1,255 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
Self-trapping of Bose-Einstein condensates in optical lattices
The self-trapping phenomenon of Bose-Einstein condensates (BECs) in optical
lattices is studied extensively by numerically solving the Gross-Pitaevskii
equation. Our numerical results not only reproduce the phenomenon that was
observed in a recent experiment [Anker {\it et al.}, Phys. Rev. Lett. {\bf 94}
(2005)020403], but also find that the self-trapping breaks down at long
evolution times, that is, the self-trapping in optical lattices is only
temporary. The analysis of our numerical results shows that the self-trapping
in optical lattices is related to the self-trapping of BECs in a double-well
potential. A possible mechanism of the formation of steep edges in the wave
packet evolution is explored in terms of the dynamics of relative phases
between neighboring wells.Comment: 8 pages, 15 figure
A note on Maxwell's equal area law for black hole phase transition
The state equation of the charged AdS black hole is reviewed in the
plane. Thinking of the phase transition, the , , graphs are
plotted and then the equal area law is used in the three cases to get the phase
transition point (P,T). The analytical phase transition point relations for P-T
of charged AdS black hole has been obtained successfully. By comparing the
three results, we find that the equal area law possibly cannot be used directly
for plane. According to the , results, we plot the
graph and find that for a highly charged black hole a very low temperature
condition is required for the phase transition
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