading to the nonconservation of the energy-momentum tensor. We investigate the cosmological implications of the theory, and we obtain the cosmological evolution equations for a flat, homogeneous and isotropic geometry, which generalize the Friedmann equations of general relativity. We consider several cosmological models by imposing some simple functional forms of the function $f(Q,T)$, corresponding to additive expressions of $f(Q,T)$ of the form $f(Q,T)=αQ+βT$, $f(Q,T)=αQ^{n+1}+βT$, and $f(Q,T)=-αQ-βT^2$. The Hubble function, the deceleration parameter, and the matter energy density are obtained as a function of the redshift by using analytical and numerical techniques. For all considered cases the Universe experiences an accelerating expansion, ending with a de Sitter type evolution. The theoretical predictions are also compared with the results of the standard $Λ$CDM model.

gr-qc↗

arXiv2019

On the integrability of the Abel and of the extended Liénard equations

We present some exact integrability cases of the extended Liénard equation $y^{\prime \prime }+f\left( y\right) \left(y^{\prime }\right)^{n}+k\left( y\right) \left(y^{\prime }\right)^{m}+g\left(y\right) y^{\prime }+h\left( y\right) =0$, with $n>0$ and $m>0$ arbitrary constants, while $f(y)$, $k(y)$, $g(y)$, and $h(y)$ are arbitrary functions. The solutions are obtained by transforming the equation Liénard equation to an equivalent first kind first order Abel type equation given by $\frac{dv}{dy} =f\left( y\right) v^{3-n}+k\left( y\right) v^{3-m}+g\left( y\right) v^{2}+h\left( y\right) v^{3}$, with $v=1/y^{\prime }$. As a first step in our study we obtain three integrability cases of the extended quadratic-cubic Liénard equation, corresponding to $n=2$ and $m=3$, by assuming that particular solutions of the associated Abel equation are known. Under this assumption the general solutions of the Abel and Liénard equations with coefficients satisfying some differential conditions can be obtained in an exact closed form. With the use of the Chiellini integrability condition, we show that if a particular solution of the Abel equation is known, the general solution of the extended quadratic cubic Liénard equation can be obtained by quadratures. The Chiellini integrability condition is extended to generalized Abel equations with $g(y)\equiv 0$ and $h(y)\equiv 0$, and arbitrary $n$ and $m$, thus allowing to obtain the general solution of the corresponding Liénard equation. The application of the generalized Chiellini condition to the case of the reduced Riccati equation is also considered.

math.CA↗

arXiv2019

Constraining chameleon field driven warm inflation with Planck 2018 data

We investigate warm inflationary scenario in which the accelerated expansion of the early Universe is driven by chameleon-like scalar fields. Due to the non-minimal coupling between the scalar field and the matter sector, the energy-momentum tensor of each fluid component is not conserved anymore, and the generalized balance equation is obtained. The new source term in the energy equation can be used to model warm inflation. On the other hand, if the coupling function varies slowly, the model reduces to the standard model used for the description of cold inflation. To test the validity of the warm chameleon inflation model, the results for warm inflationary scenarios are compared with the observational Planck2018 Cosmic Microwave Background data. In this regard, the perturbation parameters such as the amplitude of scalar perturbations, the scalar spectral index and the tensor-to-scalar ratio are derived at the horizon crossing in two approximations, corresponding to the weak and strong dissipative regimes. As a general result it turns out that the theoretical predictions of the chameleon warm inflationary scenario are consistent with the Planck 2018 observations.

gr-qc↗

arXiv2019

Energy-dependent noncommutative quantum mechanics

We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy dependent functions. The Schrödinger equation in the energy dependent noncommutative algebra is derived for a two dimensional system for an arbitrary potential. The resulting equation reduces in the small energy limit to the standard quantum mechanical one, while for large energies the effects of the noncommutativity become important. We investigate in detail three cases, in which the noncommutative strengths are determined by an independent energy scale, related to the vacuum quantum fluctuations, by the particle energy, and by a quantum operator representation, respectively. Specifically, in our study we assume an arbitrary power law energy-dependence of the noncommutative strength parameters, and of their algebra. In this case, in the quantum operator representation, the Schrödinger equation can be formulated mathematically as a fractional differential equation. For all our three models we analyze the quantum evolution of the free particle, and of the harmonic oscillator, respectively. The general solutions of the noncommutative Schrödinger equation as well as the expressions of the energy levels are explicitly obtained.

quant-ph↗

arXiv2019

Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity

We consider vacuum static spherically symmetric solutions in the hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms unifying local constraints at the Solar System level and the late-time cosmic acceleration. We adopt the scalar-tensor representation of the hybrid metric-Palatini theory, in which the scalar-tensor definition of the potential can be represented as a Clairaut differential equation. Due to their mathematical complexity, it is difficult to find exact solutions of the vacuum field equations, and therefore we adopt a numerical approach in studying the behavior of the metric functions and of the scalar field. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, the field equations are solved 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 these black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated in detail.

gr-qc↗

arXiv2019

Novel couplings between nonmetricity and matter

We present a novel theory of gravity, namely, an extension of symmetric teleparallel gravity. This is done by introducing a new class of theories where the nonmetricity $Q$ is coupled nonminimally to the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. We also present several cosmological applications.

gr-qc↗

arXiv2018

Mass - radius ratio bounds for compact objects in Lorentz-violating dRGT Massive Gravity theory

We consider the mass-radius bounds for spherically symmetric static compact objects in the de Rham-Gabadadze-Tolley (dRGT) Massive Gravity theories, free of ghosts. In this type of gravitational theories the graviton, the quantum of gravity, may have a small, but non-vanishing mass. We derive the hydrostatic equilibrium and mass continuity equations in the Lorentz-violating Massive gravity in the presence of a cosmological constant and for a non-zero graviton mass. The case of the constant density stars is also investigated by numerically solving the equilibrium equations. The influence of the graviton mass on the global parameters (mass and radius) of these stellar configurations is also considered. The generalized Buchdahl relations, giving the upper and lower bounds of the mass-radius ratio are obtained, and discussed in detail. As an application of our results we obtain gravitational redshift bounds for compact stellar type objects in the Lorentz-violating dRGT Massive Gravity, which may (at least in principle) be used for observationally testing this theory in an astrophysical context.

gr-qc↗

arXiv2018

Solving the nonlinear biharmonic equation by the Laplace-Adomian and Adomian Decomposition Methods

The biharmonic equation, as well as its nonlinear and inhomogeneous generalizations, plays an important role in engineering and physics. In particular the focusing biharmonic nonlinear Schrödinger equation, and its standing wave solutions, have been intensively investigated. In the present paper we consider the applications of the Laplace-Adomian and Adomian Decomposition Methods for obtaining semi-analytical solutions of the generalized biharmonic equations of the type $Δ^{2}y+αΔy+ωy+b^{2}+g\left( y\right) =f$, where $α$, $ω$ and $b$ are constants, and $g$ and $f$ are arbitrary functions of $y$ and the independent variable, respectively. After introducing the general algorithm for the solution of the biharmonic equation, as an application we consider the solutions of the one-dimensional and radially symmetric biharmonic standing wave equation $Δ^{2}R+R-R^{2σ+1}=0$, with $σ= {\rm constant}$. The one-dimensional case is analyzed by using both the Laplace-Adomian and the Adomian Decomposition Methods, respectively, and the truncated series solutions are compared with the exact numerical solution. The power series solution of the radial biharmonic standing wave equation is also obtained, and compared with the numerical solution.

math.AP↗

arXiv2018

Reply to "Comment on 'Can accretion disk properties observationally distinguish black holes from naked singularities?'"

In the Comment on "Can accretion disk properties observationally distinguish black holes from naked singularities?", by Bertrand Chauvineau, Phys. Rev. D {\bf 98}, 088501 (2018), the author did show that the metric used in Z. Kovács and T. Harko, Phys. Rev. D {\bf 82}, 124047 (2010), and initially introduced in K. D. Krori and D. R. Bhattacharjee, J. Math. Phys. \textbf{23}, 637 (1982) and K. K. Nandi, P. M. Alsing, J. C. Evans, and T. B. Nayak, Phys. Rev. D \textbf{63}, 084027 (2001), does not satisfy the Einstein gravitational field equations with a minimally coupled scalar field. In our reply we would like to point out that this result is actually not new, but it was already published in the literature. Moreover, a rotating solution that generalizes the Kerr metric for a nonminimally coupled scalar field does exist. We briefly discuss the nature of the singularities for the generalized metric, and point out that it can be used as a testing ground to differentiate black holes from naked singularities. We also mention the existence of some other typing or technical errors existing in the literature.

gr-qc↗

arXiv2018

The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity

Though not a part of mainstream physics, Salam's theory of strong gravity remains a viable effective model for the description of strong interactions in the gauge singlet sector of QCD, capable of producing particle confinement and asymptotic freedom, but not of reproducing interactions involving $SU(3)$ colour charge. It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require colour interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order $1 \ \rm GeV^{-1}$. We revisit the strong gravity theory and investigate the strong gravity field equations in the presence of a mixing term which induces an effective {\it strong cosmological constant}, $Λ_{f}$. This introduces a {\it strong de Sitter radius} for strongly interacting fermions, producing a confining bubble, which allows us to identify $Λ_{f}$ with the `bag constant' of the MIT bag model, $B \simeq 2 \times 10^{14} \rm gcm^{-3}$. Assuming a static, spherically symmetric geometry, we derive the strong gravity TOV equation, which describes the equilibrium properties of compact hadronic objects. From this, we determine the generalised Buchdahl inequalities for a strong gravity `particle', giving rise to upper and lower bounds on the mass/radius ratio of stable, compact, strongly interacting objects. We show, explicitly, that the existence of the lower mass bound is induced by the presence of $Λ_f$, producing a mass gap, and that the upper bound corresponds to a deconfinement phase transition. The physical implications of our results for holographic duality in the context of the AdS/QCD and dS/QCD correspondences are also discussed.

hep-th↗

arXiv2018

Loop Quantum Cosmology with a noncommutative quantum deformed photon gas

The noncommutativity of the space-time had important implications for the very early Universe, when its size was of the order of the Planck length. An important implication of this effect is the deformation of the standard dispersion relation of special relativity. Moreover, in the Planck regime gravity itself must be described by a quantum theory. We consider the implications of the modified dispersion relations for a photon gas, filling the early Universe, in the framework of Loop Quantum Cosmology, a theoretical approach to quantum gravity. We consider three types of deformations of the dispersion relations of the photon gas, from which we obtain the Planck scale corrections to the energy density and pressure. The cosmological implications of the modified equations of state are explored in detail for all radiation models in the framework of the modified Friedmann equation of Loop Quantum Cosmology. By numerically integrating the evolution equations we investigate the evolution of the basic cosmological parameters (scale factor, Hubble function, radiation temperature, and deceleration parameter) for a deformed photon gas filled Universe. In all models the evolution of the Universe shows the presence of a (nonsingular) bounce, corresponding to the transition from a contracting to an expanding phase.

gr-qc↗