Narrow Results

We find a wide variety of exact classical solutions to Yang–Mills–Chern–Simons theory coupled to an external source, ranging periodic ones to localised soliton type. The solutions are found by choosing an ansatz, which reduces the classical equation of motion to a set of coupled non-linear ordinary differential equations, which are then solved. It is seen that these classical solutions necessarily exist over a non-zero background field whose intensity is controlled by external source strength.

Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectrum is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agreement with the ones given in the literature. The numerical results are also given in a table for different parameter values.

We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann–Robertson–Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton–Jacobi equation solving the field equations. The equation relates a solution "generating function" with the scalar potential. We analyze its stability and find a later time attractor which describes a Universe approaching to an eternal-de Sitter inflation driven by the potential energy, V₀>0. The attractor exists when the potential is regular and does not have a linear and quadratic terms of the field. When the potential has a mass term, the attractor exists if the scalar field is in a symmetric phase and is weakly coupled, λ<9V₀/16. We also find that the attractor property is intact under small modifications of the potential. If the scalar field has a positive mass-squared or is strongly coupled, there exists a quasi-attractor. However, the quasi-attractor property disappears if the potential is modified. On the whole, the appearance of the eternal inflation is not rare in scalar cosmology in the presence of an attractor.

A test particle moving along geodesic line in a spacetime has three physical propagating degrees of freedom and one unphysical gauge degree. We relax the requirement of geodesic completeness of a spacetime. Instead, we require test particles trajectories to be smooth and complete only for physical degrees of freedom. Test particles trajectories for Einstein–Rosen bridge are proved to be smooth and complete in the physical sector, and particles can freely penetrate the bridge in both directions.

In this paper, we are looking for the exponential solutions (i.e. the solutions with the scale factors change exponentially over time) in the Einstein–Gauss–Bonnet (EGB) gravity. We argue that we found all possible nonconstant-volume solutions (up to permutations) in lower dimensions ((4+1) and (5+1)) and developed a scheme which allows one to find necessary conditions in arbitrary dimension.

We study Dirac neutrinos propagating in rotating background matter. First we derive the Dirac equation for a single massive neutrino in the non-inertial frame, where matter is at rest. This equation is written in the effective curved spacetime corresponding to the co-rotating frame. We find the exact solution of the Dirac equation. The neutrino energy levels for ultrarelativistic particles are obtained. Then we discuss several neutrino mass eigenstates, with a nonzero mixing between them, interacting with rotating background matter. We derive the effective Schrödinger equation governing neutrino flavor oscillations in rotating matter. The new resonance condition for neutrino oscillations is obtained. We also examine the correction to the resonance condition caused by the matter rotation.

We study the motion of relativistic fermions in a time-dependent electromagnetic field within the framework of Dirac equation. We consider the time-dependent scalar potential of the exponential form and the vector potential of linear form. We obtain the eigenfunctions and eigenvalues.

Without reference to exotic sources construction of viable wormholes in Einstein’s general relativity remained ever a myth. With the advent of modified theories, however, specifically the f(R) theory, new hopes arose for the possibility of such objects. From this token, we construct traversable wormholes in f(R) theory supported by a fluid source which respects at least the weak energy conditions. We provide an example (Example 1) of asymptotically flat wormhole in f(R) gravity without ghosts.

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).

We find that the analytical solutions to quantum system with a quartic potential $V(x)=a{x}^2+b{x}^4$ (arbitrary $a$ and $b>0$ are real numbers) are given by the triconfluent Heun functions $H_T(\alpha ,\beta ,\gamma ;z)$. The properties of the wave functions, which are strongly relevant for the potential parameters $a$ and $b$, are illustrated. It is shown that the wave functions are shrunk to the origin for a given $b$ when the potential parameter $a$ increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter $\left|a\right|$ increases or parameter $b$ decreases for a given negative potential parameter $a$. The minimum value of the double well case ($a<0$) is given by $V_{\mathrm{\text{min}}}=-a^2/(4b)$ at $x=\pm \sqrt{\left|a\right|/2b}$.

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.

Recently literature is found to be enriched with studies related to anisotropic behaviors of different compact stars in the background of $f(T)$ gravity in different energy conditions. Quintessence field, as local impacts of cosmic acceleration upon the compact stars, is also very interesting in recent studies. In this paper, the quintessential field effects on the compact stars (mainly on the neutron stars with an wide range of mass distributions), repulsive gravitational effects inside the compact stars due to dark matter distribution in them, charge distribution inside them in strong energy condition, etc. are studied. All required equations of motion using anisotropic property and concept of Massachusetts Institute of Technology bag model are acquired. Black holes surrounded by quintessential matters which satisfy the additive and linearity conditions, with the form of energy tensors were proposed and the corresponding metric was derived by Kiselev.¹ The metric, described by Krori and Barua² with Reissner–Nordström metric³ are compared to find out the different numerical values of unknown parameters. The numerical values are derived and some important parameters like anisotropic stress, adiabatic constant, surface redshift, electric intensity, compactness factor, stability etc. are analyzed deeply to get a clear idea for further study on these types of stars and to understand their nature.

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.

In astronomy, the study of compact stellar remnants — white dwarfs, neutron stars, black holes — has attracted much attention for addressing fundamental principles of physics under extreme conditions in the core of compact objects. In a recent argument, Maurya et al. [Eur. Phys. J. C 77, 45 (2017)] have proposed an exact solution depending on a specific spacetime geometry. Here, we construct equilibrium configurations of compact stars for the same spacetime that make it interesting for modeling high density physical astronomical objects. All calculations are carried out within the framework of the five-dimensional Einstein–Gauss–Bonnet gravity. Our main interest is to explore the dependence of the physical properties of these compact stars depending on the Gauss–Bonnet coupling constant. The interior solutions have been matched to an exterior Boulware–Deser solution for $5D$ spacetime. Our finding ensures that all energy conditions hold, and the speed of sound remains causal, everywhere inside the star. Moreover, we study the dynamical stability of stellar structure by taking into account the modified field equations using the theory of adiabatic radial oscillations developed by Chandrasekhar. Based on the observational data for radii and masses coming from different astronomical sources, we show that our model is compatible and physically relevant.

In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on one of the scalar fields. Instead of choosing these functions phenomenologically here, they are evaluated assuming the existence of Noether symmetry. By appropriate choice of a point transformation in the augmented space, one of the variables in the Lagrangian becomes cyclic and the evolution equations become much simpler to have solutions. Finally, the solutions are analyzed from cosmological view point.

This paper provides a simplified description for simulating the coupling of dark energy with baryonic matter by considering a super-dense pulsar PSRJ1614-2230 as the model star. The starting equation of state for modeling the dark energy is motivated by the MIT Bag model for spherically confined hadrons and the observational evidences of its repulsive nature. Einstein field equations are solved in the stellar interior using the generalized framework of Tolman–Kuchowicz spacetime metric. The solutions are then analyzed for various physical parameters such as metric potential, pressure, density, energy conditions, etc. The physical analysis of multiple parameters indicates stable star formation. The proposed stellar model is free from all singularities and also meets the requisite stability criteria. The numerical results obtained for relativistic adiabatic index indicate that the model star is stiff and stable against radially induced adiabatic perturbations.

In [Phys. Rev. D 107, 104008 (2023)], we reported a novel exact closed-form solution which describes asymptotically flat spacetimes in pure ${{ℛ}}^2$ gravity. The solution is Ricci scalar flat, viz. ${ℛ}\equiv 0$ everywhere. Whereas any metric with a null Ricci scalar would trivially satisfy the ${{ℛ}}^2$ vacuo field equation, ${ℛ}({{ℛ}}_{\mu \nu }-\frac{1}{4}{g}_{\mu \nu }{ℛ})+g_{\mu \nu }\square {ℛ}-{\nabla }_{\mu }{\nabla }_{\nu }{ℛ}=0$, in this paper, we shall show that our solution satisfies a “stronger” version of the ${{ℛ}}^2$ vacuo field equation, viz. ${{ℛ}}_{\mu \nu }-\frac{1}{4}{g}_{\mu \nu }{ℛ}+{{ℛ}}^{-1}(g_{\mu \nu }\square {ℛ}-{\nabla }_{\mu }{\nabla }_{\nu }{ℛ})=0$, despite the term ${{ℛ}}^{-1}$ being singular. Even though ${ℛ}$ identically vanishes, for our solution, the combinations ${{ℛ}}^{-1}{\nabla }_{\mu }{\nabla }_{\nu }{ℛ}$ and ${{ℛ}}^{-1}\square {ℛ}$ are free of singularity. This exceptional property sets our solution apart from the set of null-Ricci-scalar metrics and makes it a genuinely nontrivial solution. We further demonstrate that, as a member of a larger class of asymptotically de Sitter metrics, our solution is resilient against perturbations in the scalar curvature at largest distances, making it relevant for physical situations where the background deviates from asymptotic flatness.

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

We obtain the analog of collapsing Vaidya-like solution to include both a null fluid and a string fluid, with a linear equation of state (p_⊥ = kρ), in nonspherical (plane symmetric and cylindrically symmetric) anti-de Sitter space–times. It turns out that the nonspherical collapse of two fluid in anti-de Sitter space–times, in accordance with cosmic censorship, proceed to form black holes, i.e. on naked singularity ever forms, in accordance with cosmic censorship, violating hoop conjecture.

In this paper, we present a new exact solution for scalar field with cosmological constant in cylindrical symmetry. Associated cosmological models, including a model that describes a cyclic universe, are discussed.