Spherically symmetric anisotropic and inhomogeneous cosmological models

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed. This paper is dedicated to my teacher Professor V V Narlikar on the occasion of his 81st birthday.     

Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell’s equations for static spheres assuming the matter content to be a charged perfect fluid of null-conductivity. Defining three new variablesu=4πεr ²,ν=4πpr ^{2 2} andw=(4π/3)(ρ+ε)r ² whereε, ρ andε denote respectively energy densities of the electric, matter and free gravitational fields whereasp is the fluid pressure, Einstein’s field equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5,6], Xingxiang [7], Patino and Rago [8] are all shown to possess simple relations betweenu, v, andw whereas Pant and Sah’s [9] solution for which all the three functions,u, v, andw are constants is a trivial case of the present formalism, We have presented six new solutions with ε = 2ρ. For the first three solutionsw andu are constants withv as a variable whereas the remaining three solutions satisfy the equation of state for isothermal gas;v =kw =-ku where (i)k is an arbitrary constant but not equal to 1 or 1/3 (ii)k = 1 and (iii)k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz’s [3] solution which is regular for 2ρ > ε but singular for 2ρ ≤ ε.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

Higher dimensional spherically symmetric inhomogeneous cosmological model with heat flow

We study spherically symmetric inhomogeneous cosmological model with heat flow in higher dimensional space-time and present a class of solutions in which the velocity field is shear-free. Some of these solutions are analogous to the known solutions in 4-dimension while some are totally new.     

Gravitational energy in Brans-Dicke cosmological models

The behaviour of gravitational energy and scalar field during the evolution of the universe within the framework of Brans-Dicke theory has been discussed. With help of the Landau-Lifshitz pseudo-tensor for the flat Friedmann-Robertson-Walker model, it is found that (i) the total energy of the universe is always zero, (ii) the Brans-Dicke scalar field for all Ω >-0 contributes energy to the negative energy of gravitational field and this gets transferred to the vacuum energy which accelerates the expansion of the universe.     

Energy of Gravitational Field of Static Spherically Symmetric Neutron Stars

By using the Einstein-Tolman expression of the energy-momentum pseudo-tensor, the energy density ofthe gravitational field of the static spherically symmetric neutron stars is calculated in the Cartesian coordinate system.It is exciting that the energy density of gravitational field is positive and rational. The numerical results ot the energydensity of gravitational field of neutron stars are calculated. For neutron stars with M = 2M , the ratio of the energydensity of gravitational field to the energy density of pure matters would be up to 0.54 at the surface.     

Time and distance constraints on accelerating cosmological models

The absence of guidance from fundamental physics about the mechanism behind cosmic acceleration has given rise to a number of alternative cosmological scenarios. These are based either on modifications of general relativistic gravitation theory on large scales or on the existence of new fields in Nature. In this Letter we investigate the observational viability of some accelerating cosmological models in light of 32 age measurements of passively evolving galaxies as a function of redshift and recent estimates of the product of the cosmic microwave background acoustic scale and the baryonic acoustic oscillation peak scale. By using information-criteria model selection, we select the best-fit models and rank the alternative scenarios. We show that some of these models may provide a better fit to the data than does the current standard cosmological constant dominated (ΛCDM) model.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

Cylindrically symmetric inhomogeneous cosmological models with viscous fluid and varying Λ

Cylindrically symmetric non-static cosmological models representing a bulk viscous fluid distribution have been obtained which are inhomogeneous and anisotropic. Without assuming anyadhoc law, we obtain a cosmological constant as a decreasing function of time. Various physical and geometrical features of the models are also discussed.     

Exact solutions for the massless plane symmetric scalar field in general relativity,with cosmological constant

The Klein–Gordon equations are solved for the case of a plane-symmetric static massless scalar field in general relativity with cosmological constant, generalizing the solutions found by Taub, Novotny and Horsky, and Singh. A separate class of solutions is obtained in which the metrics reduce to flat space in the limit that .The static solutions can be used to generate time-dependent cosmological solutions, one of which exhibits rapid inflation followed by continued exponential expansion at all later times.     

黑体辐射中两类粒子的辐射规律

考虑到相对论效应,采用量子统计的方法,得到了满足Bose-Einstein统计分布和Fermi-Dirac统计分布的两类粒子的黑体辐射公式（包括Planck黑体辐射公式）．发现辐射谱不仅与黑体的辐射温度有关,还与辐射粒子的能量、化学势和种类有关．辐射强度与辐射粒子的能量、静质量、简并因子有关。     

普朗克卫星：揭开宇宙深层次的秘密

文章对宇宙微波背景辐射这一学科做了简单的介绍,并根据普朗克卫星2015年的主要宇宙学结果,重点阐述了测定宇宙学参数、测量引力透镜、测量B-模式极化及其与南极BICEP实验的关系、检验宇宙暴胀模型、检测暗能量模型,以及寻找“丢失的重子物质”等问题,并对观测宇宙学未来的发展进行了展望。     

重力场中的熵产生研究

重力场中的大气处于非平衡态，其温度是空间的函数，不同的等温面之间要产生热流，从而改变熵的空间分布。本文推导出重力场中的熵产生公式，并描绘出熵产生随高度变化的近似曲线。     

Differential renormalization of van der Waals spin models

An exact renormalization group equation in differential form is derived for spin systems with general many-body interactions in the van der Waals limit. This equation is solved and the free energy is determined as an integral along the renormalization trajectory in the interaction space. It is shown that the transformation can always be modified in such a way that an undetermined integration constant for the free energy vanishes exactly, also below the critical temperature. We also demonstrate how the invariance of the free energy under a parameterdependent equivalence transformation can provide information about the critical behavior of the system. In this alternative approach dangerous irrelevant variables play an essential role.On leave of absence from Istituto di Fisica e Unità GNSM del CNR, Università di Padova, Padova, Italy.     

Tetrad Fields,Reference Frames,and the Gravitational Energy–Momentum in the Teleparallel Equivalent of General Relativity

The concept and definitions of the energy–momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR) are reviewed. The importance of these definitions is justified by three major reasons. First, the TEGR is a well established and widely accepted formulation of the gravitational field, whose basic field strength is the torsion tensor of the Weitzenböck connection. Second, in the phase space of the TEGR there exists an algebra of the Poincaré group. Not only the definitions of the gravitational energy–momentum and 4-angular momentum satisfy this algebra, but also the first class constraints related to these definitions satisfy the algebra. And third, numerous applications of these definitions lead to physically consistent results. These definitions follow from a well established Hamiltonian formulation, and rely on the idea of localization of the gravitational energy. In this review, the concept of localizability of the gravitational energy is revisited, in light of results obtained in recent years. The behavior of free particles is studied in the space–time of plane fronted gravitational waves (pp-waves). Free particles are here understood as particles that are not subject to external forces other than the gravitational acceleration due to pp-waves. Since these particles acquire or loose kinetic energy locally, the transfer of energy from or to the gravitational field must also be localized. This theoretical result is considered an important and definite argument in favor of the localization of the gravitational energy–momentum, and by extension, of the gravitational 4-angular momentum.     

关于"太阳在银河系中所受引力与到银心距离r的关系"的讨论

讨论了银道面内的引力场强分布和太阳在银河系中所受引力与到银心距离r的关系，指出引力场强g并不是与r的平方成反比，这是由于银河系的大小和形状不能忽略造成的．强调了万有引力定律的适用条件．     

均匀磁场中旋转的轴对称导体上的电荷分布析

分析了均匀磁场中旋转的轴对称导体上的电荷分布，指出这里不存在普遍的面电荷密度公式。     

K-Essential Phantom Energy: Revisited

We generalize some of those results which are closely related to the canonical kinetic term in k-essence formalism by further tuning the parameter (β). The scale factor a(t) could be negative and decreasing within a specific range of β (≡−1/ω, ω : the equation-of-state parameter) during the initial evolutional period.     

Gravitational Perturbations on Local Experiments in a Satellite: The Dragging of Inertial Frame in the HYPER Project

We consider a nearly free falling Earth satellite where atomic wave interferometers are tied to a telescope pointing towards a faraway star. They measure the acceleration and the rotation relatively to the local inertial frame. We calculate the rotation of the telescope due to the aberrations and the deflection of the light in the gravitational field of the Earth. We show that the deflection due to the quadrupolar momentum of the gravity is not negligible if one wants to observe the Lense-Thirring effect of the Earth. We consider some perturbation to the ideal device and we discuss the orders of magnitude of the phase shifts due to the residual tidal gravitational field in the satellite and we exhibit the terms which must be taken into account to calculate and interpret the full signal. Within the framework of a geometric model, we calculate the various periodic components of the signal which must be analyzed to detect the Lense-Thirring effect. We discuss the results which support a reasonable optimism. As a conclusion we put forward the necessity of a more complete, realistic and powerful model in order to obtain a final conclusion on the theoretical feasibility of the experiment as far as the observation of the Lense-Thirring effect is involved.