7,211 research outputs found
On black hole spectroscopy via adiabatic invariance
In this paper, we obtain the black hole spectroscopy by combining the black
hole property of adiabaticity and the oscillating velocity of the black hole
horizon. This velocity is obtained in the tunneling framework. In particular,
we declare, if requiring canonical invariance, the adiabatic invariant quantity
should be of the covariant form . Using it,
the horizon area of a Schwarzschild black hole is quantized independent of the
choice of coordinates, with an equally spaced spectroscopy always given by
in the Schwarzschild and Painlev\'{e}
coordinates.Comment: 13 pages, some references added, to be published in Phys. Lett.
A Note on the Monge-Kantorovich Problem in the Plane
The Monge-Kantorovich mass-transportation problem has been shown to be
fundamental for various basic problems in analysis and geometry in recent
years. Shen and Zheng (2010) proposed a probability method to transform the
celebrated Monge-Kantorovich problem in a bounded region of the Euclidean plane
into a Dirichlet boundary problem associated to a nonlinear elliptic equation.
Their results are original and sound, however, their arguments leading to the
main results are skipped and difficult to follow. In the present paper, we
adopt a different approach and give a short and easy-followed detailed proof
for their main results
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