Nonstatic perfect fluid sphere in higher-dimensional space-time

It is shown that in the case of a spherical nonstatic fluid distribution undergoing shear-free motion the field equations in higher dimensional space-time can be reduced to a single second-order differential equation involving an arbitrary function of the radial co-ordinate. This result extends to higher dimensions a similar one obtained by Wyman and Faulkes earlier for 4D space-time. Solving this differential equation a number of new solutions is found, and the dynamical behaviour of one of the models is briefly discussed. The ansatz is later generalised to include the electromagnetic field as well.     

Solutions of LRS Bianchi I space-time filled with a perfect fluid

LRS Bianchi I space-time filled with a perfect fluid is considered and it is shown that the field equations are solvable for any arbitrary cosmic scale function. Solutions for a particular form of cosmic sclae functions are presented and all solutions, except for some cases, are shown to represent an empty universe for large time.     

The topology of asymptotically Euclidean static perfect fluid space-time

It is shown that a geodesically complete, asymptotically Euclidean, static perfect fluid space-time satisfying the time-like convergence condition and having a connected fluid region is diffeomorphic to ³×.     

The ideal relativistic rotating gas as a perfect fluid with spin

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ_μν. After having obtained the expression of the local spin-dependent phase-space density f(x, p)_στ in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω_μν constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω_μνσ^μν. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t^μ = σ_μνu^ν ≠ 0, in contrast to the common assumption t^μ = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.     

Axially symmetric rotating body consisting of a perfect fluid

An alternative method of obtaining the equilibrium configurations of a rotating body consisting of a perfect fluid is outlined. Basically, the method involves recasting the gravitational hydrodynamic equations into a set of partial differential equations of first order in the radial direction such that a center-outward integration can be performed. Specifically, with suitable initial conditions at the origin of anr, grid, a numerical integration is performed outward along a number of selected-rays, with the required derivatives at each step being determined numerically from the values of the functions on the different rays. Applicable to both Newtonian and relativistic formulations, the technique is similar to that often used to obtain equilibrium configurations in spherically symmetric models.     

Killing vector fields and the Einstein-Maxwell field equations with perfect fluid source

This paper is concerned with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. We consider the following question. Suppose that the space-time admits a group of motions (isometries), i.e., that the metric is invariant under a group of transformations. Does it follow that the quantities that describe the source, i.e., the electromagnetic field tensorF _ij, the charge densityε, and the four-velocityu ⁱ, energy densityμ, and pressurep of the fluid, are invariant under the group? It is found that the behavior of these quantities under the group is strongly restricted. In particular in the case of the three-dimensional special orthogonal groupSO(3), which arises in the case of spherically symmetric space-times, it is found that the source quantities are invariant. On the other hand, it is established that there exist groups under whichF _ij is not necessarily invariant. The above question is also considered for the case of homothetic motions.     

Higher-dimensional perfect fluids and empty singular boundaries

In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein’s equations consisting in a (N + 2)-dimensional static and hyperplane symmetric perfect fluid satisfying the equation of state ρ = ηp, being η an arbitrary constant and N ≥ 2. We show that this spacetime has some weird properties. In particular, in the case η > −1, it has an empty (without matter) repulsive singular boundary. We also study the behavior of geodesics and the Cauchy problem for the propagation of massless scalar field in this spacetime. For η > 1, we find that only vertical null geodesics touch the boundary and bounce, and all of them start and finish at z = ∞; whereas non-vertical null as well as all time-like ones are bounded between two planes determined by initial conditions. We obtain that the Cauchy problem for the propagation of a massless scalar field is well-posed and waves are completely reflected at the singularity, if we only demand the waves to have finite energy, although no boundary condition is required.     

Stationary axisymmetric solutions of the Einstein equations with rigidly rotating perfect fluid and nonlinear charged sources

A class of stationary, rigidly rotating perfect fluids coupled with nonlinear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found for the equation of state 3p+=const. We use a structure function for the Born-Infeld nonlinear electrodynamics which is invariant under duality rotations and a metric possessing a four-parameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the Debever-Penrose vectors.     

Slowly rotating universes with radiating perfect fluid distribution coupled with a scalar field in general relativity

Along with the presentation of some interesting new analytic solutions, the dynamics of slowly rotating radiating perfect fluid universes coupled with a scalar field are investigated, and their physical and geometrical properties are studied from various angles. The rotational perturbations of such models are examined in detail in order to substantiate the possibility that the universe is endowed with some rotation. The nature and role of the metric rotation which is related to the local dragging of inertial frames and that of the matter rotation are studied. The effects of the radiation and the scalar fields on the rotation are discussed. The periods of physical validity for some of the models and the restrictions on the radii of the models for real astrophysical situations are found. Most of the rotating models obtained here turn out to be expanding ones as well, and may be taken as good examples of real astrophysical objects in this universe.     

Matching the Kerr solution on the surface of a rotating perfect fluid

We investigate the possible shapes of the surface of a rigidly rotating perfect fluid on which is matched the Kerr metric, using the Boyer (1965) surface condition. The solution, given in Figures 1 to 5, depends on three parameters, = qK, q = a/m, - (a/gwc), wherem denotes the mass of the source, a its angular momentum per unit mass, the angular velocity of rotation, andK is an integration constant appearing in Boyer's surface condition. When < 1, as in Figures 1 to 3, there are, for givenq and, two possible surfaces, of which the smaller one touches the ring-singularity at = a, z = 0. When > 1, as in Figures 4 and 5, there is only one possible surface of kidney-shaped tori, which also touch the ring singularity. In the case of a differentially rotating perfect fluid, we find a variety of possible strictly spheroidal surfaces, depending on the choice of an arbitrary integration function() of the angular velocity . If we choose() so that, at each point on the surface, is single-valued, then the resulting distribution exhibits an equatorial acceleration, similar to what is observed on the surface of the sun. This angular velocity distribution turns out to be identical with Thorne's (1971) angular velocity of cumulative dragging.     

A class of solutions of Einstein's equations for the interior of a rigidly rotating perfect fluid

A general class of solutions of Einstein's equations for the interior of a rigidly rotating axisymmetric perfect fluid is presented, which depends on an arbitrary function. To get solutions explicitly one has to calculate two integrals involving the arbitrary function. The equipressure surfaces of all solutions of the class are spheres or planes. A family of solutions, which depend on four arbitrary real constants, is calculated explicitly. The solution of the family, which is obtained if we assign a specific value to one of its parameters, and which was found before, is futher generalized with the addition of one more parameter.     

A relativistically rotating fluid cylinder

The field equations for stationary, axisymmetric, nonconvective perfect fluid are presented. A solution corresponding to a rigidly rotating cylinder with constant pressure is derived. Some properties of this solution are discussed.     

A conformal mapping and isothermal perfect fluid model

Instead of the metric conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as minimally curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three-parameter family of perfect fluid solutions which are static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates asR ^–2, for unbounded cosmological model with a barotropic equation of state. This is the characteristic of an isothermal fluid. We thus have an ansatz for an isothermal perfect fluid model. The solution can also represent bounded fluid spheres.     

A class of static perfect fluid solutions

We consider a two-parameter family of equations of state for perfect fluids which forms the limiting case of a condition employed in a uniqueness proof of static, asymptotically flat solutions of the field equations. We find a geometric interpretation of this family and determine, for each of its members, the one-parameter family of regular spherically symmetric solutions.     

辐射源旋转台阶成像技术

 提出了用旋转台阶对辐射源成像的方法。对台阶响应曲线微分可得到辐射源2维出射强度沿台阶方向的1个投影,通过旋转台阶体,可得到完整的正弦图,从而可用层析重建算法重建出辐射源区的强度分布。用钨合金台阶体在1个60Co源上进行成像实验,从400个角度的台阶响应数据重建出60Co源活性区图像,表明该方法是可行的。此方法可推广到大孔径圆孔台阶体,用于测量X射线焦点等小尺寸辐射源的尺寸。     

Stationary perfect fluid solutions with differential rotation

In the framework of a class of metrics allowing for a timelike and a spacelike symmetries, usually referred to as stationary and axisymmetric gravitational fields, coupled to differentially rotating perfect fluids, the existing exact solutions to the corresponding Einstein equations are analyzed from the point of view of the fulfillment of the energy conditions and the existence of an axis of rotation. The main conclusion is that none of the reported exact solutions fulfills all these physical requirements, and at most, they can be thought of as stationary cyclic symmetric cosmological spacetimes.     

Inhomogeneous cosmology with spinning fluid in high-dimensional space-time

We study the evolution of an inhomogeneous cosmology with spinning fluid in high-dimensional space-time. Using the Szekeres class II metric and the energy-momentum tensor derived by Ray and Smalley, we find evolving solutions, including an exponential inflation.     

Bianchi type-V model with a perfect fluid and A-term

A self-consistent system of gravitational field with a binary mixture of perfect fluid and dark energy given by a cosmological constant has been considered in Bianchi Type-V universe. The perfect fluid is chosen to be obeying either the equation of state p=γρ with γ ε |0,1| or a van der Waals equation of state. The role of A-term in the evolution of the Bianchi Type-V universe has been studied.