Quantum Fluctuations of Black Hole Geometry

By using the minisuperspace model for the interior metric ofstatic black holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and the expansions of null rays as quantum operators. Then, the exact wave function is found as a mass eigenstate, and the radius of the apparent horizon is quantum-mechanically defined. In the evolution of the metric variables, the wave function changes from a WKB solution giving the classical trajectories to a tunneling solution. By virtue of the quantum fluctuations of the metric evolution beyond the WKB approximation, we can observe a static black hole state with the apparent horizon separating from the event horizon.Comment: 18 pages, DPNU-93-3

The X-ray jet in the Crab Nebula: radical implications for pulsar theory?

The recent Chandra image of the Crab nebula shows a striking, axisymmetric polar jet. It is shown that jets are formed in axisymmetric, magnetized pulsar winds and that the jet luminosity scales relative to the total as (\gamma_0\sigma_{eq})^{-4/3}, where \sigma_{eq} is the ratio of Poynting flux to particle kinetic energy output at the equator at the base of the flow and \gamma_0 the initial Lorentz factor of the flow. The results are applied to the image of the Crab nebula, and the limit is set for the Crab pulsar of \sigma_{eq} \leq 100. It is argued that conventional pulsar theory needs to be reexamined in light of these limits.Comment: 13 page

A new method for extracting conodonts and radiolarians from chert with NaOH solution

Microfossils are important components of sedi- mentary rocks used for palaeontological, biostratigraphic, palaeoenvironmental and palaeoclimatic investigations. They are usually extracted from rocks using an acid solution, which might vary depending on the embedding rock lithology. Here we propose a new method using common NaOH (sodium hydroxide; soda) to digest cherts (micro- and cryptocrystalline quartz) instead of the standard technique based on HF (hydrofluoric acid). This new method allows the collection of undamaged specimens of different kinds of microfossils, such as conodonts, radiolarians, teeth and dermal scales, the miner- ology of which is still preserved (e.g. biogenic apatite in cono- donts). The use of soda is thus recommended, as it is less dangerous, less expensive, and it better preserves the extracted microfossils both in shape and mineralogy

The most general axially symmetric electrovac spacetime adimitting separable equations of motion

We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the solution is its invariance under the duality transformation involving mass and NUT parameter, and the radial and angle coordinates. It is the general solution for a rotating (gravitational dyon) particle which is endowed with both gravoelectric and gravomagnetic charges, and there exists a duality transformation from one to the other. It also happens to be a transform of the Kerr - NUT solution. Like the Kerr family, it is also possible to make this solution radiating which asymptotically conforms to the Vaidya null radiation.Comment: 9 pages, RevTex, Accepted by Class. Quantum Grav. Title, Abstract and some expressions have been modified, typos corrected. The solution and main result remain unaltere

Transformation of the Poynting flux into the kinetic energy in relativistic jets

The acceleration of relativistic jets from the Poynting to the matter dominated stage is considered. The are generally two collimation regimes, which we call equilibrium and non-equilibrium, correspondingly. In the first regime, the jet is efficiently accelerated till the equipartition between the kinetic and electro-magnetic energy. We show that after the equilibrium jet ceases to be Poynting dominated, the ratio of the electro-magnetic to the kinetic energy decreases only logarithmically so that such jets become truly matter dominated only at extremely large distances. Non-equilibrium jets remain generally Poynting dominated till the logarithmically large distances. In the only case when a non-equilibrium jet is accelerated till the equipartition level, we found that the flow is not continued to the infinity but is focused towards the axis at a finite distance from the origin.Comment: Submitted to MNRAS Minor changes in the Conclusion

Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the $\Lambda=0$ case. Linear perturbations on this background lead to approximate black hole solutions. The critical exponent is found to be $\gamma = 2/5$.Comment: 22 pages, 6 figures. Major changes in the discussions of Sects. 2 and 5. The value of the critical exponent has been revised to \gamma = 2/

Dual geometries and spacetime singularities

The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity may be avoided in its dual representation (Weyl-type general relativity). This dual representation provides a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.Comment: 11 pages, LaTeX, no figures, version accepted for publication in PR

Axisymmetric Stationary Solutions as Harmonic Maps

We present a method for generating exact solutions of Einstein equations in vacuum using harmonic maps, when the spacetime possesses two commutating Killing vectors. This method consists in writing the axisymmetric stationry Einstein equations in vacuum as a harmonic map which belongs to the group SL(2,R), and decomposing it in its harmonic "submaps". This method provides a natural classification of the solutions in classes (Weil's class, Lewis' class etc).Comment: 17 TeX pages, one table,( CINVESTAV- preprint 12/93