Conformally flat charged dust

It is proved that the most general conformally flat singularity-free solution for charged dust in static equilibrium must be spherically symmetric and the solution is unique. It matches with exterior Reissner-Nordström metric. The manifest form of the metric conformal to Minkowskian metric is also given.On study leave from Jadavpur University, Calcutta-700032, India.     

Cosmological sector for localized mass and spin in 2+1 dimensional topologically massive gravity

The cosmological sector to the full non-linear topologically massive gravity (TMG) is obtained for localized sources of mass m and spin σ besides the asymptotically spinning conical flat sector previously obtained [A. Edery, M.B. Paranjape, gr-qc/9606029, to be published]. In a small region near but outside the sources, the metric resembles the spinning conical flat metric but we find that the mass m creates a negative deficit angle of 3m as opposed to m. Furthermore, it is not possible to recover the results of pure Einstein gravity in the limit μ→∞ unlike the flat sector.     

The trace anomaly in coloured black holes

The influence of the trace anomaly of the energy-momentum tensor of gauge theories is discussed in a spherically symmetric space-time. It is found that for pure electric and magnetic fields, the point β(g) = ?g represents a phase transition from any asymptotically flat metric to an asymptotically non-flat metric which turns out to be confining in the electric case.     

Twistor Spinors with Zero on Lorentzian 5-Space

We present in this paper a C ¹-metric of Lorentzian signature (1,4) on an open neighbourhood of the origin in \(\mathbb{R}^{5}\), which admits a solution to the twistor equation for spinors with a unique isolated zero at the origin. The metric is not conformally flat in any neighbourhood of the origin and the associated conformal Killing vector to the twistor generates a one-parameter group of essential conformal transformations. The construction is based on the Eguchi-Hanson metric in dimension 4.     

Spacelike metric foliations

In this paper, we investigate spacelike metric foliations in lightlike complete spacetimes. When such a foliation satisfies the strong energy condition Ric^V (e) ≥ 0 for timelike vectors e, it must be totally geodesic, and the metric is of higher rank, in the sense that each point of the spacetime is contained inside a flat, totally geodesic, timelike rectangle. If in addition Ric^V(e) = 0, then the metric is (at least locally) a product metric, with the leaves of the foliation tangent to one of the factors.     

Accelerated Levi-Civita-Bertotti-Robinson metric in D dimensions

A conformally flat accelerated charge metric is found in an arbitrary dimension D. It is a solution of the Einstein-Maxwell-null fluid equations with a cosmological constant in D ≥ 4 dimensions. When the acceleration is zero, our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.     

Flat connections and Wigner-Yanase-Dyson metrics

On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the α-embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that in both cases, the existence of such a pair of connections is possible if and only if the metric is given by the Wigner-Yanase-Dyson skew information.     

On Rosen's bi-metric theory of gravitation

The field equations of Rosen's bi-metric theory of gravitation [1] are solved exactly. The solutions are the same as in the author's theory of gravitation [2]. These solutions are, however, incompatible with Rosen's conservation laws and his second (flat) metric. Incompatibility with the conservation laws arises in second order. Incompatibility with the flat metric arises in first order but only for time-dependent fields. Rosen's theory is defensible only as a static first order theory and predicts the red shift light deflection and time-delay correctly.     

M-theory on eight-manifolds

We show that in certain compactifications of M-theory on eight-manifolds to three-dimensional Minkowski space-time the four-form field strength can have a non-vanishing expectation value, while an N = 2 supersymmetry is preserved. For these compactifications a warp factor for the metric has to be taken into account. This warp factor is non-trivial in three space-time dimensions due to Chern-Simons corrections to the fivebrane Bianchi identity. While the original metric on the internal space is not Kahler, it can be conformally transformed to a metric that is Kähler and Ricci flat, so that the internal manifold has SU(4) holonomy.     

An asymptotically flat vacuum solution

An asympototically flat algebraically general vacuum metric is obtained. The solution is characterized by two commuting spacelike Killing vectors with flat integral surfaces and depends on one arbitrary function.     

Solution of the stationary vacuum equations of relativity for conformally flat 3-spaces

The solution of Einstein's vacuum gravitational equations for stationary space—times with a conformally flat 3-space is presented. There is no other solution of this problem than the Ehlers-rotation generalizations of the three conformastat space—times including the Schwarzschild metric.     

A new class of asymptotically flat stationary axisymmetric vacuum gravitational fields

We present the full four-dimensional metric for a stationary axisymmetric solution of the vacuum Einstein equations related to the Ernst potential which we obtain by application of anarbitrary number of rank-zero HKX transformations to the general static Weyl solution. The metric function is determined in a completely algebraically way. We perform a suitable Ehlers transformation to ensure asymptotic flatness and give the expression for the total mass of this asymptotically flat solution by analyzing the behavior of the solution on the positive z axis.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

An exact solution of Einstein's equation with a dilaton field

An exact solution of Einstein gravity coupled to a dilaton field is found. The solution is conformally flat and is invariant under Lorentz transformations. The singularities and conformal structure of the metric are examined.     

The Lewis metric and flat space-time

It is shown that the stationary solution of the Einstein equationsin vacuo, with the cylindrical symmetry obtained by Lewis, does not contain a space-time that is globally Minkowskian. It is shown that the inclusion of a certain constant of integration excludes this flat space-time metric.     

Exact solutions of Einstein and Einstein-scalar equations in 2 + 1 dimensions

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant Λ and null fluid) in 2 + 1 dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For Λ = 0, the spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einsteinmassless scalar equations is given, which has a curvature singularity atr = 0 and the scalar field diverges atr = 0 as well as at infinity.     

An approximate global solution of Einstein’s equations for a rotating finite body

We obtain an approximate global stationary and axisymmetric solution of Einstein’s equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find second-order approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic and quo-harmonic coordinates. In both cases, interior and exterior solutions are matched, in the sense of Lichnerowicz, on the surface of zero pressure to obtain a global solution. The resulting metric depends on three arbitrary constants: mass density, rotational velocity and the star radius at the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined by these three parameters. It is easy to check that Kerr’s metric cannot be the exterior part of that metric.     

矢引力子场度规场引力理论的共形平直静止解及引力场的能量动量赝张量的正常性

本文求出了VGM引力理论的共形平直静止解。文中把胡宁表达式引入VGM,它同样是守恒的能量动量表达式。对于单个集中质量的引力场,与GR一样,可证实引力质量与惯性质量相等。但Einstein的等效原理在这理论中并不成立。利用所求得的解,可知当n<1/4时,引力场的能量动量赝张量就是正常的。 关键词：     

The Monodromy Matrix Method of Solving an Exterior Boundary Value Problem for a Given Stationary Axisymmetric Perfect Fluid Solution

A procedure is described for matching a given stationary axisymmetric perfect fluid solution to a not necessarily asymptotically flat vacuum exterior. Using data on the zero pressure surface, the procedure yields the Ernst potential of the matching vacuum metric on the symmetry axis. From this the full metric can be constructed by established procedures.