31,681 research outputs found
The "universal property" of Horizon Entropy Sum of Black Holes in Four Dimensional Asymptotical (anti-)de-Sitter Spacetime Background
We present a new ``universal property'' of entropy, that is the ``entropy
sum'' relation of black holes in four dimensional (anti-)de-Sitter asymptotical
background. They depend only on the cosmological constant with the necessary
effect of the un-physical ``virtual'' horizon included in the spacetime where
only the cosmological constant, mass of black hole, rotation parameter and
Maxwell field exist. When there is more extra matter field in the spacetime,
one will find the ``entropy sum'' is also dependent of the strength of these
extra matter field. For both cases, we conclude that the ``entropy sum'' does
not depend on the conserved charges , and , while it does depend on
the property of background spacetime. We will mainly test the ``entropy sum''
relation in static, stationary black hole and some black hole with extra matter
source (scalar hair and higher curvature) in the asymptotical (anti-)de-sitter
spacetime background. Besides, we point out a newly found counter example of
the mass independence of the ''entropy product'' relation in the spacetime with
extra scalar hair case, while the ``entropy sum'' relation still holds. These
result are indeed suggestive to some underlying microscopic mechanism.
Moreover, the cosmological constant and extra matter field dependence of the
``entropy sum'' of all horizon seems to reveal that ``entropy sum'' is more
general as it is only related to the background field. For the case of
asymptotical flat spacetime without any matter source, we give a note for the
Kerr black hole case in appendix. One will find only mass dependence of
``entropy sum'' appears. It makes us believe that, considering the dependence
of ``entropy sum'', the mass background field may be regarded as the next order
of cosmological constant background field and extra matter field.Comment: 14 pages, no figures, JHEP forma
Thermodynamic relations for entropy and temperature of multi-horizons black holes
We present some entropy and temperature relations of multi-horizons, even
including the "virtual" horizon. These relations are related to product,
division and sum of entropy and temperature of multi-horizons. We obtain the
additional thermodynamic relations of both static and rotating black holes in
three and four dimensional (A)dS spacetime. Especially, a new dimensionless,
charges-independence and like relation is presented. This
relation does not depend on the mass, electric charge, angular momentum and
cosmological constant, as it is always a constant. These relations lead us to
get some interesting thermodynamic bound of entropy and temperature, including
the Penrose inequality which is the first geometrical inequality of black
holes. Besides, based on these new relations, one can obtain the first law of
thermodynamics and Smarr relation for all horizons of black hole.Comment: 12 pages, no figures, title changed, references adde
A Unique "Nonnegative" Solution to an Underdetermined System: from Vectors to Matrices
This paper investigates the uniqueness of a nonnegative vector solution and
the uniqueness of a positive semidefinite matrix solution to underdetermined
linear systems. A vector solution is the unique solution to an underdetermined
linear system only if the measurement matrix has a row-span intersecting the
positive orthant. Focusing on two types of binary measurement matrices,
Bernoulli 0-1 matrices and adjacency matrices of general expander graphs, we
show that, in both cases, the support size of a unique nonnegative solution can
grow linearly, namely O(n), with the problem dimension n. We also provide
closed-form characterizations of the ratio of this support size to the signal
dimension. For the matrix case, we show that under a necessary and sufficient
condition for the linear compressed observations operator, there will be a
unique positive semidefinite matrix solution to the compressed linear
observations. We further show that a randomly generated Gaussian linear
compressed observations operator will satisfy this condition with
overwhelmingly high probability
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