In this paper we obtain the geodesic equations of motion of a test particle (charged particle and photon) in the Kerr-Newman de/anti de Sitter black hole by using the Hamilton-Jacobi equation. We determine the positio...In this paper we obtain the geodesic equations of motion of a test particle (charged particle and photon) in the Kerr-Newman de/anti de Sitter black hole by using the Hamilton-Jacobi equation. We determine the positions of the inner, outer and cosmological horizons of the black hole. In terms of the effective potentials, the trajectory of the test particle within the inner horizon is studied. It appears that there are stable circular orbits of a charged particle and photon within the inner horizon and that the combined effect of the charge and rotation of the Kerr-Newman de/anti de Sitter black hole and the coupling between the charge of the test particle and the electromagnetic field of the black hole may account for this.展开更多
We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving...We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.展开更多
In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like ...In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like extremal surfaces can be described by a system Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.展开更多
In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F b...In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.展开更多
The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were...The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.展开更多
文摘In this paper we obtain the geodesic equations of motion of a test particle (charged particle and photon) in the Kerr-Newman de/anti de Sitter black hole by using the Hamilton-Jacobi equation. We determine the positions of the inner, outer and cosmological horizons of the black hole. In terms of the effective potentials, the trajectory of the test particle within the inner horizon is studied. It appears that there are stable circular orbits of a charged particle and photon within the inner horizon and that the combined effect of the charge and rotation of the Kerr-Newman de/anti de Sitter black hole and the coupling between the charge of the test particle and the electromagnetic field of the black hole may account for this.
文摘We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.
基金Supported by National Natural Science Foundation of China under Grant Nos.11026151,11101001the Anhui Provincial University’s Natural Science Foundation under Grant No.KJ2010A130
文摘In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like extremal surfaces can be described by a system Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.
文摘In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
文摘The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.
