Existence of static wormhole solutions in $$ gravity

This work investigates some feasible regions for the existence of traversable wormhole geometries in \(f(R,G)\) gravity, where \(R\) and \(G\) represent the Ricci scalar and the Gauss-Bonnet invariant respectively. Three different matter contents anisotropic fluid, isotropic fluid and barotropic fluid have been considered for the analysis. Moreover, we split \(f(R,G)\) gravity model into Strobinsky like \(f(R)\) model and a power law \(f(G)\) model to explore wormhole geometries. We select red-shift and shape functions which are suitable for the existence of wormhole solutions for the chosen \(f(R,G)\) gravity model. It has been analyzed with the graphical evolution that the null energy and weak energy conditions for the effective energy-momentum tensor are usually violated for the ordinary matter content. However, some small feasible regions for the existence of wormhole solutions have been found where the energy conditions are not violated. The overall analysis confirms the existence of the wormhole geometries in \(f(R,G)\) gravity under some reasonable circumstances.     

Cosmic strings in a five dimensional spherically symmetric background in $$ gravity

We study the physical behavior of a five dimensional non-static spherically symmetric cosmological models in the presence of massive strings in the framework of \(f(R,T)\) gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011). Here \(R\) is the Ricci scalar and \(T\) is the trace of the stress energy tensor and the fifth dimension is not observed because it is compact. We solve the field equations (i) using a relation between the scale factors given by Samantha and Dhal (Int. J. Theor. Phys. 52:1334, 2013) and (ii) equations of state for string models. The models obtained correspond to \(p\)-string, geometric string and massive string models in this modified theory in five dimensions. Cosmological parameters of the models are determined and their dynamical properties are discussed.     

FLRW cosmological models with quark and strange quark matters in $$ gravity

In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of \(f(R,T)\) gravity in the background of Friedmann-Lemaître-Robertson-Walker (FLRW) metric. To get exact solutions of modified field equations we have used \(f(R,T ) = R + 2 f(T)\) model given by Harko et al. with two different parametrization of geometrical parameters i.e. the parametrization of the deceleration parameter \(q \), and the scale factor \(a \) in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in \(f(R,T)\) gravity and General Relativity (GR). All models in \(f(R,T)\) gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Akta? and Aygün in \(f(R,T)\) gravity. However, we have also discussed the physical consequences of our obtained models.     

New holographic dark energy model with constant bulk viscosity in modified $$ gravity theory

The aim of this paper is to study new holographic dark energy (HDE) model in modified \(f(R,T)\) gravity theory within the framework of a flat Friedmann-Robertson-Walker model with bulk viscous matter content. It is thought that the negative pressure caused by the bulk viscosity can play the role of dark energy component, and drive the accelerating expansion of the universe. This is the motive of this paper to observe such phenomena with bulk viscosity. In the specific model \(f(R,T)=R+\lambda T\), where \(R\) is the Ricci scalar, \(T\) the trace of the energy-momentum tensor and \(\lambda \) is a constant, we find the solution for non-viscous and viscous new HDE models. We analyze new HDE model with constant bulk viscosity, \(\zeta =\zeta _{0}= \text{const.}\) to explain the present accelerated expansion of the universe. We classify all possible scenarios (deceleration, acceleration and their transition) with possible positive and negative ranges of \(\lambda \) over the constraint on \(\zeta _{0}\) to analyze the evolution of the universe. We obtain the solutions of scale factor and deceleration parameter, and discuss the evolution of the universe. We observe the future finite-time singularities of type I and III at a finite time under certain constraints on \(\lambda \). We also investigate the statefinder and \(\mathit{Om}\) diagnostics of the viscous new HDE model to discriminate with other existing dark energy models. In late time the viscous new HDE model approaches to \(\varLambda \mathit{CDM}\) model. We also discuss the thermodynamics and entropy of the model and find that it satisfies the second law of thermodynamics.     

Relativistic satellite orbits: central body with higher zonal harmonics

Satellite orbits around a central body with arbitrary zonal harmonics are considered in a relativistic framework. Our starting point is the relativistic Celestial Mechanics based upon the first post-Newtonian approximation to Einstein’s theory of gravity as it has been formulated by Damour et al. (Phys Rev D 43:3273–3307, 1991; 45:1017–1044, 1992; 47:3124–3135, 1993; 49:618–635, 1994). Since effects of order \((\mathrm{GM}/c^2R) \times J_k\) with \(k \ge 2\) for the Earth are very small (of order \( 7 \times 10^{-10}\,\times \,J_k\)) we consider an axially symmetric body with arbitrary zonal harmonics and a static external gravitational field. In such a field the explicit \(J_k/c^2\)-terms (direct terms) in the equations of motion for the coordinate acceleration of a satellite are treated first with first-order perturbation theory. The derived perturbation theoretical results of first order have been checked by purely numerical integrations of the equations of motion. Additional terms of the same order result from the interaction of the Newtonian \(J_k\)-terms with the post-Newtonian Schwarzschild terms (relativistic terms related to the mass of the central body). These ‘mixed terms’ are treated by means of second-order perturbation theory based on the Lie-series method (Hori–Deprit method). Here we concentrate on the secular drifts of the ascending node \(<\!{\dot{\Omega }}\!>\) and argument of the pericenter \(<\!{\dot{\omega }}\!>\). Finally orders of magnitude are given and discussed.     

Scalar field cosmology in $$ gravity via Noether symmetry

This paper investigates the existence of Noether symmetries of isotropic universe model in \(f(R,T)\) gravity admitting minimal coupling of matter and scalar fields. The scalar field incorporates two dark energy models such as quintessence and phantom models. We determine symmetry generators and corresponding conserved quantities for two particular \(f(R,T)\) models. We also evaluate exact solutions and investigate their physical behavior via different cosmological parameters. For the first model, the graphical behavior of these parameters indicate consistency with recent observations representing accelerated expansion of the universe. For the second model, these parameters identify a transition form accelerated to decelerated expansion of the universe. The potential function is found to be constant for the first model while it becomes \(V(\phi )\approx \phi ^{2}\) for the second model. We conclude that the Noether symmetry generators and corresponding conserved quantities appear in all cases.     

Spherical accretion of matter by charged black holes on $$ Gravity

We studied the spherical accretion of matter by charged black holes on \(f(T)\) Gravity. Considering the accretion model of a isentropic perfect fluid we obtain the general form of the Hamiltonian and the dynamic system for the fluid. We have analysed the movements of an isothermal fluid model with \(p=\omega e\) and where \(p\) is the pressure and \(e\) the total energy density. The analysis of the cases shows the possibility of spherical accretion of fluid by black holes, revealing new phenomena as cyclical movement inside the event horizon.     

Geodesics around oscillatons made of exponential scalar field potential

Some of the spherically symmetric solutions to the Einstein–Klein–Gordon (EKG) equations can describe the astronomical soliton objects made of a real time-dependent scalar fields. The solutions are known as oscillatons which are non-singular satisfying the flatness conditions asymptotically with periodic (separated) time-dependency. In this paper, we investigate the geodesic motion around an oscillaton. The Spherically Symmetric Geometry allows the bound orbits in the plan \(\theta=\frac{\pi}{2}\) under a given initial conditions. The potential for the scalar field \(\varPhi=\varPhi(r,t)\), is an exponential function of the form \(V(\varPhi)=V_{0}\exp(\lambda\sqrt{k_{0}}\varPhi)\).     

Study of some chaotic inflationary models in $$ gravity

In this paper, we discuss an inflationary scenario via scalar field and fluid cosmology for an anisotropic homogeneous universe model in \(f(R)\) gravity. We consider an equation of state which corresponds to a quasi-de Sitter expansion and investigate the effect of the anisotropy parameter for different values of the deviation parameter. We evaluate potential models like linear, quadratic and quartic models which correspond to chaotic inflation. We construct the observational parameters for a power-law model of \(f(R)\) gravity and construct the graphical analysis of tensor–scalar ratio and spectral index which indicates the consistency of these parameters with Planck 2015 data.     

Satellite de-orbiting via controlled solar radiation pressure

We analyze the families of central configurations of the spatial 5-body problem with four masses equal to 1 when the fifth mass m varies from 0 to \(+\infty \). In particular we continue numerically, taking m as a parameter, the central configurations (which all are symmetric) of the restricted spatial (\(4+1\))-body problem with four equal masses and \(m=0\) to the spatial 5-body problem with equal masses (i.e. \(m=1\)), and viceversa we continue the symmetric central configurations of the spatial 5-body problem with five equal masses to the restricted (\(4+1\))-body problem with four equal masses. Additionally we continue numerically the symmetric central configurations of the spatial 5-body problem with four equal masses starting with \(m=1\) and ending in \(m=+\infty \), improving the results of Alvarez-Ramírez et al. (Discrete Contin Dyn Syst Ser S 1: 505–518, 2008). We find four bifurcation values of m where the number of central configuration changes. We note that the central configurations of all continued families varying m from 0 to \(+\infty \) are symmetric.     

Anisotropic model with decaying cosmological term

A spatially homogeneous and anisotropic locally rotationally symmetric Bianchi type-I spacetime with cosmological term \(\varLambda \) in \(f(R,T) \) theory has been studied. The exact solution of the field equations is obtained under a variation law of the Hubble parameter \((H) \) which yields a time dependent deceleration parameter (Banerjee and Das in Gen. Relativ. Gravit. 37:10, 2005). The model presents a cosmological scenario which describes early deceleration and late time acceleration. The physical parameters of the model have been analysed.     

The anisotropic distribution of the dark energy within the scope of LRS Bianchi type I model

We investigate the anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dark matter and anisotropic dark energy. We assume that the shear scalar \((\sigma )\) is proportional to expansion scalar \((\theta )\). A special law is introduced for two skewness parameters that describe the deviation of pressure from isotropy. This law can lead to models: the hybrid expansion, the big rip and the little rip. The behavior of the Universe is discussed depending on the numerical parameters of the models.     

Behaviour of physical parameters in extended gravity with hyperbolic function

In this paper, we have constructed the cosmological model of the universe in f(R, T) theory of gravity in a Bianchi type \(\mathrm{VI}_h\) universe for the functional f(R, T) in the form \(f(R,T)=\mu R+\mu T\), where R and T are respectively Ricci scalar and trace of energy momentum tensor and \(\mu \) is a constant. We have made use of the hyperbolic scale factor to find the physical parameters and metric potentials defined in the space-time. The physical parameters are constrained from different representative values to build up a realistic cosmological model aligned with the observational behaviour. The state finder diagnostic pair is found to be in the acceptable range. The energy conditions of the model are also studied.     

Dark energy cosmological models with cosmic string

In this paper we have studied the anisotropic Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi type-I and LRS Bianchi type-III geometries filled with dark energy and one dimensional cosmic string in the Saez-Ballester theory of gravitation. To get physically valid solution we take hybrid expansion law of the average scale factor which is a product of power and exponential type of functions that results in time dependent deceleration parameter (\(q\)). The equation of state parameter of dark energy (\(\omega _{\mathit{de}}\)) has been discussed and we have observed that for the three models it crosses the phantom divide line (\(\omega _{\mathit{de}} = -1\)) and shows quintom like behavior. The density of dark energy (\(\rho _{\mathit{de}}\)) is an increasing function of redshift and remains positive throughout the evolution of the universe for the three models. Moreover in Kantowski-Sachs and LRS Bianchi type-I geometries the dark energy density dominates the string tension density (\(\lambda \)) and proper density (\(\rho \)) throughout the evolution of the universe. The physical and geometrical aspects of the statefinder parameters (\(r,s\)), squared speed of sound (\(v_{s}^{2} \)) and \(\omega _{\mathit{de}}\)–\(\omega ^{\prime }_{\mathit{de}}\) plane are also discussed.     

Is the GeV-TeV emission of PKS 0447-439 from the proton synchrotron radiation?

We study the multi-wavelength emission features of PKS 0447-439 in the frame of the one-zone homogeneous lepto-hadronic model. In this model, we assumed that the steady power-laws with exponential cut-offs distributions of protons and electrons are injected into the source. The non-linear time-dependent kinematic equations, describing the evolution of protons, electrons and photons, are defined; these equations self-consistently involve synchrotron radiation of protons, photon-photon interaction, synchrotron radiation of electron/positron pairs, inverse Compton scattering and synchrotron self-absorption. The model is applied to reproduce the multi-wavelength spectrum of PKS 0447-439. Our results indicate that the spectral energy distribution (SED) of PKS 0447-439 can be reproduced well by the model. In particular, the GeV-TeV emission is produced by the synchrotron radiation of relativistic protons. The physically plausible solutions require the magnetic strength \(10~\text{G}\lesssim B \lesssim 100~\text{G}\). We found that the observed spectrum of PKS 0447-439 can be reproduced well by the model whether \(z = 0.16\) or \(z = 0.2\), and the acceptable upper limit of redshift is \(z=0.343\).     

Toward Spectroscopically Detecting the Global Latitudinal Temperature Variation on the Solar Surface

A very slight rotation-induced latitudinal temperature variation (presumably on the order of several kelvin) on the solar surface is theoretically expected. While recent high-precision solar brightness observations reported its detection, confirmation by an alternative approach using the strengths of spectral lines is desirable, for which reducing the noise due to random fluctuation caused by atmospheric inhomogeneity is critical. Toward this difficult task, we carried out a pilot study of spectroscopically investigating the relative variation of temperature (\(T\)) at a number of points in the solar circumference region near to the limb (where latitude dependence should be detectable, if any exists) based on the equivalent widths (\(W\)) of 28 selected lines in the 5367?–?5393 Å and 6075?–?6100 Å regions. We paid special attention to i) clarifying which types of lines should be employed and ii) how much precision is attainable in practice. We found that lines with strong \(T\)-sensitivity (\(|\log W/\log T|\)) should be used and that very weak lines should be avoided because they inevitably suffer strong relative fluctuations (\(\Delta W/W\)). Our analysis revealed that a precision of \(\Delta T/T \approx 0.003\) (corresponding to ≈?15 K) can be achieved at best by a spectral line with comparatively large \(|\log W/\log T|\), although this can possibly be further improved When a number of lines are used all together. Accordingly, if many such favorable lines could be measured with subpercent precision of \(\Delta W/W\) and by averaging the resulting \(\Delta T/T\) from each line, the random noise would eventually be reduced to ??1 K and detection of a very subtle amount of global \(T\)-gradient might be possible.     

Correlation Between the Magnetic Field and Plasma Parameters at 1 AU

The physical parameters of the solar wind observed in-situ near 1 AU have been studied for several decades, and relationships between them, such as the positive correlation between the solar wind plasma temperature, \(T\), and velocity, \(V\), and the negative correlation between density, \(N\), and velocity, \(V\), are well known. However, the magnetic field intensity, \(B\), does not appear to be well correlated with any individual plasma parameter. In this article, we discuss previously under-reported correlations between \(B\) and the combined plasma parameters \(\sqrt{N V^{2}} \) as well as between \(B\) and \(\sqrt{NT}\). These two correlations are strong during periods of corotating interaction regions and high-speed streams, and moderate during intervals of slow solar wind. The results indicate that the magnetic pressure in the solar wind is well correlated both with the plasma dynamic pressure and the thermal pressure.     

Nonlinear pulsations of stars with initial mass 3 $${M_ \odot }$$ on the asymptotic giant branch

Pulsation period changes in Mira type variables are investigated using the stellar evolution and nonlinear stellar pulsation calculations. We considered the evolutionary sequence of stellar models with initial mass \({M_{ZAMS}} = \;3{M_ \odot }\) and population I composition. Pulsations of stars in the early stage of the asymptotic giant branch are shown to be due to instability of the fundamental mode. In the later stage of evolution when the helium shell source becomes thermally unstable the stellar oscillations occur in either the fundamental mode (for the stellar luminosuty \(L < 5.4 \times {10^3}{L_ \odot }\)) or the first overtone (\(L > 7 \times {10^3}{L_ \odot }\)). Excitation of pulsations is due to the κ-mechanism in the hydrogen ionization zone. Stars with intermediate luminosities \(5.4 \times {10^3}{L_ \odot } < L < 7 \times {10^3}{L_ \odot }\) were found to be stable against radial oscillations. The pulsation period was determined as a function of evolutionary time and period change rates \(\dot \Pi \) were evaluated for the first ten helium flashes. The period change rate becomes the largest in absolute value \((\dot \Pi /\Pi \approx - {10^{ - 2}}y{r^{ - 1}})\) between the helium flash and the maximum of the stellar luminosity. Period changes with rate \(\left| {\dot \Pi /\Pi } \right| \geqslant - {10^{ - 3}}y{r^{ - 1}}\) take place during ≈500 yr, that is nearly one hundredth of the interval between helium flashes.     

Anisotropic new holographic dark energy model in Saez–Ballester theory of gravitation

This work is devoted to the investigation of new holographic dark energy (infrared cutoff is the Hubble radius) in locally rotationally symmetric Bianchi type-\(I\) universe within the framework of Saez–Ballester (Phys. Lett. A 113:467, 1986) scalar–tensor theory of gravitation. We construct interacting and non-interacting dark energy models by solving the field equations using a relationship between the metric potentials. This leads to a variable deceleration parameter model which exhibits a transition of the universe from deceleration to acceleration. We evaluate various cosmological parameters of our models. We have observed that the energy density parameters, equation of state and important cosmological planes (\(\omega _{\mathit{de}} - \omega _{\mathit{de}}'\) and \(r - s\)) yield the results compatible with the modern observational data. We have, also, discussed the stability analysis of our models.