32,448 research outputs found
Minimum Cycle Base of Graphs Identified by Two Planar Graphs
In this paper, we study the minimum cycle base of the planar graphs obtained
from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds
Stability of black holes based on horizon thermodynamics
On the basis of horizon thermodynamics we study the thermodynamic stability
of black holes constructed in general relativity and Gauss-Bonnet gravity. In
the framework of horizon thermodynamics there are only five thermodynamic
variables . It is not necessary to consider concrete matter fields,
which may contribute to the pressure of black hole thermodynamic system. In
non-vacuum cases, we can derive the equation of state, . According to
the requirements of stable equilibrium in conventional thermodynamics, we start
from these thermodynamic variables to calculate the heat capacity at constant
pressure and Gibbs free energy and analyze the local and global thermodynamic
stability of black holes. It is shown that is the necessary condition for
black holes in general relativity to be thermodynamically stable, however this
condition cannot be satisfied by many black holes in general relativity. For
black hole in Gauss-Bonnet gravity negative pressure can be feasible, but only
local stable black hole exists in this case.Comment: 6 pages, 7 figure
Noncommutative geometry inspired black holes in Rastall gravity
Under two different metric ansatzes, the noncommutative geometry inspired
black holes (NCBH) in the framework of Rastall gravity are derived and
analyzed. We consider the fluid-type matter with the Gaussian-distribution
smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown
that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in
Rastall gravity, unlike its counterpart in general relativity (GR), is not a
regular black hole. It has at most one event horizon. After showing a finite
maximal temperature, the black hole will leave behind a point-like massive
remnant at zero temperature. Considering a more general metric ansatz and a
special equation of state of the matter, we also find a regular NCBH in Rastall
gravity, which has a similar geometric structure and temperature to that of
NCSBH in GR.Comment: 12 pages, 5 figures. to match the published versio
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