21,688 research outputs found
On the concavity of the arithmetic volumes
In this note, we study the differentiability of the arithmetic volumes along
arithmetic R-divisors, and give some equality conditions for the
Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big
arithmetic R-divisors.Comment: 35 page
Thermodynamic Properties of Small Localized Black Holes
In a previous paper, we developed a numerical method to obtain a static black
hole localized on a 3-brane in the Randall-Sundrum infinite braneworld, and
presented examples of numerical solutions that describe small localized black
holes. In this paper we quantitatively analyze the behavior of the numerically
obtained black hole solutions, focusing on thermodynamic quantities. The
thermodynamic relations show that the localized black hole deviates smoothly
from a five-dimensional Schwarzschild black hole, which is a solution in the
limit of a small horizon radius. We compare the thermodynamic behavior of these
solutions with that of the exact solution on the 2-brane in the 4D braneworld.
We find similarities between them.Comment: 6 pages, 6 figures, RevTex, references adde
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