广义相对论中静态荷电球体的一组内解

本文在假定物质密度ρ_m=μr~α,电荷密度 ρ_e=ρ_0r~βe~(-λ/2)的情况下,严格求解 Einstein-Maxwell 场方程,得出了静态荷电球体的一组内解,把文[4]、[6]的结果作为自己的特例包括在内。     

非平衡热力学中恒星结构稳定性的研究——Ⅲ.质量耗损情况下的PPI反应

恒星是开放系统.本文以非线性非平衡热力学中超熵产生判据来研究质量耗损(dρ/dt=- ε/c~2,ρ为总质量密度,ε为单位体积的产能率,c为光速)下,PPI反应所决定的太阳型恒星结构的稳定性问题。结果表明:时,恒星结构肯定稳定.式中X、Y分别为氢、氦丰度,A_1、A_3分别为H~1和H_e~3的原子量,β～10~(-4)—10~(-5)(当8×10~6K≤T≤1.5×10~7K时),(ρ_1为H’的质量密度),(N_A为阿佛伽德罗常数,Q_1=-1.442 MeV,Q_2=5.493 MeV,Q_3=12.859 MeV).     

恒星内部核素~(56)Fe、~(56)Co、~(56)Ni和~(56)Mn电子俘获过程中微子能量损失高斯修正

采用高斯修正法,研究了核素~(56)Fe、~(56)Co、~(56)Ni和~(56)Mn电子俘获过程中微子能量损失.结果表明:对核素的Gamow-Teller(G-T)共振跃迁能级分布的高斯修正使中微子能量损失率增加.在低能跃迁电子俘获过程为主导地位的反应中,高斯修正对中微子能量损失的影响很小,而对高能G-T共振跃迁为主要的电子俘获过程的中微子能量损失的影响将大大增加.如核素~(56)Fe在密度ρ_7=100(ρ_7以10~7 mol·cm~(-3)为单位),高斯函数半宽度△=14.3,18.3,22.3 Mev时,修正差异大约达2个数量级,核素~(56)Ni在△=6.3,18.3Mev差异分别达60%和40%.     

矢引力子场度规场的一个内部解

本文从考虑矢引力子场的爱因斯坦方程出发,在一特殊密度分布情况下,求得了内部解。     

研究高密物质的平均场方法的改进

本文对以前提出的改进的平均场模型(简称 MMFT)做了进一步的讨论。发现该模型有新的解 ml=2 ; 加入ρ介子,计算了核物质对称能 α_4;用新的参数计算了加ρ与未加ρ的中子物质的态方程,将二者作了比较,并与ml=4.3的结果做了比较;引用二体关联函数对矢量介子平均场的形式做了初步的理论探讨;用中子星结构方程计算了相应于各种态方程的中子星最大质量,结果是: MMFT-2(ml=2): M_(max)=2.22M(不含ρ介子) M_(max)=2.27M(加入ρ介子) MMFT-1(ml=4.3):M_(max)=1.69M(不含ρ介子) M_(max)=1.89M(加入ρ介子)     

五维Bianchi-Ⅴ型理想流体宇宙模型

本文给出了态方程为P=(γ-1)ρ的理想流体的五维Bianchi-V型宇宙模型的普遍解,并讨论了γ=2/3和γ=1/2的两个具体的解。这两个解随着时间的增长将趋于五维膨胀各向同性宇宙模型。此外,还考察了解的奇点的性质。     

吸积盘与恒星在星云盘中形成时的角动量损失

本文根据吸秘盘理论与天文观测结果,给出一个恒星在星云盘中形成的模型.通过计算角动量方程,获得了质量定常分布ρ(r)～r_(-β)(β=0,1,2)时的一般性解.对1M恒星的数值解表明:恒星在转动磁化的星云盘中形成时,角动量确实发生了巨大转移;并且,β=2的解能较满意地解释太阳系的角动量奇异性.     

地震位移场对极移的激发

本文讨论了地震位移场对极移的激发问题.与已有的文献中采用的液核静力方程不同,我们采用文[1]中提出改进的液核静力方程.这样核幔间的连续性条件都可以得到满足.本文所用的地震参数取自文[2]. 在微分方程求解过程中,把整个球体分成两部分:内部是球心附近的一个小球,外部为一球壳.在内部我们应用幂级数渐近解,外部采用Runge-Kutta数值解.这样可以避免数值解过程中球心处的奇异性问题.计算结果表明,虽然用同样的地震参数,由于液核方程的不同,我们的结果比文[2]的结果大三倍左右.这说明,不同的液核方程的影响是比较大的.     

磁弧剪切动力学的一个精确解

我们在文[1]里对磁弧剪切作了数值解,得到了剪切速度ω和磁场B_z的分析解,但对二维速度(u,v)的振幅占δ′/ζ仅有只依赖于时间的近似解。本文在密度为常数条件下得到了磁弧剪切在线性演化阶段的较精确的解析解,比较了密度为常数和密度重力分层两种情形下的数值解,证实当β(=气压/磁压)很小(量级为10~(-2))时两者差别不大,因此本文结果近似可用于密度不为常数的实际太阳大气中的磁弧剪切动力学过程。解析解的主要结果是导出振幅δ′/ζ的高度依赖关系:随着时间增加,振幅δ′/ζ随高度下降越来越慢。这导致磁弧顶越升越高而脚根基本上不朝外移动,这样闭合的磁弧将有可能逐渐变为开场。     

磁单极子-带电粒子的Fokker-Planck方程

本文研究了在非相对论情况下磁单极子-带电粒子的Fokker-Planck方程,计算了此方程中的速度一阶二阶平均量。我们发现,和带电粒子间的相互作用很类似,磁单极-带电粒子的碰撞积分是对数式发散的,这表明远程碰撞仍然起主要作用,近距碰撞可略而不计。此外在热力学平衡分布下,给出了磁单极子-带电粒子作用的三个弛豫时间——慢化、偏转和能量交换时间——的解析表达式,并同早已熟知的荷电粒子间的弛豫时间作了比较,发现前者一般比后者大一因子:(光速/热速)~2。因此通常条件下磁单极和荷电粒子间的作用是微弱的。但在某些天体物理条件下磁单极对荷电粒子群的影响是不可忽略的,从而可期磁流体力学方程应作相应的修改,最后我们列出了含磁单极的等离子体中的封闭的MHD方程组。     

Effects of electromagnetic field on the stability of locally isotropic gravastars

We have studied a new solution of charged gravastars with isotropic matter configuration in the framework of f(R, T) theory of gravity. For this purpose, we have assumed the electric charge as a constant. This stellar structure divided into three different regions: The preliminary part shows the interior charged region in which pressure equals to the negative density, second is the intermediate charged shell which is assumed to be very thin and filled with ultrarelativistic stiff fluid and the last corresponds to the electrovacuum region which is defined by an exterior Reissner-Nordström solution. Under these assumptions, we have found some physical aspects like length, energy, entropy and equation of state for charged spherical gravastar distribution. Moreover, we present an exact solution that free from event horizon and non-singular for this our new model.     

Highly excited hydrogen lines in stellar spectra. I

The solution of the hydrogenic Schrödinger equation are given with two boundary conditions imposed on the wave function, for distances of the order of magnitude of one hundred times the Bohr radius from the central nucleus. Thus the shifts and splitting of the H-H₂₆ lines are given which arise from the non-vacant environment. The Inglis-Teller limit is revised since from the shifts it follows that it gives a correct charged particle density only in the case of extremely high electron and ion densities. The gas density is derived from the number of the visible Balmer lines, and usually the widths and the contours but not the coalescence include information on the charged particle density.     

Gravitational sources of purely electromagnetic origin

The Einstein-Maxwell field equations for charged dust corresponding to static axially-symmetric metric of Levi-Civita have been studied. It has been shown that when the metric potentialsg _ij are functions of only one of the coordinates, viz.,r, the interior charged dust becomes purely of electromagnetic origin, in the sense that the physical quantities like the energy density, the effective gravitational mass, etc., are dependent only on the charge density and vanish when this charge density vanishes. Such models are known as electromagnetic mass models in the classical electrodynamics. An interior charged dust solution corresponding to this case has been obtained which, in a sense, represents an infinite dust distribution of electromagnetic origin. In the second case, viz., when the metric potentials are functions of the coordinatesr andz both, it has been shown that some of the situations correspond to electromagnetic mass models. An example to illustrate this case has been obtained. This represents the source of the Reissner-Nordström-Curzon field (an analogue of the Reissner-Nordström solution obtained by Curzon) which according to Curzon describes the exterior field of an electron.     

Variety of Well behaved parametric classes of relativistic charged fluid spheres in general relativity

The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure–density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I₁) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³ corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5M _Θ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.     

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.     

A source for the Reissner-Nordstrøm metric

An exact solution of the coupled Einstein-Maxwell equations representing the gravitational field in the interior of a sphere of charged incoherent matter in equilibrium is obtained which is a charged analogue of the static perfect fluid sphere solution with spheroidal 3-space obtained by Vaidya & Tikekar.     

Some electrically charged relativistic stellar models in general relativity

Some new families of electrically charged stellar models of ultra-compact star have been studied. With the help of particular form of one of the metric potentials the Einstein–Maxwell field equations in general relativity have been transformed to a system of ordinary differential equations. The interior matter pressure, energy–density, and the adiabatic sound speed are expressed in terms of simple algebraic functions. The constant parameters involved in the solution have been set so that certain physical criteria satisfied. Based on the analytic model developed in the present work, the values of the relevant physical quantities have been calculated by assuming the estimated masses and radii of some well known potential strange star candidates like X-ray pulsar Her X-1, millisecond X-ray pulsar SAX J 1808.4-3658, and 4U 1820-30. The analytical equations of state of the charged matter distribution may play a significant role in the study of the internal structure of highly compact charged stellar objects in general relativity.     

3-Dimensional Energetic Particle Distribution Past an Instantaneous Uni-Directional Injection

The exact analytic expression for the density of energetic charged particles, which were injected by an instantaneous point source at a particular pitch angle into the interplanetary medium, has been derived. We start from the Boltzmann kinetic equation with the collision integral describing the isotropic particle scattering by "massive" magnetic clouds. The solution has been obtained without any expansion parameters in the 3-dimensional vector form, then it was projected into the cylindrical coordinate system. The space-time particle distribution is disscussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A family of charge analogue of Durgapal solution

We obtain a new parametric class of exact solutions of Einstein–Maxwell field equations which are well behaved. We present a charged super-dense star model after prescribing particular forms of the metric potential and electric intensity. The metric describing the super dense stars joins smoothly with the Reissner–Nordstrom metric at the pressure free boundary. The electric density assumed is where n may take the values 0,1,2,3,4 and so on and K is a positive constant. For n=0,1 we rediscover the solutions by Gupta and Maurya (Astrophys. Space Sci. 334(1):155, 2011) and Fuloria et al. (J. Math. 2:1156, 2011) respectively. The solution for n=2 have been discussed extensively keeping in view of well behaved nature of the charged solution of Einstein–Maxwell field equations. The solution for n=3 and n=4 can be also studied likewise. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982). The outmarch of pressure, density, pressure-density ratio and the velocity of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Neutron stars and Pulsars.     

Well-behaved relativistic charged super-dense star models

A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g ₄₄ with that of Durgapal’s fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ _b =2×10¹⁴ g/cm³ and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22M _Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059K+4.22)M _Θ and r _b ≈−0.021464K+20 km respectively.