Geodesics on extensions of Lie groups and stability: the superconductivity equation

The equations of motion of an ideal charged fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations of a general, respectively a central extension of the group of volume preserving diffeomorphisms with right invariant metrics. For this, quantization of the magnetic flux is required. We do curvature computations in both cases in order to get informations about the stability.     

Spherical Solutions due to the Exterior Geometry of a Charged Weyl Black Hole

Firstly we derive peculiar spherical Weyl solutions, using a general spherically symmetric metric due to a massive charged object with definite mass and radius. Afterwards, we present new analytical solutions for relevant cosmological terms, which appear in the metrics. Connecting the metrics to a new geometric definition of a charged Black Hole, we numerically investigate the effective potentials of the total dynamical system, considering massive and massless test particles, moving on such Black Holes.     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

Letter: Gödel-Type Space-Time Metrics

A simple group theoretic derivation is given of the family of space-time metrics with isometry group SO(2,1) × SO(2) × first described by Gödel, of which the Gödel stationary cosmological solution is the member with a perfect-fluid stress-energy tensor. Other members of the family are shown to be interpretable as cosmological solutions with an electrically charged perfect fluid and a magnetic field.     

New Charged Dilaton Solutions in 2+1 Dimensions and Solutions with Cylindrical Symmetry in 3+1 Dimensions

We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a compactification of charged solutions in 3+1 dimensions with cylindrical symmetry. These solutions contain naked singularities for certain values of the parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1 dimensions are generated treating the static charged solutions as seed metrics and performing SL(2;R) transformations.     

A charged spherically symmetric solution

We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.     

Remarks on the Charged, Magnetized Tomimatsu-Sato delta = 2 Solution

The full metric describing a charged, magnetizedgeneralization of the Tomimatsu-Sato (TS) = 2solution is presented in a concise explicit form. We useit to investigate some physical properties of the solution; in particular, we point out theexistence of naked ring singularities in thehyperextreme TS metrics, the fact previously overlookedby the researchers, and we also demonstrate that thering singularities can be eliminated by sufficientlystrong magnetic fields in the subextreme case, while inthe hyperextreme case the magnetic field can movesingularities to the equatorial plane.     

The isometry groups of simply connected 3-dimensional unimodular Lie groups

For each simply connected 3-dimensional unimodular Lie group the left invariant Riemannian metrics up to automorphism are classified in Ha and Lee (2009) [2]. Using this classification, we determine on each such a Lie group the full group of isometries which depends on left invariant Riemannian metrics.     

Diagonalizing cohomogeneity-one Einstein metrics

We investigate when it is possible to globally diagonalize an Einstein metric of cohomogeneity-one under the action of a compact connected Lie group G with isotropy subgroup K. Restricting our attention to the non-monotypic case in which cohomogeneity-one metrics are not automatically diagonalizable, we make use of a subset of the ODEs of the Einstein condition to globally diagonalize the Einstein metric in certain cases. The program we use is inspired by a result well-known to relativists which states that Einstein metrics must be diagonalizable in the Bianchi IX case. We present a full classification of all the cohomogeneity-one metrics on which this method can be used.     

Real Kasner and related complex “windmill” vacuum spacetime metrics

The Kasner family of vacuum solutions of Einstein's field equations admits a simply-transitiveH ₄, a four-parameter local homothetic group of motions which has an AbelianG ₃ subgroup. It is shown that a complex transformation of coordinates and constants exists which maps this family from the normal Kasner form into a form of vacuum metrics whose Weyl tensors are each Petrov type I and which were published in 1932 by Lewis. These metrics also admit a similarH ₄; however for one particular metric (for one parameter value) theH ₄ becomes aG ₄ and the resultant metric is one which was rediscovered by Petrov in 1962. These Lewis metrics are thus shown to be Kasner metrics over complex fields. Here they are calledwindmill metrics because of the rotating relationship between the coordinates and the Killing vector fields admitted. The principal null directions of thereal Kasner and the windmill metrics are discussed; the two families then provide illustrations of two degenerate classes of spacetime metrics whose Weyl tensors are of Petrov type I, as discussed elsewhere by Arianrhod and McIntosh. An extension of the windmill-type generation of metrics to some other families of metrics is also discussed.     

无限长均匀带电直线组电场分布的复势解法

给出无限长均匀带电直线的复势,接着讨论平行直线排列与平行环形排列两种情况下,无限长均匀带电直线组的复势与电场,并由此得出相应的电场线与等势线方程.     

A spherically symmetric solution of the Maxwell-Einstein equations

A spherically symmetric solution of the already unified field theory ofRainich (i.e. of the source-free Maxwell-Einstein equations) is presented which represents a static massless charged particle. It is not equivalent to the Reissner-Nordström solution with zero mass, although both metrics repel uncharged test particles.On leave of absence from the Department of Mathematics, The University, Bristol.     

Invariant solutions to the conformal Killing–Yano equation on Lie groups

We search for invariant solutions of the conformal Killing–Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a bi-invariant metric or 2-step nilpotent, the only invariant solutions occur on the 3-dimensional sphere or on a Heisenberg group. We classify the 3-dimensional Lie groups with left invariant metrics carrying invariant conformal Killing–Yano 2-forms.     

Simply-transitive homothety groups

In this paper the spin-coefficient formalism of Penrose and Rindler is applied to the problem of finding space-times that admit a simply-transitive group of homotheties. The method is illustrated by an application to algebraically special vacuum space-times. Vacuum metrics with a fivedimensional homothety group are also considered.     

Proof of the Projective Lichnerowicz Conjecture for Pseudo-Riemannian Metrics with Degree of Mobility Greater than Two

Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the space of metrics geodesically equivalent to it. We prove that complete metrics on (n≥ 3)−dimensional manifolds with degree of mobility ≥ 3 do not admit complete metrics that are geodesically equivalent to them, but not affinely equivalent to them. As the main application we prove an important special case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the standard round sphere (up to a finite cover and multiplication of the metric by a constant).     

Statistical entropies of extremal Kaluza-Klein AdS black holes in arbitrary dimensions

We have investigated the microscopic interpretations of the entropies for the four-dimensional extremal Kaluza-Klein AdS black hole and its higher-dimensional generalizations by using the Kerr/CFT correspondence. These newly-found Kaluza-Klein AdS black holes are charged rotating asymptotically AdS black hole solutions of gauged supergravity in four and higher dimensions. With suitable boundary conditions on the perturbations of the near-horizon geometry, it is shown that the asymptotic symmetry generators form a two-dimensional Virasoro algebra with a central term. By utilizing the central charge and the temperature of the dual conformal field theory, Cardy formula reproduces the expected Bekenstein-Hawking entropy. Directly working on the ordinary metrics of the extremal Kaluza-klein AdS black holes without taking the near-horizon limit, we also re-derive their microscopic entropies.     

有机高分子中光生极化子的物理机制

有机聚合物中光生载流子（荷电极化子）产生的物理机制是一个非常重要的物理问题，但一直存在争议，文章介绍了作者对此问题的最新研究结果：荷电极化子和中性激子一样，是由光激发直接产生的，而不是激子解体的结果，其生成时间在100fs的量级．荷电极化子的量子产率约为25％，并且与激发能量无关，与实验观测的结果一致．     

General nonextremal rotating black holes in minimal five-dimensional gauged supergravity

We construct the general solution for nonextremal charged rotating black holes in five-dimensional minimal gauged supergravity. They are characterized by four nontrivial parameters: namely, the mass, the charge, and the two independent rotation parameters. The metrics in general describe regular rotating black holes, providing the parameters lie in appropriate ranges so that naked singularities and closed timelike curves (CTCs) are avoided. We calculate the conserved energy, angular momenta, and charge for the solutions, and show how supersymmetric solutions arise in a Bogomol'nyi-Prasad-Sommerfield limit. These have naked CTCs in general, but for special choices of the parameters we obtain new regular supersymmetric black holes or smooth topological solitons.