2,476 research outputs found

### Effects of dark energy on P-V criticality of charged AdS black holes

In this Letter, we investigate the effects of dark energy on $P-V$
criticality of charged AdS black holes by considering the case of the RN-AdS
black holes surrounded by quintessence. By treating the cosmological constant
as thermodynamic pressure, we study its thermodynamics in the extended phase
space. It is shown that quintessence dark energy does not affect the existence
of small/large black hole phase transition. For the case $\omega_q=-2/3$ we
derive analytic expressions of critical physical quantities, while for cases
$\omega_q\neq-2/3$ we appeal to numerical method for help. It is shown that
quintessence dark energy affects the critical physical quantities near the
critical point. Critical exponents are also calculated. They are exactly the
same as those obtained before for arbitrary other AdS black holes, which
implies that quintessence dark energy does not change the critical exponents.Comment: 13 pages, 2 figure

### Holographic Heat engine within the framework of massive gravity

Heat engine models are constructed within the framework of massive gravity in
this paper. For the four-dimensional charged black holes in massive gravity, it
is shown that the heat engines have a higher efficiency for the cases $m^2>0$
than for the case $m=0$ when $c_1<0, c_2<0$. Considering a specific example, we
show that the maximum efficiency can reach $0.9219$ while the efficiency for
$m=0$ reads $0.5014$. The existence of graviton mass improves the heat engine
efficiency significantly. The situation is more complicated for the
five-dimensional neutral black holes. Not only the $c_1, c_2, m^2$ exert
influence on the efficiency, but also the constant $c_3$ corresponding to the
third massive potential contributes to the efficiency. When $c_1<0, c_2<0,
c_30$ is higher than that of
the case $m=0$. By studying the ratio $\eta/\eta_C$, we also probe how the
massive gravity influences the behavior of the heat engine efficiency
approaching the Carnot efficiency.Comment: 9pages,4figure

### Ratio of critical quantities related to Hawking temperature-entanglement entropy criticality

We revisit the Hawking temperature$-$entanglement entropy criticality of the
$d$-dimensional charged AdS black hole with our attention concentrated on the
ratio $\frac{T_c \delta S_c}{Q_c}$. Comparing the results of this paper with
those of the ratio $\frac{T_c S_c}{Q_c}$, one can find both the similarities
and differences. These two ratios are independent of the characteristic length
scale $l$ and dependent on the dimension $d$. These similarities further
enhance the relation between the entanglement entropy and the
Bekenstein-Hawking entropy. However, the ratio $\frac{T_c \delta S_c}{Q_c}$
also relies on the size of the spherical entangling region. Moreover, these two
ratios take different values even under the same choices of parameters. The
differences between these two ratios can be attributed to the peculiar property
of the entanglement entropy since the research in this paper is far from the
regime where the behavior of the entanglement entropy is dominated by the
thermal entropy.Comment: Comments welcome. 11 pages, 3 figure

### Heat engine in the three-dimensional spacetime

We define a kind of heat engine via three-dimensional charged BTZ black
holes. This case is quite subtle and needs to be more careful. The heat flow
along the isochores does not equal to zero since the specific heat $C_V\neq0$
and this point completely differs from the cases discussed before whose
isochores and adiabats are identical. So one cannot simply apply the paradigm
in the former literatures. However, if one introduces a new thermodynamic
parameter associated with the renormalization length scale, the above problem
can be solved. We obtain the analytical efficiency expression of the
three-dimensional charged BTZ black hole heat engine for two different schemes.
Moreover, we double check with the exact formula. Our result presents the first
specific example for the sound correctness of the exact efficiency formula. We
argue that the three-dimensional charged BTZ black hole can be viewed as a toy
model for further investigation of holographic heat engine. Furthermore, we
compare our result with that of the Carnot cycle and extend the former result
to three-dimensional spacetime. In this sense, the result in this paper would
be complementary to those obtained in four-dimensional spacetime or ever
higher. Last but not the least, the heat engine efficiency discussed in this
paper may serve as a criterion to discriminate the two thermodynamic approaches
introduced in Ref.[29] and our result seems to support the approach which
introduces a new thermodynamic parameter $R=r_0$.Comment: Revised version. Discussions adde

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