Narrow Results

The IceCube Observatory at the South Pole is composed of a cubic kilometer scale neutrino telescope buried beneath the icecap and a square-kilometer surface water Cherenkov tank detector array known as IceTop. The combination of the surface array with the in-ice detector allows the dominantly electromagnetic signal of air showers at the surface and their high-energy muon signal in the ice to be measured in coincidence. This ratio is known to carry information about the nuclear composition of the primary cosmic rays. This paper reviews the recent results from cosmic-ray measurements performed with IceTop/IceCube: energy spectrum, mass composition, anisotropy, search for PeV γ sources, detection of high energy muons to probe the initial stages of the air shower development, and study of transient events using IceTop in scaler mode.

Recently, an anisotropic cosmological model was proposed. An arbitrary one-form, which picks out a privileged axis in the universe, was added to the Friedmann–Robertson–Walker (FRW) line element. The distance-redshift relation was modified such that it is direction-dependent. In this paper, we use the Union2 dataset and 59 high-redshift gamma-ray bursts (GRBs) to give constraints on the anisotropy of the universe. The results show that the magnitude of anisotropy is about D = -0.044±0.018, and the privileged axis points toward the direction (l₀, b₀) = (306.1°±18.7°, -18.2°±11.2°) in the galactic coordinate system. The anisotropy is small and the isotropic cosmological model is an excellent approximation.

This paper is devoted to identify some physical causes of energy density inhomogeneity and stability of self-gravitating relativistic fluids in plane symmetry such as Weyl tensor, local anisotropy, dissipative terms and their specific combination. We first develop a relationship between matter variables and the Weyl tensor and then formulate dynamical equations using Bianchi identities. For the non-dissipative dust fluid, we conclude that the system will remain homogeneous if and only if it is conformally flat which implies the shear-free condition. However, the converse is not true for the non-dissipative isotropic fluid. For non-dissipative anisotropic fluid, the inhomogeneity factor is identified to be one of the structure scalars. A particular case of geodesic with dissipation is also discussed.

A new conformally non-flat interior spacetime embedded in five-dimensional (5D) pseudo Euclidean space is explored in this paper. We proceed our calculation with the assumption of spherically symmetric anisotropic matter distribution and Karmarkar condition (necessary condition for class one). This solution is free from geometrical singularity and well-behaved in all respects. We ansatz a new type of metric potential $g_{11}$ and solve for the metric potential $g_{00}$ via Karmarkar condition. Further, all the physical parameters are determined from Einstein’s field equations using the two metric potentials. All the constants of integration are determined using boundary conditions. Due to its conformally non-flat character, it can represent bounded configurations. Therefore, we have used it to model two compact stars Vela X-1 and Cyg X-2. Indeed, the obtained masses and radii of these two objects from our solution are well matched with those observed values given in [T. Gangopadhyay et al., Mon. Not. R. Astron. Soc.431, 3216 (2013)] and [J. Casares et al., Mon. Not. R. Astron. Soc.401, 2517 (2010)]. The equilibrium of the models is investigated from generalized TOV-equation. We have adopted [L. Herrera’s, Phys. Lett. A165, 206 (1992)] method and static stability criterion of Harisson–Zeldovich–Novikov [B. K. Harrison et al., Gravitational Theory and Gravitational Collapse (University of Chicago Press, 1965); Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics, Vol. 1, Stars and Relativity (University of Chicago Press, 1971)] to analyze the stability of the models.

This paper studies the gravitational collapse of charged anisotropic spherical stellar objects in $f({𝒢})$ gravity. For this purpose, we derive dynamical equations by considering Misner–Sharp mechanism and explore physical impact of charge, anisotropy and effective pressure on the rate of collapse. We establish the relationship between matter variables, Weyl tensor and the Gauss–Bonnet (GB) terms. For constant value of $f({𝒢})$, it turns out that conformal flatness condition is no longer valid due to the effect of anisotropic factor in the present scenario. To obtain conformally flat metric, we impose the condition of isotropic matter distribution which provides energy density homogeneity and conformal flatness of the metric. We conclude that GB terms lead to decrease in the collapse rate due to their anti-gravitational effects.

This paper is devoted to examine the cracking of spherically symmetric anisotropic fluid configuration for polytropic equation of state. For this purpose, we formulate the corresponding field equations as well as generalized Tolman–Oppenheimer–Volkoff equation. We introduce density perturbations in matter variables and then construct the force distribution function. In order to examine the occurrence of cracking/overturning, we consider two models corresponding to two values of the polytropic index. It is found that the first model exhibits overturning for the considered values of polytropic constant while the second model neither exhibits cracking nor overturning for larger values of polytropic constant.

In this research paper, we address the issues of expansion and gravitational collapse of anisotropic spherical source in the presence of cosmological constant. For this purpose, we have solved the Einstein field equations with gravitating source and cosmological constant. The absence of radial heat flux in the gravitating source provide the parametric form of two-metric functions in terms of a single-metric function. The expansion scalar and the mass function of the gravitating source is evaluated for the given metric. The trapping condition is applied to mass function which implies the existence of horizons, like the horizons of Schwarzschild de-Sitter black holes. The trapping condition provides the parametric form of the unknown metric function. The value of expansion scalar has been analyzed in detail to see its positivity and negativity, which correspond to expansion and collapse, respectively. So, the values of parameter $\alpha$ for which expansion scalar is positive have been used to analyze the other physical variables including density, pressures and anisotropy. The same quantities have been evaluated for the values of $\alpha$ that result in the negative values of expansion scalar leading to collapse. The effects of positive cosmological constant have been noted in both expansion and collapse solutions. Due to the presence of cosmological constant after collapse, there would occur inner and outer horizons or a unique horizon depending on the value of mass of the gravitating source.

In this paper, we present new physically viable interior solutions of the Einstein field equations for static and spherically symmetric anisotropic compact stars satisfying the Karmarkar condition. For presenting the exact solutions, we provide a new suitable form of one of the metric potential functions. Obtained solutions satisfy all the physically acceptable properties of realistic fluid spheres and hence solutions are well-behaved and representing matter distributions are in equilibrium state and potentially stable by satisfying the TOV equation and the condition on stability factor, adiabatic indices. We analyze the solutions for two well-known compact stars Vela X-1 (Mass = 1.77 M${}_{\odot }$, R = 9.56 km) and Cen X-3 (Mass = 1.49 M${}_{\odot }$, R = 9.17 km).

The objective of this work is to explore a new parametric class of exact solutions of the Einstein field equations coupled with the Karmarkar condition. Assuming a new metric potential $e^{\lambda (r)}$ with parameter (n), we find a parametric class of solutions which is physically well-behaved and represents compact stellar model of the neutron star in Vela X-1. A detailed study specifically shows that the model actually corresponds to the neutron star in Vela X-1 in terms of the mass and radius. In this connection, we investigate several physical properties like the variation of pressure, density, pressure–density ratio, adiabatic sound speeds, adiabatic index, energy conditions, stability, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent conformity with the already available evidences in theory. Further, we study the variation of physical properties of the neutron star in Vela X-1 with the parameter (n).

In this paper, we searched two new exact solutions of Einstein’s field equations for modeling of compact cold stars using embedded class one spacetime continuum. We find out the expressions for pressure, density, anisotropy, redshift, metric potentials and other physical variables in terms of algebraic and trigonometric expressions and observe that all variables show well-behaved trends inside the compact stellar configurations. The causality condition is well maintained by our stellar models, i.e. the radial velocity and transverse velocity are less than l. The stability of our models is assessed via different stability criteria. The Buchdahl condition holds good for our solution. Herrera’s cracking method is applied to check the stability of stellar models. We generate anisotropic compact star models, whose masses and radii are in close agreement with the observed values for compact stars 4U 1538-52, LMCX-4, PSRJ1614-2230. A comparative analysis of the proposed models is carried out based on two different solutions reported in the paper. The appropriate graphical analysis is provided to authenticate the viability of the models.

In this paper, we consider a non-static cylindrically symmetric self-gravitating system with anisotropic matter configuration and investigate its stability regions by using a homogenous model. We establish perturbed form of dynamical equations by using Eulerian and Lagrangian approaches. The conservation of baryon number is applied to obtain adiabatic index as well as perturbed pressure. A variational principle is used to find characteristic frequency which helps to compute the instability criteria. It is found that dynamical instability can be prevented till the radius of a cylinder exceeds the limit R$>$18. We conclude that the system becomes unstable against radial oscillations as the radial pressure increases relative to tangential pressure.

We consider a spatially homogeneous and anisotropic Bianchi type-I universe which is filled by pressureless dark matter (DM) and Tsallis holographic dark energy (THDE). We assume the two dark components of the universe are interacting with each other throughout a sign-changeable mutual interaction term. Various infra-red (IR) cutoffs are studied, and it is obtained that all models display classical instability by themselves at the future $(z\to -1)$. Moreover, we find out that some models can cross the phantom line. In order to have a more comprehensive study, the statefinder diagnostic and the ${\omega }_D-{\omega }_D^{\prime }$ plane are also investigated showing that the model parameters significantly affect the evolution trajectories in the $r-s$ and ${\omega }_D-{\omega }_D^{\prime }$ planes.

This paper is devoted to formulating exact solutions of axially symmetric spacetime through gravitational decoupling technique. For this purpose, we first evaluate an exact solution in the framework of cosmic strings by assuming some additional constraints on the metric coefficients and extend it to obtain two concrete anisotropic cosmological models. We investigate energy conditions as well as the speed of sound constraint to ensure the physical viability of the developed solutions. It is concluded that both anisotropic models meet all the energy bounds as well as stability criterion. The expanding behavior of the universe is also confirmed through different cosmological parameters.

In this paper, we explore a family of exact solutions to the Einstein field equations (EFEs) describing a spherically symmetric, static distribution of fluid spheres with pressure anisotropy in the setting of embedding class one spacetime continuum. A detailed theoretical analysis of this class of solutions for compact stars PSR J16142230, Her X-1, LMC X-4 and 4U 1538-52 is carried out. The solutions are verified by examining various physical aspects, viz., anisotropy, gravitational redshift, causality condition, equilibrium (TOV-equation), stable static criterion and energy conditions, in connection to their cogency. Due to the well-behaved nature of the solutions for a large range of positive real $n$ values, we develop models of above stellar objects and discuss their behavior with graphical representations of the class of solutions of the first two objects extensively. The solutions studied by Fuloria [Astrophys. Space Sci.362, 217 (2017)] for $n=4$ and Tamta and Fuloria [Mod. Phys. Lett. A34, 2050001 (2019), https://doi.org/10.1142/S0217732320500017] for $n=8,12$ are particular cases of our generalized solution.

In this paper, we provide a new parametric class of solutions to Einstein–Maxwell field equations to study the relativistic structure of a compact star via embedding class I condition. The interior of the star is delineated by Karmarkar condition and at the boundary of the star, we match the class of solutions with Bardeen and Reissner–Nordstrom exterior spacetimes. We assume one of the metric potentials as $e^{\lambda (r)}=1+c_1{r}^2{\mathrm{\text{csc}}}^n(1+c_2{r}^2)$ to obtain other metric potential. Subsequently, we solve Maxwell field equations. We verify and compare all the thermodynamic properties like matter density, anisotropy, radial and tangential pressures, compactification factor, energy conditions, and stability conditions, namely, adiabatic index, balancing forces via modified TOV equations, Harrision–Zeldovich criteria, casualty condition, Herrera cracking condition, etc., of our class of charged solutions. All the physical and stability conditions are with the viable trend throughout the interior of the stellar object. For a suitable range of values of $n$ and parameters, it is depicted from this study that the present class of charged solutions yields effective results to obtain realistic and viable modeling of the neutron star in EXO 1785-248 in both the Bardeen and Reissner–Nordstrom exterior spacetimes.

This paper is devoted for the formulation of new anisotropic solutions for non-static spherically symmetric self-gravitating systems through gravitational decoupling technique. Initially, we add a gravitational source in the perfect matter distribution for inducing the effects of anisotropy in the considered model. We then decouple the field equations through minimal geometric deformation approach and derive three new anisotropic solutions. Among these, two anisotropic solutions are evaluated by applying specific constraints on anisotropic source and the third solution is obtained by employing the barotropic equation of state. The physical acceptability and stability of the anisotropic models are investigated through energy conditions and causality condition, respectively. We conclude that all the derived anisotropic solutions are physically viable as well as stable.

A new compact stars nonsingular model is presented with the generalized Bardeen–Hayward mass function. Generalized Bardeen–Hayward described the regular black hole, however, due to its regularity or nonsingular nature we were inspired to construct an anisotropic compact stars model. Along with the ansatz mass function, we coupled it with a linear equation of state (EoS) to find the solutions of field equations. Indeed, the new solutions are physically viable in all physical ground. The energy conditions and Tolman–Oppenheimer–Volkoff (TOV)-equation are well satisfied signifying that the mass distribution is physically possible and at equilibrium. Also, the static stability criterion, the causality condition and Abreu’s stability condition hold good and therefore configurations are physically static stable. The same condition is further supported by the condition that the adiabatic index, which is greater than the Newtonian limit, i.e. ${\mathrm{\Gamma }}_r(r)>4/3$. It is also noticed that the bag constant $B_g$ is proportional to the surface density in our model.

This paper explores a new embedding anisotropic charged version of a solution to Einstein–Maxwell field equations in four-dimensional spacetime through the Karmarkar conditions and the gravitational decoupling via minimal geometric decoupling (MGD) technique by choosing Pant’s interior solution [Astrophys. Space Sci. 331, 633 (2011)] as a seed solution to coupled system. Later, we integrate the coupled system within the MGD and explore a family of solutions to represent the realistic structure of nonrotating compact objects. Through the matching of the interior solutions so obtained to the exterior Reissner–Nordström metric, we tune the arbitrary constants for feasible models. After that, we subject our model to a rigorous test for a chosen parameter space to verify the physical viability of the solution for the neutron stars in EXO 1785-248 for a range of values of the decoupling constant $\sigma$. Further, we prove that the constant $\sigma$ is inherently connected to critical physical properties such as the gravitational and surface redshifts, compactification factor, mass/radius relation, etc., of the same compact star candidate EXO 1785-248. The solutions thus obtained exhibit physically viable features which are thoroughly demonstrated through graphical plots.

The main objective of this paper is to examine the physical features and stability of anisotropic compact stellar objects in energy–momentum squared gravity. For this purpose, we apply Krori–Barua metric solutions and consider three different models of this modified theory to examine the physical characteristics of Her X-1, 4U 1538-52 and SAX J1808.4-3658 compact stars. We analyze the behavior of various physical quantities such as energy density, pressure components, energy conditions, equation of state parameter and anisotropic factor in the interior of these stars. We then use the estimated values of the sound speed and of the adiabatic index to explore the stability of these compact stars. It is found that all the required conditions are satisfied corresponding to all the selected models. We are therefore allowed to conclude that this modified theory provides viable and stable anisotropic compact stars.

According to standard cosmology, the universe is homogeneous and isotropic at large scales. However, some anisotropies can be observed at the local scale in the universe through various ways. Here, we have studied the Bianchi Type I model by customizing the scale factors to understand the anisotropic nature of the universe. We have considered two cases with slight modifications of scale factors in different directions in the generalized Bianchi Type I metric equation, and compared the results with the $\mathrm{\Lambda }$CDM model and also with available cosmological observational data. Through this study, we also want to predict the possible degree of anisotropy present in the early universe and its evolution to current time by calculating the value of density parameter for anisotropy $({\mathrm{\Omega }}_{\sigma })$ for both low and high redshift $(z)$ along with the possible relative anisotropy that exist among different directions. It is found that there was a relatively higher amount of anisotropy in the early universe and the anisotropic nature of the universe vanishes at the near past and the present epochs. Thus, at near past and present stages of the universe there is no effective distinction between this anisotropic model and the standard $\mathrm{\Lambda }$CDM model.