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Register a new userThe phase transition of higher dimensional Charged black holes
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In this paper,we have studied phase transitions of higher dimensional charge black hole with spherical symmetry. we calculated the local energy and local temperature, and find that these state parameters satisfy the first law of thermodynamics. We analyze the critical behavior of black hole thermodynamic system by taking state parameters $(Q,Phi)$ of black hole thermodynamic system, in accordance with considering to the state parameters $(P,V)$ of Van der Waals system respectively. we obtain the critical point of black hole thermodynamic system, and find the critical point is independent of the dual independent variables we selected. This result for asymptotically flat space is consistent with that for AdS spacetime, and is intrinsic property of black hole thermodynamic system.
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In this paper, we extend the study of the relationship between the photon sphere and the thermodynamic phase transition, especially the reentrant phase transition, to this black hole background. According to the number of the thermodynamic critical points, the black hole systems are divided into four cases with different values of Born-Infeld parameter b, where the black hole systems can have no phase transition, reentrant phase transition, or Van der Waals-like phase transition. For these different cases, we obtain the corresponding phase structures in pressure-temperature diagram and temperature-specific volume diagram. The tiny differences between these cases are clearly displayed. On the other hand, the radius rps and the minimal impact parameter ups of the photon sphere are calculated via the effective potential of the radial motion of photons. For different cases, rps and ups are found to have different behaviors. In particular, with the increase of rps or ups, the temperature possesses a decrease-increase-decrease-increase behavior for fixed pressure if there exists the reentrant phase transition. While for fixed temperature, the pressure will show an increase-decrease-increase-decrease behavior instead. These behaviors are quite different from that of the Van der Waals-like phase transition. Near the critical point, the changes of rps and ups among the black hole phase transition confirm an universal critical exponent 12. Therefore, all the results indicate that, for the charged Born-Infeld-AdS black holes, not only the Van der Waals-like phase transition, but also the reentrant phase transition can be reflected through the photon sphere.
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the black hole horizon can act as the order parameter to characterize the black hole phase transition. We also disclose that different from the five-dimensional neutral black holes, the charged ones allow the repulsive interaction among its microstructure for small black hole of higher temperature. Another significant difference between them is that the microscopic interaction changes during the small-large black hole phase transition for the charged case, where the black hole microstructure undergoes a sudden change. These results are helpful for peeking into the microstructure of charged black holes in the Gauss-Bonnet gravity.
In this work we calculate the angular eigenvalues of the $(n+4)$-dimensional {it simply} rotating Kerr-(A)dS spheroidal harmonics using the Asymptotic Iteration Method (AIM). We make some comparisons between this method and that of the Continued Fraction Method (CFM) and use the latter to check our results. We also present analytic expressions for the small rotation limit up to $O(c^3)$ with the coefficient of each power up to $O(alpha^2)$, where $c=aomega$ and $alpha=a^2 Lambda$ ($a$ is the angular velocity, $omega$ the frequency and $Lambda$ the cosmological constant).
Here we have developed the general parametrization for spherically symmetric and asymptotically flat black-hole spacetimes in an arbitrary metric theory of gravity. The parametrization is similar in spirit to the parametrized post-Newtonian (PPN) approximation, but valid in the whole space outside the event horizon, including the near horizon region. This generalizes the continued-fraction expansion method in terms of a compact radial coordinate suggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for the four-dimensional case. As the first application of our higher-dimensional parametrization we have approximated black-hole solutions of the Einstein-Lovelock theory in various dimensions. This allows one to write down the black-hole solution which depends on many parameters (coupling constants in front of higher curvature terms) in a very compact analytic form, which depends only upon a few parameters of the parametrization. The approximate metric deviates from the exact (but extremely cumbersome) expressions by fractions of one percent even at the first order of the continued-fraction expansion, which is confirmed here by computation of observable quantities, such as quasinormal modes of the black hole.
We compute the gravitational wave energy $E_{rm rad}$ radiated in head-on collisions of equal-mass, nonspinning black holes in up to $D=8$ dimensional asymptotically flat spacetimes for boost velocities $v$ up to about $90,%$ of the speed of light. We identify two main regimes: Weak radiation at velocities up to about $40,%$ of the speed of light, and exponential growth of $E_{rm rad}$ with $v$ at larger velocities. Extrapolation to the speed of light predicts a limit of $12.9,%$ $(10.1,~7.7,~5.5,~4.5),%$. of the total mass that is lost in gravitational waves in $D=4$ $(5,,6,,7,,8)$ spacetime dimensions. In agreement with perturbative calculations, we observe that the radiation is minimal for small but finite velocities, rather than for collisions starting from rest. Our computations support the identification of regimes with super Planckian curvature outside the black-hole horizons reported by Okawa, Nakao, and Shibata [Phys.~Rev.~D {bf 83} 121501(R) (2011)].
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