107 research outputs found
Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly
We investigate the phase transitions of black holes with conformal anomaly in
canonical ensemble from different perspectives. Some interesting and novel
phase transition phenomena have been discovered. Firstly, we discuss the
behavior of the specific heat and the inverse of the isothermal
compressibility. It is shown that there are striking differences in Hawking
temperature and phase structure between black holes with conformal anomaly and
those without it. In the case with conformal anomaly, there exists local
minimum temperature corresponding to the phase transition point. Phase
transitions take place not only from an unstable large black hole to a locally
stable medium black hole but also from an unstable medium black hole to a
locally stable small black hole. Secondly, we probe in details the dependence
of phase transitions on the choice of parameters. The results show that black
holes with conformal anomaly have much richer phase structure than those
without it. There would be two, only one or no phase transition points
depending on the parameters we have chosen. The corresponding parameter region
are derived both numerically and graphically. Thirdly, geometrothermodynamics
are built up to examine the phase structure we have discovered. It is shown
that Legendre invariant thermodynamic scalar curvature diverges exactly where
the specific heat diverges. Furthermore, critical behaviors are investigated by
calculating the relevant critical exponents. It is proved that these critical
exponents satisfy the thermodynamic scaling laws, leading to the conclusion
that critical exponents and the scaling laws can reserve even when we consider
conformal anomaly.Comment: some new references adde
Non-extended phase space thermodynamics of Lovelock AdS black holes in grand canonical ensemble
Recently, extended phase space thermodynamics of Lovelock AdS black holes has
been of great interest. To provide insight from a different perspective and
gain a unified phase transition picture, non-extended phase space
thermodynamics of -dimensional charged topological Lovelock AdS black
holes is investigated detailedly in the grand canonical ensemble. Specifically,
the specific heat at constant electric potential is calculated and phase
transition in the grand canonical ensemble is discussed. To probe the impact of
the various parameters, we utilize the control variate method and solve the
phase transition condition equation numerically for the case . There
are two critical points for the case while there is only one for
other cases. For , there exists no phase transition point. To figure out
the nature of phase transition in the grand canonical ensemble, we carry out an
analytic check of the analog form of Ehrenfest equations proposed by Banerjee
et al. It is shown that Lovelock AdS black holes in the grand canonical
ensemble undergo a second order phase transition. To examine the phase
structure in the grand canonical ensemble, we utilize the thermodynamic
geometry method and calculate both the Weinhold metric and Ruppeiner metric. It
is shown that for both analytic and graphical results that the divergence
structure of the Ruppeiner scalar curvature coincides with that of the specific
heat. Our research provides one more example that Ruppeiner metric serves as a
wonderful tool to probe the phase structures of black holes
P-V criticality of conformal anomaly corrected AdS black holes
The effects of conformal anomaly on the thermodynamics of black holes are
investigated in this Letter from the perspective of criticality of AdS
black holes. Treating the cosmological constant as thermodynamic pressure, we
extend the recent research to the extended phase space. Firstly, we study the
- criticality of the uncharged AdS black holes with conformal anomaly and
find that conformal anomaly does not influence whether there exists Van der
Waals like critical behavior. Secondly, we investigate the - criticality
of the charged cases and find that conformal anomaly influences not only the
critical physical quantities but also the ratio . The ratio
is no longer a constant as before but a function of conformal anomaly parameter
. We also show that the conformal parameter should satisfy a
certain range to guarantee the existence of critical point that has physical
meaning. Our results show the effects of conformal anomaly
P-V Criticality of Topological Black Holes in Lovelock-Born-Infeld Gravity
To understand the effect of third order Lovelock gravity, criticality
of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated.
The thermodynamics is further explored with some more extensions and details
than the former literature. A detailed analysis of the limit case
is performed for the seven-dimensional black holes. It
is shown that for the spherical topology, criticality exists for both the
uncharged and charged cases. Our results demonstrate again that the charge is
not the indispensable condition of criticality. It may be attributed to
the effect of higher derivative terms of curvature because similar phenomenon
was also found for Gauss-Bonnet black holes. For , there would be no
criticality. Interesting findings occur in the case , in which positive
solutions of critical points are found for both the uncharged and charged
cases. However, the diagram is quite strange. To check whether these
findings are physical, we give the analysis on the non-negative definiteness
condition of entropy. It is shown that for any nontrivial value of ,
the entropy is always positive for any specific volume . Since no
criticality exists for in Einstein gravity and Gauss-Bonnet gravity, we
can relate our findings with the peculiar property of third order Lovelock
gravity. The entropy in third order Lovelock gravity consists of extra terms
which is absent in the Gauss-Bonnet black holes, which makes the critical
points satisfy the constraint of non-negative definiteness condition of
entropy. We also check the Gibbs free energy graph and the "swallow tail"
behavior can be observed. Moreover, the effect of nonlinear electrodynamics is
also included in our research.Comment: 13 pages, 7 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
than for the case when . Considering a specific example, we
show that the maximum efficiency can reach while the efficiency for
reads . 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 exert
influence on the efficiency, but also the constant corresponding to the
third massive potential contributes to the efficiency. When is higher than that of
the case . By studying the ratio , 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 temperatureentanglement entropy criticality of the
-dimensional charged AdS black hole with our attention concentrated on the
ratio . Comparing the results of this paper with
those of the ratio , one can find both the similarities
and differences. These two ratios are independent of the characteristic length
scale and dependent on the dimension . These similarities further
enhance the relation between the entanglement entropy and the
Bekenstein-Hawking entropy. However, the ratio
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
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 .Comment: Revised version. Discussions adde
Revisiting van der Waals like behavior of f(R) AdS black holes via the two point correlation function
Van der Waals like behavior of AdS black holes is revisited via two
point correlation function, which is dual to the geodesic length in the bulk.
The equation of motion constrained by the boundary condition is solved
numerically and both the effect of boundary region size and gravity are
probed. Moreover, an analogous specific heat related to is
introduced. It is shown that the graphs of AdS black holes
exhibit reverse van der Waals like behavior just as the graphs do. Free
energy analysis is carried out to determine the first order phase transition
temperature and the unstable branch in curve is removed by a
bar . It is shown that the first order phase transition temperature is
the same at least to the order of for different choices of the
parameter although the values of free energy vary with . Our result
further supports the former finding that charged AdS black holes behave
much like RN-AdS black holes. We also check the analogous equal area law
numerically and find that the relative errors for both the cases
and are small enough. The fitting functions between and for both cases are also
obtained. It is shown that the slope is around 3, implying that the critical
exponent is about . This result is in accordance with those in former
literatures of specific heat related to the thermal entropy or entanglement
entropy.Comment: Revised version. Match the published version. 14pages,5figure
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