Perfect fluid metrics conformal to the Schwarzschild exterior spacetime

We construct perfect fluid spacetimes by performing a conformal transformation on a non-conformally flat vacuum solution, namely the Schwarzschild exterior metric. It should be noted that conformally Ricci flat perfect fluid solutions, except those that are conformally flat, are rarely reported explicitly. In this article it is demonstrated that perfect fluid metrics conformal to the Schwarzschild exterior line element are necessarily static. The Einstein field equations for the static case reduce to a fully determined system of three differential equations in three unknowns and the conformal factor is uniquely determined in closed form. The solution is analysed for physical plausibility by establishing the positivity of the energy density and pressure profiles graphically. Additionally, the solution is observed to be causal in an appropriate limit and both the energy density and pressure is shown to be decreasing outwards towards the boundary. Finally, the weak, strong and dominant energy conditions are found to be satisfied in the region under investigation. Accordingly, the most common elementary physical conditions are met and the model is seen to be suitable for a core-envelope stellar model.     

Construction of singular vertex operators as degenerate primary conformal fields

A general construction of null fields is given through the use of a vertex operator representation of conformal quantum fields. Singular vertex operators are constructed as possessing the conformal properties of a degenerate primary field. A systematic approach to obtaining the partial differential equations for correlation functions is suggested.     

Hidden conformal symmetry and pair production near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter spacetime

We show that the study of the hidden conformal symmetry that is associated with the Kerr/CFT correspondence can also apply to the cosmological horizon in the Kerr-Newman-Taub-NUT-de Sitter spacetime. This symmetry allows employing some two dimensional conformal field theory methods to understand the properties of the cosmological horizon. The entropy can be understood by using the Cardy formula, and the equation for the scattering process in the near region is in agreement with that obtained from a two point function in the two-dimensional conformal field theory. We also show that pair production can occur near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter for near extremal conditions.     

A NUT-like electrovac spacetime

A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field is obtained. The solution is algebraically special. A particular case of the solution is considered which includes Brill’s solution. The details regarding the solution are also discussed.     

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let ₁(x) and ₂(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution ₁(x)₂(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that ₁(x)₂(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft     

On the relation between a conformal structure in spacetime and nets of local algebras of observables

In this Letter, we study the question of how to reconstruct the conformal structure (causality relation) of spacetime from a net of local algebras of observables on the underlying manifold.Partly supported by DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

A gravitational field in the Plebanski spacetime

The gravitational wave equation in the Plebanski spacetime has been reduced to a one-dimensional wave equation with a real short-range potential. We then find that the superradiance phenomenon occurs.     

Projective spacetime

It is suggested that the world is locally projectively flat rather than Euclidean. From this postulate it is shown that an (N+1)-particle system has the global geometry of the symmetric spaceSO(4,N+1)/SO(4)×SO(N+1). A complex representation also exists, with structureSU(2,N+1)/S[U(2)×U(N+1)]. Several aspects of these geometrics are developed. Physical states are taken to be eigenfunctions of the Laplace-Beltrami operators. The theory may provide a rational basis for comprehending the groupsSO(4, 2),SU(2)×U(1),SU(3), etc., of current interest.     

A statistical mechanical problem in Schwarzschild spacetime

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.     

A vacuum spacetime with closed null geodesics

Here we present a vacuum spacetime with closed null geodesics (CNGs). These CNGs are obtained by analytically solving the geodesic equations. This spacetime is locally isometric to the plane wave spacetime and has very different global properties from metrics of the latter type.     

Quantum spacetime

After a review and reformulation of previous results, further developments in the construction and interpretation of a quantum-theoretic model of general relativistic spacetime are presented. A theorem is proved that clarifies the nature of the boundaries separating the four-dimensional facets of the resulting piecewise linear model, and a simple example of such a spacetime is detailed. The precise way in which any such model unifies the essential features of both quantum theory and general relativity is discussed.     

一种用于时空立体视觉的光源模式设计

时空立体视觉是一种全新的三维重建技术,它利用主动光源来改变图像灰度,通过比较某时间段内的图像序列来完成立体匹配。针对时空立体视觉的特点,设计了一种由多级对偶的和沿一维单调变化的"锯齿式"灰度条纹组成的光源,提高了鲁棒性。三维重建实验结果说明了该光源的有效性。     

Noncontinuous Minkowskian spacetime

A model for a noncontinuous spacetime is considered, which is based on a generalization of the manifold concept, known as d-space. As a consequence of its construction, the model possesses a metric of Lorentzian signature and a generalized form of Lorentz invariance. The model may be considered as defining a class of discrete spacetimes within the framework of the d-space representation of general relativity.     

时空的结构

Cassini飞船在其飞向土星的旅程中 ,它的轨道被太阳所偏转的状态已被测控的无线电波所测定 ,这又一次证实了爱因斯坦广义相对论中关于时空结构的论断 .爱因斯坦曾指出 ,一个质量巨大的物体将会使其周围的结构发生变形 ,而这种变形会影响到通过其附近的光波轨道并造成光波轨道的改道 .现在意大利位于三地 (Pavia ,Rome ,Bologna )的三所大学以Bertotti教授为首的科学家们 ,细致地核对了由Cassini飞船上发回的无线电数据 ,并发现光波轨道的偏转完全符合广义相对论的规范理论 .同时他们宣称 ,他们的测量仪器已达到非常灵敏的程度 ,可为其他…     

A model of conformal kinematics

A new realization of the conformal group in the classical phase space of a positive mass relativistic scalar particle is obtained. A physical interpretation in the spirit of conformal relativity is discussed.     

A conformal holomorphic field theory

A formulation of a field theory on the complex Minkowski space in terms of complex differential geometry is proposed. It is also shown that our model of field theory differs from the standard model on the real Minkowski space only in the limit of high energy.