Some properties of the n-dimensional plane symmetric solution

An n-dimensional static plane symmetric solution of Einstein field equation, which is judged as the source of n-dimensional Taub solution, is presented in our previous work. The properties of geodesics of this solution are studied in this Letter. The essence of the source is also investigated. A phantom with dust and photon is suggested as the substance of the source matter.     

Spherically symmetric nonstatic perfect fluid solutions with shear

In this paper we investigate solutions of Einstein's field equations for the spherically symmetric perfect fluid case with shear and with vanishing acceleration. If these solutions have shear, they must necessarily be nonstatic. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three known classes of solutions. The fourth class of solutions with shear leads to a generalized Emden-Fowler equation. This equation is discussed by means of Lie's method of point symmetries.     

Letter: Parametrization of the Kerr-NUT Solution

The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere.     

Shear-free spherically symmetric perfect fluid solutions with conformal symmetry

In 1987, Dyer, McVittie and Oattes determined the general relativistic field equations for a shear-free perfect fluid with spherical symmetry and a conformal Killing vector in thet-r plane, which depend on an arbitrary constantm. Two particular solutions of these equations were given recently by Maharaj, Leach and Maartens, as well as a partial solution thought to be valid for almost allm. In this paper, this solution is completed for four values ofm, and it is shown that it cannot be completed for any others by currently available techniques; however, a new solution of a different form, but also depending on a Weierstrass elliptic function, is found for a further value ofm. None of these metrics are conformally flat; one of them has a constant expansion rate.     

Thin-shell wormhole solutions in Einstein-Hoffmann-Born-Infeld theory

We adopt the Hoffmann-Born-Infeld?s (HBI) double Lagrangian approach in general relativity to find black holes and investigate the possibility of viable thin-shell wormholes. By virtue of the non-linear electromagnetic parameter, the matching hypersurfaces of the two regions with two Lagrangians provide a natural, lower-bound radius for the thin-shell wormholes which provides the main motivation to the present study. In particular, the stability of thin-shell wormholes supported by normal matter in higher-dimensional Einstein-HBI-Gauss-Bonnet (EHBIGB) gravity is highlighted.     

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solutions of the vacuum Brans-Dicke theory of gravity only two are really independent. Further, by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only the Brans class I solution with a certain restriction on the solution parameters may represent an exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.     

Radiating black hole solutions in arbitrary dimensions

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in N-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based (radiating) black hole solutions to Einstein equations, in both four dimensions (4D) and higher dimensions (HD), are particular cases from this family. The spherically symmetric static black hole solutions for Type I fluid can also be retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.     

Spherically symmetric charged perfect fluid distributions executing shear-free motion

A method to obtain exact solutions characterizing spherically symmetric charged perfect fluid distributions undergoing shear-free motion has been discussed. This method makes use of the criterion that the solution be free from movable critical points as has been employed earlier by Shah and Vaidya. Two solutions have been obtained, one of which is new and the other is the recent solution due to Sussman.     

Bardeen black hole surrounded by perfect fluid dark matter

We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge g and dark matter parameter \begin{document}$\alpha$\end{document} as thermodynamic variables, we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The results show that there exists a critical radius \begin{document}$r_{+}^{C}$\end{document} where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range \begin{document}$0<r_{+}<r_{+}^{C}$\end{document} . In addition, the critical radius \begin{document}$r_{+}^{C}$\end{document} increases with the magnetic charge g and decreases with the dark matter parameter \begin{document}$\alpha$\end{document} . Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter \begin{document}$\alpha$\end{document} , in a certain range, with the increase of the rotation parameter a and magnetic charge g, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.     

Asymptotes of solutions of a perfect fluid coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry

Asymptotes of solutions of a perfect fluid when coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry are studied. In particular, it is found that the problem of self-similar solutions of the first kind for a fluid with the equation of state, p = kρ, can be reduced to solving a master equation of the form,

From Laurent series to exact meromorphic solutions: The Kawahara equation

Meromorphic traveling wave solutions of the Kawahara equation and the modified Kawahara equations are studied. An algorithm for constructing meromorphic solutions in explicit form is described. The classification problem for meromorphic solutions of autonomous nonlinear ordinary differential equations is discussed.     

A class of generalised Robinson-Trautman solutions in non-comoving coordinates

A new class of algebraically special solutions is found for Einstein's equations based on the generalised Robinson-Trautman formulation introduced by Wainwright. The solution metrics depend on all four spacetime coordinates t,x,y and r, and in the x,y subspace are either spherically symmetric (parameter K ₀ > 0) or spatially flat (K ₀ = 0). The inhomogeneous spacetimes, of Petrov type II, have singularities at t = 0 and r = 0. The source is a stiff perfect fluid that expands with shear and acceleration but without rotation. The dynamical configuration in the era t ∼ 0 depends directly on a function h(x,y) of the metric. Trapped surfaces are found, associated with the singularity r = 0, which is shown to be censored.     

Three-dimensional stationary cyclic symmetric Einstein–Maxwell solutions; black holes

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2 + 1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants F_μνF^μν and T_μνT^μν, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein–Maxwell equations, reducible to three nonlinear equations for the three unknown functions, two new classes of solutions – having anti-de Sitter spinning metric limit – are derived. The relationship of various families with those reported by different authors’ solutions has been established. Among the classes of solutions with cosmological constant a relevant place is occupied by the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata–Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via SL(2,R)-transformations where the Clement spinning charged solution, the Martinez–Teitelboim–Zanelli black hole solution, and Dias–Lemos metric merit mention.     

Explicit exact solitary wave solutions for generalized symmetric regualrized long—wave equations with high—order nonlinear terms

In this paper,we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by meas of proper transformation and undeterined assumption method.     

Exact solutions for nonstatic perfect fluid spheres with shear and an equation of state

It is shown that fairly general assumptions about the relevant physical and mathematical quantities in the study of nonstatic and spherically symmetric perfect fluid configurations usually single out the Friedmann-Lemaître solutions as the only physically plausible ones. In addition three new classes of exact solutions having shear and acceleration are presented, as well as a generalization of Wesson's stiff fluid solution.     

理想流体球的爱因斯坦场方程内部严格解研究

当静态的具有球对称性的理想流体的密度是径向坐标的函数时，Oppenheimer-Volkoff(OV) 方程成为Riccati方程-根据OV方程的一个已知特解，能将它变换成可积分的Bernoulli方程 ，严格地求得OV方程的通解和另一特解，进一步得到理想流体球的爱因斯坦场方程的内部严 格解，即度规分量的解析表示式- 关键词： 爱因斯坦场方程 OV方程 理想流体球内部严格解     

Spin symmetric solutions of Dirac equation with PSschl-Teller potential

The approximate analytical solutions of the Dirac equation with the Poeschl-Teller potential is presented for arbitrary spin-orbit quantum number κ within the framework of the spin symmetry concept. The energy eigenvalues and the corresponding two Dirac spinors are obtained approximately in closed forms. The limiting cases of the energy eigenvalues and the two Dirac spinors are briefly discussed.     

New exact solutions and Bäcklund transformation for Boiti-Leon-Manna-Pempinelli equation

Based on the binary Bell polynomials, the bilinear form for the Boiti-Leon-Manna-Pempinelli equation is obtained. The new exact solutions are presented with an arbitrary function in y, and soliton interaction properties are discussed by the graphical analysis. Further, the bilinear Bäcklund transformation is derived by the binary Bell polynomials, and the corresponding Lax pair is obtained by linearizing the bilinear equation.