Kerr Geodesics, the Penrose Process and Jet Collimation by a Black Hole

We re-examine the possibility that astrophysical jet collimation may arise from the geometry of rotating black holes and the presence of high-energy particles resulting from a Penrose process, without the help of magnetic fields. Our analysis uses the Weyl coordinates, which are revealed better adapted to the desired shape of the jets. We numerically integrate the 2D-geodesics equations. We give a detailed study of these geodesics and give several numerical examples. Among them are a set of perfectly collimated geodesics with asymptotes $\rho =\rho_{1}$ parallel to the $z-$ axis, with $\rho_{1}$ only depending on the ratios $\frac{\mathcal{Q}}{E^{2}-1}$ and $\frac{a}{M}$, where $a$ and $M$ are the parameters of the Kerr black hole, $E$ the particle energy and $\mathcal{Q}$ the Carter's constant.Comment: Accepted by Astronomy and Astrophysics. AA style with 3 EPS figures. Content amended after AA's refereeing. Discussion of geodesics also corrected and expanded earlier. Conclusions amended accordingl

Static cylindrical symmetry and conformal flatness

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat cylindrically symmetric static source cannot be matched through Darmois conditions to the Levi-Civita spacetime. Further evidence is given that when the Newtonian mass per unit length reaches 1/2 the spacetime has plane symmetry.Comment: 13 pages, Late

On the pre-nucleonsynthesis cosmological period

Physics, as known from our local, around—earth experience, meets some of itsapplicability limits at the time just preceding the period of primeval nucleosynthesis. Attentionis focussed here on the effects of the nucleon size. Radiation—belonging nucleons arefound to produce an extremely high pressure at kT ≈ some tens or hundreds of MeV. Quarkdeconfinement at higher energies would not change the results

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)

Unbound Geodesics From The Ergosphere And The Messier 87 Jet Profile

International audienc

Letter: Parametrization of the Kerr-NUT Solution

International audienceThe dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere