On Neutralization of Charged Black Holes

For non-spinning, charged (Reissner–Nordström) black holes, the particles with an opposite sign of charge with respect to that of the black hole will be pulled into the black hole by the extra electromagnetic force. Such a hole will be quickly neutralized so that there should not exist significantly charged, non-spinning black holes in the universe. The case of spinning, charged (Kerr–Newmann, KN) black holes is more complicated. For a given initial position and initial velocity of the particle, an oppositely charged particle does not always more easily fall into the black hole than a neutral particle. The possible existence of a magnetosphere further complicate the picture. One therefore cannot straightforwardly conclude that a charged spinning black hole will be neutralized. In this paper, we make the first step to investigate the neutralization of KN black holes without introducing a magnetosphere. We track the particle trajectories under the influence of the curved space–time and the electromagnetic field carried by the spinning, charged black hole. A statistical method is used to investigate the neutralization problem. We find a universal dependence of the falling probability into the black hole on the charge of the test particle, with the oppositely charged particles having a higher probability of falling. We therefore conclude that charged, spinning black holes without a magnetosphere should be quickly neutralized, consistent with people’s intuition. The neutralization problem of KN black holes with a corotating force-free magnetosphere is subject to further studies

Saddlepoint approximation for Student's t-statistic with no moment conditions

A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximation's applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint approximation of the Student's t-statistic remains valid without any moment condition. This confirms the folklore that the Student's t-statistic is robust against outliers. The saddlepoint approximation not only provides a very accurate approximation for the Student's t-statistic, but it also can be applied much more widely in statistical inference. As a result, saddlepoint approximations should always be used whenever possible. Some numerical work will be given to illustrate these points.Comment: Published at http://dx.doi.org/10.1214/009053604000000742 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comment on " a unified scheme for flavored mesons and baryons"

We would comment on the results of the paper "a unified scheme for flavored mesons and baryons" (P.C.Vinodkumar, J.N.Panandya, V.M.Bannur, and S.B.Khadkikar Eur. Phys. J. A4(1999)83), and point out some inconsistencies and mistakes in the work for solving the Dirac equation. In terms of an example for a single particle we investigate the reliability of the perturbative method for computing the Coulomb energy and discuss the contribution to the wavefunction at origin from the Coulomb potential. We conclude that the accuracy of their numerical results needs to be reconsidered.Comment: Latex file, 11page