Entropy in the Kerr-Newman Black Hole

Entropy of the Kerr-Newman black hole is calculated via the brick wall method with maintaining careful attention to the contribution of superradiant scalar modes. It turns out that the nonsuperradinat and superradiant modes simultaneously contribute to the entropy with the same order in terms of the brick wall cutoff $\epsilon$. In particular, the contribution of the superradiant modes to the entropy is negative. To avoid divergency in this method when the angular velocity tends to zero, we propose to intr oduce a lower bound of angular velocity and to treat the case of the angular momentum per unit mass $a=0$ separately. Moreover, from the lower bound of the angular velocity, we obtain the $\theta$-dependence structure of the brick wall cutoff, which natu rally requires an angular cutoff $\delta$. Finally, if the cutoff values, $\epsilon$ and $\delta$, satisfy a proper relation between them, the resulting entropy satisfies the area law.Comment: 16 pages, Latex, no figures, References are included, Subsection A and B are reduced to subsection A, Abstract is rewritten, Minor corrections are include

A note on the factorization method of Niederreiter

AbstractIn this paper, we explicitly obtain the coefficient matrix arising from a linearization of Niederreiter's factorization algorithm and analyze the complexity of setting it up. It turns out that its setup cost is linear both in the degree of a polynomial to be factored and in the size of the base field

Electrical Investigation of the Oblique Hanle Effect in Ferromagnet/Oxide/Semiconductor Contacts

We have investigated the electrical Hanle effect with magnetic fields applied at an oblique angle ({\theta}) to the spin direction (the oblique Hanle effect, OHE) in CoFe/MgO/semiconductor (SC) contacts by employing a three-terminal measurement scheme. The electrical oblique Hanle signals obtained in CoFe/MgO/Si and CoFe/MgO/Ge contacts show clearly different line shapes depending on the spin lifetime of the host SC. Notably, at moderate magnetic fields, the asymptotic values of the oblique Hanle signals (in both contacts) are consistently reduced by a factor of cos^2({\theta}) irrespective of the bias current and temperature. These results are in good agreement with predictions of the spin precession and relaxation model for the electrical oblique Hanle effect. At high magnetic fields where the magnetization of CoFe is significantly tilted from the film plane to the magnetic field direction, we find that the observed angular dependence of voltage signals in the CoFe/MgO/Si and CoFe/MgO/Ge contacts are well explained by the OHE, considering the misalignment angle between the external magnetic field and the magnetization of CoFe.Comment: 19 pages, 8 figure