4,246 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
Entropy relations and the application of black holes with the cosmological constant and Gauss–Bonnet term
AbstractBased on entropy relations, we derive the thermodynamic bound for entropy and the area of horizons for a Schwarzschild–dS black hole, including the event horizon, Cauchy horizon, and negative horizon (i.e., the horizon with negative value), which are all geometrically bound and comprised by the cosmological radius. We consider the first derivative of the entropy relations to obtain the first law of thermodynamics for all horizons. We also obtain the Smarr relation for the horizons using the scaling discussion. For the thermodynamics of all horizons, the cosmological constant is treated as a thermodynamic variable. In particular, the thermodynamics of the negative horizon are defined well in the r<0 side of space–time. This formula appears to be valid for three-horizon black holes. We also generalize the discussion to thermodynamics for the event horizon and Cauchy horizon of Gauss–Bonnet charged flat black holes because the Gauss–Bonnet coupling constant is also considered to be thermodynamic variable. These results provide further insights into the crucial role played by the entropy relations of multi-horizons in black hole thermodynamics as well as improving our understanding of entropy at the microscopic level
Nonholonomic Motion Planning for a Free-Falling Cat Using Quasi-Newton Method
The motion planning problem of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the rotational motion of the cat subjects to nonholonomic constraints. The equation of dynamics of a free-falling cat is obtained by using the model of two symmetric rigid bodies. The control of system can be converted to the motion planning problem for a driftless system. Based on the input parameterization, the continuous optimal control problem is transformed into the discrete one. The quasi-Newton method of motion planning for nonholonomic multibody system is proposed. The effectiveness of the numerical algorithm is demonstrated by numerical simulation
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