New Class Of Exact Solutions Research Articles

Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

Integrability, Similarity Reductions and New Classes of Exact Solutions for (3+1)-D Potential Yu–Toda–Sasa–Fukuyama Equation

Solutions with pure radiation and gyratons in 3D massive gravity theories

We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in 2 + 1 dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e. with possibly non-zero T uu and T ux in canonical coordinates. Since any ‘reasonable’ geometry in 3D (i.e. admitting a null geodesic congruence) is either expanding Robinson–Trautman ( Θ≠0 ) or Kundt ( Θ=0 ), we focus on these two classes. Assuming expansions Θ=1/r (‘GR-like’ Robinson–Trautman) or Θ=0 (general Kundt), we systematically integrate the field equations of TMG and NMG and identify new classes of exact solutions. The case of NMG contains an additional assumption of g ux being quadratic in r, which is automatically enforced in TMG as well as in 3D GR. In each case, we reduce the field equations as much as possible and identify new classes of solutions. We also discuss various special subclasses and study some explicit solutions.

Anisotropic compact stellar objects with a slow rotation effect

A new class of exact solutions depicting anisotropic compact objects is presented in the current work. This spherically symmetric matter distribution assumes a specific form of anisotropy to obtain the exact solution for the field equations. The obtained interior solutions are smoothly matched with the Schwarzschild exterior metric over the bounding surface of a compact star and together with the condition that the radial pressure vanishes at the boundary, the form of the model parameters are attained. One of the interesting features of the obtained solutions is the codependency of the metric potentials. We have considered the pulsar 4U1608-52 with its current estimated data (mass =1.57-0.29+0.30M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$=1.57^{+0.30}_{-0.29} ~M\\odot $$\\end{document} and radius =9.8±1.8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$=9.8 \\pm 1.8$$\\end{document} km [Özel in Astrophys J 820(1):28, 2016]) to study the model graphically. Moreover, we have studied the physical features and some important stability conditions for the model. Tabular comparison with other known pulsars infers that the obtained model represents a compact star within a radius of 8–12 km. Finally, we have found the angular momentum that causes the dragging of inertial frames of the slowly rotating equilibrium compact objects.

A New Class of Exact Solutions for Magnetohydrodynamics Equations to Describe Convective Flows of Binary Liquids

A New Class of Exact Solutions for Magnetohydrodynamics Equations to Describe Convective Flows of Binary Liquids

A New Class of Exact Solutions to Magnetohydrodynamics Equations for Describing Convective Flows of Binary Fluids

A New Class of Exact Solutions to Magnetohydrodynamics Equations for Describing Convective Flows of Binary Fluids

Study of a Minimally Deformed Anisotropic Solution for Compact Objects with Massive Scalar Field in Brans–Dicke Gravity Admitting the Karmarkar Condition

In the present paper, we focused on exploring the possibility of providing a new class of exact solutions for viable anisotropic stellar systems by means of the massive Brans–Dicke (BD) theory of gravity. In this respect, we used the decoupling of gravitational sources by minimal geometric deformation (MGD) (e−η=Ψ+βh) for compact stellar objects in the realm of embedding class-one space-time to study anisotropic solutions for matter sources through the modified Einstein field equations. For this purpose, we used the ansatz for Ψ relating to the prominent, well-known and well-behaved Finch–Skea model via Karmarkar condition, and the determination scheme for deformation function h(r) was proposed via mimic requirement on radial pressure component: θ11(r)=pr(r) and matter density: θ00(r)=ρ(r) for the anisotropic sector. Moreover, we analyzed the main physical highlights of the anisotropic celestial object by executing several physical tests for the case θ11(r)=pr(r). We have clearly shown how the parameters α, β and ωBD introduced by massive BD gravity via the MGD approach incorporating the anisotropic profile of the matter distribution have an immense effect on many physical parameters of compact bodies such as LMC X-4, LMC X-4, Her X-1, 4U 1820-30, 4U 1608-52, SAX J1808.4–658 and many others that can be fitted.

Analysis of the boundary condition and equation of state in radiating stars

A model of a radiating star undergoing gravitational collapse is constructed by systematically studying both the boundary condition and equation of state for the first time. The resulting system of partial differential equations is analysed using Lie symmetries. The group analysis produces new classes of exact solutions with acceleration, expansion and shear in the presence of the cosmological constant. Known exact solutions are recovered as special cases of our solutions. In particular, we regain the Euclidean star model which is the relativistic version of the Newtonian star. The range of the equation of state parameters allows the solution to be interpreted as barotropic matter stars or dark energy stars. A particular case shows that the model is physically reasonable and the energy conditions are satisfied.

Effects of electric field and anisotropy on the mass-radius relationship of a particular class of compact stars

For a static, spherically symmetric, anisotropic and charged distribution of matter, we present a new class of exact solutions to the Einstein-Maxwell system. By assuming specific forms of the electric field and anisotropy, we transform the master equation of the Einstein-Maxwell system to Bessel and modified Bessel differential equations. The subsequent solutions turn out to be generalizations of the isotropic and uncharged stellar model of Finch and Skea (1989), the isotropic and charged stellar model of Hansraj and Maharaj (2006) and the anisotropic and charged stellar model of Maharaj et al. (2017). We analyze the physical viability of the solutions and utilize one particular class of solutions to examine the effects of charge and anisotropy on the mass-radius relationship of compact stars.

New exact models of ideal gas in 5D EGB using curvature coordinates

Exploiting the use of curvature coordinates (also called Schwarzschild coordinates), new classes of exact solutions are discovered. By prescribing the timelike potential two new solutions are found one of which displays all the necessary qualitative features demanded of closed compact astrophysical objects. Since the analysis reduces to a single first order nonlinear differential equation, the single integration constant is obtained in terms of the mass and radius through matching of the interior and exterior metrics. Invoking the second matching condition results in constraining the value of the Gauss–Bonnet coupling constant in terms of the mass and radius of the star. Stability, causality and energy conditions are satisfied for a suitable choice of parameter space. In attempting to specify the radially oriented potential it was only possible to find a defective spacetime and to regain the interior Schwarzschild metric for an incompressible fluid sphere.

A new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics

Abstract In this paper, by using invariants of Riemann and general solutions of Euler–Poisson–Darboux–Riemann equations, a new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics is given.

A New Class of Exact Solutions to the Navier–Stokes Equations with Allowance for Internal Heat Release

A New Class of Exact Solutions to the Navier–Stokes Equations with Allowance for Internal Heat Release

Stellar models with generalized polytropic equation of state

We find new classes of exact solutions to the Einstein field equations where the matter distribution satisfies a generalized polytropic equation of state. The matter distribution is uncharged with anisotropic pressures. Equations of state for polytropes and quark matter are contained as special cases. The matter variables and metric potentials can be obtained explicitly. Known solutions, for the choice of the gravitational potential made in this analysis, arise as special cases for particular choice of the equation of state parameters. A detailed physical analysis indicates that the model is well behaved.

Self-gravitating anisotropic model in general relativity under modified Van der Waals equation of state: a stable configuration

The purpose of this paper consists in presenting models of compact stars described by a new class of exact solutions to the field equations, in the context of general relativity, for a fluid configuration which is locally anisotropic in the pressure. With current sensitivities, we considered a non-linear form of modified Van der Waals equation of state viz., p_{r}=alpha rho ^{2} +frac{beta rho }{1+gamma rho }, as well as a gravitational potential Z(x) as a generating function by exploiting an anisotropic source of matter which served as a basis for generating the confined compact stars. The exact solutions are formed by correlating an interior space-time geometry to an exterior Schwarzschild vacuum. Then, we analyze the physical viability of the model generated and compare it with observational data of some heavy pulsars coming from the Neutron Star Interior Composition Explorer. The model satisfies all the required pivotal physical and mathematical properties in the compact structures study, offering empirical evidence in support of the evolution of realistic stellar configurations. It is shown to be regular, viable, and stable under the influence generated by the parameters coming from the theory namely, alpha , beta , gamma , delta , everywhere within the astral fluid in the investigated high-density regime that supports the existence of realistic heavy pulsars such as PSR J0348+0432, PSR J0740+6620 and PSR J0030+0451.

A New Class of Exact Solutions to the Navier-Stokes Equations with Allowance Made for Internal Heat Release

A New Class of Exact Solutions to the Navier-Stokes Equations with Allowance Made for Internal Heat Release

New, Spherical Solutions of Non-Relativistic, Dissipative Hydrodynamics.

We present a new family of exact solutions of dissipative fireball hydrodynamics for arbitrary bulk and shear viscosities. The main property of these solutions is a spherically symmetric, Hubble flow field. The motivation of this paper is mostly academic: we apply non-relativistic kinematics for simplicity and clarity. In this limiting case, the theory is particularly clear: the non-relativistic Navier–Stokes equations describe the dissipation in a well-understood manner. From the asymptotic analysis of our new exact solutions of dissipative fireball hydrodynamics, we can draw a surprising conclusion: this new class of exact solutions of non-relativistic dissipative hydrodynamics is asymptotically perfect.

Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies

We investigate classical and quantum geometric information flow theories (respectively, GIFs and QGIFs) when the geometric flow evolution and field equations for nonholonomic Einstein systems, NES, are derived from Perelman-Lyapunov type entropic type functionals. In this work, the term NES encodes models of gravitational and matter fields interactions and their geometric flow evolution subjected to nonholonomic (equivalently, non-integrable, anholonomic) constraints. There are used canonical geometric variables which allow a general decoupling and integration of systems of nonlinear partial differential equations describing GIFs and QGIFs and (for self-similar geometric flows) Ricci soliton type configurations. Our approach is different from the methods and constructions elaborated for special classes of solutions characterized by area--hypersurface entropy, related holographic and dual gauge--gravity models, and conformal field theories, involving generalizations of the Bekenstein-Hawking entropy and black hole thermodynamics. We formulate the theory of QGIFs which in certain quasi-classical limits encodes GIFs and models with flow evolution of NES. There are analysed the most important properties (inequalities) for NES and defined and computed QGIF versions of the von Neumann, relative and conditional entropy; mutual information, (modified) entanglement and R\'{e}nyi entropy. We construct explicit examples of generic off-diagonal exact and parametric solutions describing stationary solitonic gravitational hierarchies and deformations of black hole configurations. Finally, we show how Perelman's entropy and geometric thermodynamic values, and extensions to GIF and QGIF models can be computed for various new classes of exact solutions which cannot be described following the Bekenstein-Hawking approach.

Решения нелинейной параболической системы второго порядка, моделирующие движение диффузионной волны

The paper continues a long series of our research and considers a secondorder nonlinear evolutionary parabolic system. The system can be a model of various convective and diffusion processes in continuum mechanics, including mass transfer in a binary mixture. In hydrology, ecology, and mathematical biology, it describes the propagation of pollutants in water and air, as well as population dynamics, including the interaction of two different biological species. We construct solutions that have the type of diffusion (heat) wave propagating over a zero background with a finite velocity. Note that the system degenerates on the line where the perturbed and zero (unperturbed) solutions are continuously joined. A new existence and uniqueness theorem is proved in the class of analytical functions. In this case, the solution has the desired type and is constructed in the form of characteristic series, the convergence of which is proved by the majorant method. We also present two new classes of exact solutions, the construction of which, due to ansatzes of a specific form, reduces to integrating systems of ordinary differential equations that inherit a singularity from the original formulation. The obtained results are expected to be helpful in modeling the evolution of the Baikal biota and the propagation of pollutants in the water of Lake Baikal near settlements

A Reissner-Nordström+Λ Black Hole in the Friedman-Robertson-Walker Universe

A charged, non-rotating, spherically symmetric black hole which has cosmological constant $\Lambda$ (Reissner-Nordstr\"om+$\Lambda$ or RN+$\Lambda$), active gravitational mass $M$ and electric charge $Q$ is studied with exterior Friedman-Robertson-Walker (FRW) universe in (2+1) dimensional spacetime. We find a new classes of exact solutions of the charged black hole where the generalized Birkoff's theorem is assumed to be valid. It is found that the cosmological constant is negative inside the black hole. We confirm it from the geodesic equations too. The cosmological constant is found to be dependent on $R, Q$ and $a(v)$ which correspond to the areal radius, charge, of the black hole and the scale factor of the universe respectively. We note that the expansion of the universe affects the size and the mass of the black hole. An important observation is that, for an observer at infinity, both the mass and charge of black hole increase with the contraction of the universe and decrease with the expansion of the universe.

A Tolman-like Compact Model with Conformal Geometry.

In this investigation, we study a model of a charged anisotropic compact star by assuming a relationship between the metric functions arising from a conformal symmetry. This mechanism leads to a first-order differential equation containing pressure anisotropy and the electric field. Particular forms of the electric field intensity, combined with the Tolman VII metric, are used to solve the Einstein–Maxwell field equations. New classes of exact solutions generated are expressed in terms of elementary functions. For specific parameter values based on the physical requirements, it is shown that the model satisfies the causality, stability and energy conditions. Numerical values generated for masses, radii, central densities, surface redshifts and compactness factors are consistent with compact objects such as PSR J1614-2230 and SMC X-1.

Charged stars in 4D Einstein\u2013Gauss\u2013Bonnet gravity

An alternative gravity theory that has attracted considerable attention recently is the novel four-dimensional Einstein–Gauss–Bonnet (4EGB) gravity. This idea was proposed to bypass the Lovelock’s theorem and to permit nontrivial higher curvature effects on the four-dimensional local gravity. In this approach, the Gauss–Bonnet (GB) coupling constant alpha is rescaled by a factor of alpha /(D -4) in D dimensions and taking the limit D rightarrow 4. In this article, we analyze the effects of charge on static compact stars in the regularized 4D EGB gravity theory. Two classes of new exact solutions are found for a particular choice of the gravitational potential and assuming a relationship between the electric field intensity and the spatial potential. A graphical analysis indicates that the matter and electromagnetic variables are well behaved for specific values of the parameter space. Finally, based on physical grounds appropriate bounds on the model parameters we show that compact objects with the value of adiabatic index gamma is consistent with expectations.