Conformally flat supergeometry in five dimensions

Averaged null energy condition violation in a conformally flat spacetime

We show that the averaged null energy condition can be violated by a conformally coupled scalar field in a conformally flat spacetime in 3+1 dimensions. The violation is dependent on the quantum state and can be made as large as desired. It does not arise from the presence of anomalies, although anomalous violations are also possible. Since all geodesics in conformally flat spacetimes are achronal, the achronal averaged null energy condition is likewise violated.

Conformally flat FRW metrics

We find a new family of non-separable coordinate transformations bringing the FRW metrics into the manifestly conformally flat form. Our results are simple and complete, while our derivation is quite explicit. We also calculate all the FRW curvatures, including the Weyl tensor.

On the conformally flat Rindler-like geometry

The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the acceleration $g$ from the static expression of the Rindler-like metric. The timelike radial geodesics are computed and proves to be hyperbolae when a specific choice of the constants of integration is operated.

Noise kernels of stochastic gravity in conformally-flat spacetimes

The central object in the theory of semiclassical stochastic gravity is the noise kernel which is the symmetric two point correlation function of the stress-energy tensor. Using the corresponding Wightman functions in Minkowski, Einstein and open Einstein spaces, we construct the noise kernels of a conformally coupled scalar field in these spacetimes. From them we show that the noise kernels in conformally-flat spacetimes, including the Friedmann-Robertson-Walker universes, can be obtained in closed analytic forms by using a combination of conformal and coordindate transformations.

AdS geometry from CFT on a general conformally flat manifold

We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We explicitly show that the induced metric associated with the primary flow equation becomes AdS whose boundary is the curved manifold. Interestingly, it turns out that such an AdS metric with conformally flat boundary is obtained from the usual Poincare AdS by a simple bulk diffeomorphism transformation. We also demonstrate that the emergence of such an AdS space…

Conformally Flat Noncircular Spacetimes

The general metric for conformally flat stationary cyclic symmetric noncircular spacetimes is explicitly given. In spite of the complexity introduced by the inclusion of noncircular contributions, the related metric is derived via the full integration of the conformal flatness constraints. It is also shown that the conditions for the existence of a rotation axis (axisymmetry) are the same ones which restrict the above class of spacetimes to be static. As a consequence, a known theorem by Collinson is just part of a more general result: any conformally flat stationary cyclic symmetric spacetime…

Conformally flat black holes in Poincaré gauge theory

General criteria for the existence of conformally flat Riemannian solutions in 3D Poincaré gauge theory without matter are formulated. Using these criteria, we show that the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Town\-send gravity, is also an exact vacuum solution of the Poincaré gauge theory. The related conserved charges, calculated from the Hamiltonian boundary term, are shown to satisfy the first law of black hole thermodynamics. The form of the boundary term is verified by using the covariant Hamiltonian approach.

A note on Quantum Fields in Conformally flat Space-times

We develop a technique relating scalar fields with different masses in different conformally flat space-times. We apply this technique to the case of FRW space-times, with $k=\pm 1,0$, and discuss several examples. We also study various energy conditions and discuss how they constrain the space-times related by this technique. In addition, we use this technique to study correlators for the related space-times in an example.

Anisotropic fluid in a time dependent conformally flat spacetime

The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress tensor corresponding to an anisotropic fluid with negative regular energy density and positive pressures. For the static approximation, the generators of the infinitesimal transformation resemble those recently obtained by Majhi and Padmanabhan for the coordinate transformation leading to the "near horizon" Schwarzschild metric in Kruskal coordinates. The sta…

Kaluza-Klein reduction of conformally flat spaces

Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions. The corresponding equations are particularly elegant for the reduction from four to three dimensions. Assuming circular symmetry leads to explicit solutions which also arise from specific two-dimensional dilaton gravity actions.

Conformally flat Kaluza-Klein spaces, pseudo-/para-complex space forms and generalized gravitational kinks

The equations describing the Kaluza-Klein reduction of conformally flat spaces are investigated in arbitrary dimensions. Special classes of solution related to pseudo-Kahler and para-Kahler structures are constructed and classified according to spacetime dimension, signature and gauge field rank. Remarkably, rank two solutions include gravitational kinks together with their centripetal and centrifugal deformations.

反德西特超几何再探

The anti-de Sitter supergeometry revisited

本文重新考察四维$\cal N$-扩展反德西特超空间，给出其作为共形平坦超空间的两种显式实现，并应用于超粒子模型、超共形高自旋多重态及$κ$对称性等问题。