52,856 research outputs found
Notes on Five-dimensional Kerr Black Holes
The geometry of five-dimensional Kerr black holes is discussed based on
geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal
space are naturally introduced by using special null geodesics. We show that
the geodesics of AdS Kerr black hole are integrable, which generalizes the
result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr
black holes are isospectrum deformations of Ricci-flat Kerr black holes in the
sense that the eigenvalues of the Weyl curvature are preserved.Comment: 23 pages, 5 figures; analyses on the Weyl curvature of AdS Kerr black
holes are extended, an appendix and references are adde
How Ordinary Elimination Became Gaussian Elimination
Newton, in notes that he would rather not have seen published, described a
process for solving simultaneous equations that later authors applied
specifically to linear equations. This method that Euler did not recommend,
that Legendre called "ordinary," and that Gauss called "common" - is now named
after Gauss: "Gaussian" elimination. Gauss's name became associated with
elimination through the adoption, by professional computers, of a specialized
notation that Gauss devised for his own least squares calculations. The
notation allowed elimination to be viewed as a sequence of arithmetic
operations that were repeatedly optimized for hand computing and eventually
were described by matrices.Comment: 56 pages, 21 figures, 1 tabl
Electron transmission through step- and barrier-like potentials in graphene ribbons
The list of textbook tunneling formulas is extended by deriving exact
expressions for the transmission coefficient in graphene ribbons with armchair
edges and the step-like and barrier-like profiles of site energies along the
ribbon. These expressions are obtained by matching wave functions at the
interfaces between the regions, where quasiparticles have constant but
different potential energies. It is shown that for an high barrier and
low-energy electrons and holes, the mode transmission of charge carriers in
this type of ribbons is described by the textbook formula, where the constant
barrier is replaced by an effective, energy-dependent barrier, .
For the lowest/highest electron/hole mode, goes, respectively, to zero
and nonzero value in metallic and semiconducting ribbons. This and other
peculiarities of through-barrier/step transmission in graphene are discussed
and compared with related earlier results.Comment: Edited, misprints correcte
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