Projective measurements and generation of entangled Dirac particles in Schwarzschild spacetime

It is shown that the projective measurements made by Bob who locates near the event horizon of the Schwarzschild black hole will create entangled particles detected by Alice who stays stationary at the asymptotically flat region. It is found that the degree of entanglement decreases as the frequency of the detected particles increases and approaches to zero as the frequency ω_k → ∞. It is also noted that the degree of entanglement increases as the Hawking temperature increases. Especially, the particle state is unentangled when the Hawking temperature is zero and approaches a maximally entangled Bell state when the black hole evaporates completely.     

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.     

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…     

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.     

Bosonization in curved spacetime

The bosonization of a pair of two-dimensional Weyl fermions, of opposite chiralities, is considered. When the fermions are in different metrics the bosonization procedure gives a unique expression for the gravitational anomaly.     

Trips in Kerr-NUT spacetime

With reference to the recently published article (Abdujabbarov et al. in Gen Relativ Gravit 40:2515–2532, 2008), we question the correctness of the method employed and the physical consistency of the claimed results.     

Parton coalescence and spacetime

The influence of spacetime dynamics in hadronization via parton coalescence at RHIC is investigated using covariant parton transport theory: Key observables, the quark number scaling of elliptic flow and the enhancement of the p/π ratio, show strong dynamical effects and differ from earlier results based on the simple coalescence formulas.     

Nonequilibrium thermodynamics of spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.     

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.     

Tolerance for spacetime singularities

A common reaction to the Penrose-Hawking singularity theorems is that Einstein's general theory of relativity contains the seeds of its own destruction. This attitude is critically examined. A more tolerant attitude toward spacetime singularities is recommended.     

Five-dimensional axisymmetric spacetime solutions

We give a method by which a class of 5D potential solutions and a class of 5D spacetime solutions with magnetic field can be generalized, and show some examples.     

Superfields in higher-dimensional spacetime

We give the constraints in six- and ten-dimensional globally-supersymmetric gauge theories on the superfield covariant derivatives, which reduce to the usual ones for the extended theories in four dimensions. We also compute the six-dimensional action. including the Fayet-Iliopoulos term.     

Probing non-Riemannian spacetime geometry

The equations of motion for matter in non-Riemannian spacetimes are derived via a multipole method. It is found that only test bodies with microstructure couple to the non-Riemannian spacetime geometry. Consequently it is impossible to detect spacetime torsion with the satellite experiment Gravity Probe B, contrary to some recent claims in the literature.     

Projective connections

We compare the approaches of E. Cartan and of T.Y. Thomas and J.H.C. Whitehead to the study of ‘projective connections’. Although the quoted phrase has quite different meanings in the two contexts considered, we show that a class of projectively equivalent symmetric affine connections–or, more generally, sprays–on a manifold (the latter meaning) gives rise, in a global way, to a unique Cartan connection on a principal bundle over the manifold (the former meaning). The principal bundle on which the Cartan connection is defined is itself a geometric object, and exists independently of any particular connection. In the course of the discussion we derive a Cartan normal projective connection for a system of second-order ordinary differential equations (extending the results of Cartan from a single equation to many) and we generalize the concept of a normal Thomas–Whitehead connection from affine to general sprays.     

Complex spacetime tangent bundle

It is demonstrated that the spacetime tangent bundle, in the case of a Finsler spacetime, is complex, provided that the gauge curvature field vanishes. This is accomplished by determining the conditions for the vanishing of the Nijenhuis tensor in the anholonomic frame adapted to the spacetime connection.     

Generalised splitting of spacetime

Normally, when a spacetime splitting is considered the ADM 3+1 split is brought to mind. In this paper, the idea of spacetime splitting is extended to include anm + n splitting of spacetime. The global spacetime has dimension (m + n) and the foliating spaces have dimensionm. There aren independent normals to each of these foliating spaces, thus givingn different extrinsic curvatures. The generalised Gauss-Weingarten and the generalised Gauss-Codazzi equations associated with this splitting are derived. These generalised equations reduce to the familar ADM equations when a 3+1 split is considered. The generalised equations are found to have a particularly elegant form when an orthogonal splitting of spacetime is examined.     

A singular conformal spacetime

The infinite cosmological “constant” limit of the de Sitter solutions to Einstein’s equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe.