164,711 research outputs found

### Extended phase space thermodynamics for third order Lovelock black holes in diverse dimensions

Treating the cosmological constant as thermodynamic pressure and its
conjugate as thermodynamic volume, we investigate the critical behavior of the
third order Lovelock black holes in diverse dimensions. For black hole horizons
with different normalized sectional curvature $k=0,\pm1$, the corresponding
critical behaviors differ drastically. For $k=0$, there is no critical point in
the extended thermodynamic phase space. For $k=-1$, there is a single critical
point in any dimension $d\geq 7$, and for $k=+1$, there is a single critical
point in $7$ dimension and two critical points in $8,9,10,11$ dimensions. We
studied the corresponding phase structures in all possible cases.Comment: pdflatex, 22 pages, 36 eps figures included. V2: minor corrections
and new reference

### Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality

The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is
extended, taking the inverse of the GB coupling constant as a new thermodynamic
pressure $P_{\mathrm{GB}}$. We studied the critical behavior associated with
$P_{\mathrm{GB}}$ in the extended thermodynamic phase space at fixed
cosmological constant and electric charge. The result shows that when the black
holes are neutral, the associated critical points can only exist in five
dimensional GB-AdS black holes with spherical topology, and the corresponding
critical exponents are identical to those for Van der Waals system. For charged
GB-AdS black holes, it is shown that there can be only one critical point in
five dimensions (for black holes with either spherical or hyperbolic
topologies), which also requires the electric charge to be bounded within some
appropriate range; while in $d>5$ dimensions, there can be up to two different
critical points at the same electric charge, and the phase transition can occur
only at temperatures which are not in between the two critical values.Comment: 23 pages. V2: modified all P_{GB}-r_+ plots using dimensionless
variables, added comments on the relationship to Einstein limi

### Uniqueness of directed complete posets based on Scott closed set lattices

In analogy to a result due to Drake and Thron about topological spaces, this
paper studies the dcpos (directed complete posets) which are fully determined,
among all dcpos, by their lattices of all Scott-closed subsets (such dcpos will
be called $C_{\sigma}$-unique).
We introduce the notions of down-linear element and quasicontinuous element
in dcpos, and use them to prove that dcpos of certain classes, including all
quasicontinuous dcpos as well as Johnstone's and Kou's examples, are
$C_{\sigma}$-unique. As a consequence, $C_{\sigma}$-unique dcpos with their
Scott topologies need not be bounded sober.Comment: 12 pages. arXiv admin note: substantial text overlap with
arXiv:1607.0357

### Generalized Projective Representations for sl(n+1)

It is well known that $n$-dimensional projective group gives rise to a
non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial
functions of the projective space. Using Shen's mixed product for Witt algebras
(also known as Larsson functor), we generalize the above representation of
$sl(n+1)$ to a non-homogenous representation on the tensor space of any
finite-dimensional irreducible $gl(n)$-module with the polynomial space.
Moreover, the structure of such a representation is completely determined by
employing projection operator techniques and well-known Kostant's
characteristic identities for certain matrices with entries in the universal
enveloping algebra. In particular, we obtain a new one parameter family of
infinite-dimensional irreducible $sl(n+1)$-modules, which are in general not
highest-weight type, for any given finite-dimensional irreducible
$sl(n)$-module. The results could also be used to study the quantum field
theory with the projective group as the symmetry.Comment: 24page

### Critical phenomena of static charged AdS black holes in conformal gravity

The extended thermodynamics of static charged AdS black holes in conformal
gravity is analyzed. The $P-V$ criticality of these black holes has some
unusual features. There exists a single critical point with critical
temperature $T_c$ and critical pressure $P_c$. At fixed $T>T_c$ (or at fixed
$P>P_c$), there are two zeroth order phase transition points but no first order
phase transition points. The systems favors large pressure states at constant
$T$, or high temperature states at constant $P$.Comment: 16 pages, 3 figures; published versio

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