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Embedding of the (θ, φ) sector of metric (37) for r + = √ 10, l = 1, σ = 0 and φ ∼ φ + 2π. For this slice we see the characteristic shape of the super-entropic black holes. Increasing the value of σ effectively stretches the plot vertically.
Source publication
We apply the hyperboloid membrane limit to the general Kerr-AdS metrics and
their recently studied super-entropic cousins and obtain a new class of
rotating black holes, for which the rotational parameters in multiple
directions attain their maximal value---equal to the AdS radius. These new
solutions have a potential application in the description...
Context in source publication
Context 1
... as- sociated with the super-entropic limit. These are present because here we have not taken the maximum possible number of hyperboloid membrane limits, but rather chose to set one rota- tional parameter to l using the super-entropic limit. To visualize the punctures, we can embed the (θ, φ) sector of the horizon in E 3 , with the result shown in Fig. 2 and it is straightforward to show that the Weyl tensor vanishes, indicating the boundary is con- formally flat. We were unable to determine the conformal ...
Citations
... where A is the area of the outer horizon and V is the thermodynamic volume of the black hole. There are some counterexamples violating this conjecture, leading to what might be called super-entropic black holes [83][84][85]. Violation of the RII conjecture means that the associated entropy exceeds the maximal bound implied by the inequality (5.1) or equivalently the extended black hole volume is no longer bounded from below [83]. Subsequent studies have indicated that violation of this conjecture in AdS black holes is somehow related to a new kind of fundamental thermodynamic instabilities [62,72] and we show this is also valid for charged BTZ-like black holes. ...
We investigate thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions, namely higher-dimensional charged black holes in which the electromagnetic sector exhibits the same properties with that of the usual three-dimensional BTZ solution. We first present the Euclidean on-shell action in arbitrary dimensions, inserting a radial cutoff. We then extract the corresponding thermodynamic quantities from the semi-classical partition function in different ensembles and find that there exist two possible thermodynamic schemes, with different outcomes. Regarding the traditional scheme (scheme I), where the length cutoff is identified with the AdS radius, we show that charged BTZ-like black holes are super-entropic, namely they violate the reverse isoperimetric inequality conjecture, and their super-entropicity is strongly connected to a fundamental thermodynamic instability. This class of solutions is the first demonstration of super-entropic black holes which possess second-order critical points and, since thermodynamic instabilities always arise, it is not possible to physically interpret the corresponding van der Waals critical phenomenon in this scheme. In the second scheme (II) where the length cutoff is considered as an independent variable, namely the system respects the conjectured reverse isoperimetric inequality, we show that the solutions are thermodynamically stable in an ensemble where the length cutoff is kept fixed, and hence one can provide an explanation for the van der Waals critical phenomenon. Furthermore, in order to verify the consistency of the second scheme, we study the Joule-Thomson expansion and we extract the Joule-Thomson coefficient, the inversion temperature, the inversion curves, and the isenthalpic curves. The results indicate that this class of AdS black holes can be considered as interacting statistical systems. Additionally, ...
... This interesting type of solutions was first obtained in Ref. 9 and immediately received much interest, in particular, with respect to their thermodynamics (see, e.g., Refs. [10][11][12]. Subsequently, further types of black holes with noncompact event horizons of finite area were found: black bottles, whose event horizons are topologically spheres with a single puncture. 13 To analyze the structure of spacetime, one of the most powerful tools is geodesics. ...
In this paper, we derive the geodesic equation for massive particles and light for the black spindle spacetime. The solution for light can be formulated in terms of the Weierstraß ℘-, σ-, and ζ-function, whereas a part of the solutions for massive particles is given in terms of derivatives of the Kleinian σ-function. We analyze the possible orbit types using parametric diagrams and effective potentials. Furthermore, we visualize the orbits in a coordinate system, where the spindle-like topology of the horizon is visible.
... The solution emerged as a certain limit of the Carter-Plebanski metric [17,18] where the metric function governing the longitudinal angle develops a certain double root. That it can be interpreted as the ultra-spinning limit of the Kerr-AdS solution, where the rotation parameter a is taken to be critically large (equal to the AdS radius ) was suggested in a letter by Klemm [1], and the corresponding limiting procedure was explicitly found in [2,19,20]. The result is a non-compact horizon of finite area, which is roughly spherical near its equator but becomes hyperbolic near the axis. ...
... In a series of papers, Hennigar et al. [2,19,20] explored the thermodynamic implications of having such an extraordinary spacetime. These papers argued a distinct definition of thermodynamic variables from the standard Kerr-AdS variables, and intriguingly discovered that the black hole appeared to be superentropic. ...
... For the ultra-spinning case, the thermodynamic quantities cannot simply be obtained by taking the a → limit of the thermodynamic quantities of Kerr-AdS black holes, as these diverge in the limit a → . Instead, the thermodynamics of ultra-spinning black holes were constructed in [2,19,20] "afresh", starting from the Superentropic metric and applying the standard procedures, such as the method of conformal completion [45]. In this way, a new set of consistent (and finite) thermodynamic quantities, that are evidently disconnected from those of Kerr-AdS black holes, were obtained and shown to satisfy the corresponding (degenerate) first law, and violate the reverse isoperimetric inequality. ...
A bstract
We study a critical limit in which asymptotically-AdS black holes develop maximal conical deficits and their horizons become non-compact. When applied to stationary rotating black holes this limit coincides with the “ultraspinning limit” and yields the Superentropic black holes whose entropy was derived recently and found to exceed the maximal possible bound imposed by the Reverse Isoperimetric Inequality [1, 2]. To gain more insight into this peculiar result, we study this limit in the context of accelerated AdS black holes that have unequal deficits along the polar axes, hence the maximal deficit need not appear on both poles simultaneously. Surprisingly, we find that in the presence of acceleration, the critical limit becomes smooth, and is obtained simply by taking various upper bounds in the parameter space that we elucidate. The Critical black holes thus obtained have many common features with Superentropic black holes, but are manifestly not superentropic. This raises a concern as to whether Superentropic black holes actually are superentropic. ¹ We argue that this may not be so and that the original conclusion is likely attributed to the degeneracy of the resulting first law.
... This is because some thermodynamic quantities will be divergent or zero when the super-entropic limit is taken directly. So, the thermodynamic quantities of super-entropic black hole were given usually by using the standard thermodynamic calculation method [1,[5][6][7][8][9]. So, a question arises to whether there are certain relations between the thermodynamic quantities of the non super-entropic rotating AdS black hole and the corresponding super-entropic one, and whether the thermodynamic quantities of the superentropic black hole can be directly derived from those of the non super-entropic rotating AdS black hole by taking the super-entropic limit, if one first removes the divergence or zero in the thermodynamic quantities when the super-entropic limit is taken. ...
The super-entropic black hole, which possesses noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Smarr relation. In this paper, we first show that there exists the Christodoulou-Ruffini squared mass formula for the four-dimensional Kerr-Newman-AdS super-entropic black hole. We then construct a set of very simple relations for thermodynamic quantities between the non super-entropic and super-entropic Kerr-Newman-AdS4 black holes. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS4 super-entropic black hole can be derived from those of the Kerr-Newman-AdS4 black hole by taking the super-entropic limit directly. These relations have been checked to be also valid for the singly rotating Kerr-AdS black hole in arbitrary dimensions and the double rotating charged black hole from the five-dimensional minimal gauged supergravity. Therefore, we conjecture that the thermodynamic quantities of all super-entropic black holes obey the relations, which are constructed in this paper, with those of the corresponding non super-entropic rotating AdS black holes, and thus can be obtained directly by taking the super-entropic limit.
... The solution emerged as a certain limit of the Carter-Plebanski metric [17,18] where the metric function governing the longitudinal angle develops a certain double root. That it can be interpreted as the ultra-spinning limit of the Kerr-AdS solution, where the rotation parameter a is taken to be critically large (equal to the AdS radius ) was suggested in a letter by Klemm [1], and the corresponding limiting procedure was explicitly found in [2,19,20]. The result is a non-compact horizon of finite area, which is roughly spherical near its equator but becomes hyperbolic near the axis. ...
... In a series of papers, Hennigar et al. [2,19,20] explored the thermodynamic implications of having such an extraordinary spacetime. These papers argued a distinct definition of thermodynamic variables from the standard Kerr-AdS variables, and intriguingly discovered that the black hole appeared to be superentropic. ...
... For the ultra-spinning case, the thermodynamic quantities cannot simply be obtained by taking the a → limit of the thermodynamic quantities of Kerr-AdS black holes, as these diverge in the limit a → . Instead, the thermodynamics of ultra-spinning black holes were constructed in [2,19,20] "afresh", starting from the Superentropic metric and applying the standard procedures, such as the method of conformal completion [45]. In this way, a new set of consistent (and finite) thermodynamic quantities, that are evidently disconnected from those of Kerr-AdS black holes, were obtained and shown to satisfy the corresponding (degenerate) first law, and violate the reverse isoperimetric inequality. ...
We study a critical limit in which asymptotically-AdS black holes develop maximal conical deficits and their horizons become non-compact. When applied to stationary rotating black holes this limit coincides with the "ultraspinning limit" and yields the Superentropic black holes whose entropy was derived recently and found to exceed the maximal possible bound imposed by the Reverse Isoperimetric Inequality. To gain more insight into this peculiar result, we study this limit in the context of accelerated AdS black holes that have unequal deficits along the polar axes, hence the maximal deficit need not appear on both poles simultaneously. Surprisingly, we find that in the presence of acceleration, the critical limit becomes smooth, and is obtained simply by taking various upper bounds in the parameter space that we elucidate. The Critical black holes thus obtained have many common features with Superentropic black holes, but are manifestly not superentropic. This raises a concern as to whether Superentropic black holes actually are superentropic. We argue that this may not be so and that the original conclusion is likely attributed to the degeneracy of the resulting first law.
... Super-entropic black holes describe an exotic class of rotating AdS black hole solutions with noncompact event horizons and finite horizon area, whose entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality (3.7). First obtained by taking a particular limit of the Carter metric [99], there is now an entire class of rotating and/or charged super-entropic black holes in four and higher dimensions [60,96,100,101] for which R 1 ⩾ does not hold 16 . ...
... 17 Lorentzian Taub-NUT solutions have many peculiar properties and are usually discarded as physically irrelevant; however this viewpoint has recently been challenged [105]. 18 Although natural in the case of spherical Taub-NUT solutions [110], a similar restriction is often imposed for the planar and hyperbolic counterparts as well [111,112]; recently this has been questioned [101]. ...
... Picking up the threads of [104], the thermodynamic properties and possible phase transitions of Taub-NUT-AdS solutions and their generalizations have been further studied [101,112,113] and extended to include rotation [114] and deformations to dyonic black holes [115]. It is somewhat remarkable that extended phase space thermodynamics provides a sensible framework for the study of these unusual solutions and that a plausible explanation may exist for objects characterized by negative volume. ...
We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach, the mass of the black hole is no longer regarded as internal energy, rather it is identified with the chemical enthalpy. This leads to an extended dictionary for black hole thermodynamic quantities, in particular a notion of thermodynamic volume emerges for a given black hole spacetime. This volume is conjectured to satisfy the reverse isoperimetric inequality - an inequality imposing a bound on the amount of entropy black hole can carry for a fixed thermodynamic volume. New thermodynamic phase transitions naturally emerge from these identifications. Namely, we show that black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. We also review the recent attempts at extending the AdS/CFT dictionary in this setting, discuss the connections with horizon thermodynamics, applications to Lifshitz spacetimes, and outline possible future directions in this field.
This paper focuses on the new approach to the nature of a nut parameter [Formula: see text], usually treated as a dual charge to the mass. Instead of thinking about it as a gravitational analog of the magnetic monopole, we will show that the Taub–NUT spacetime conceals a peculiar rotation coming from the Misner strings depending on the nut value. Besides reconciling several confusing results present in the literature, this allows us to establish more the less a consistent description of the black hole thermodynamics for the Lorentzian Taub–NUT spacetime with essential contribution from the Misner strings to the angular momentum and total entropy.
The superentropic black hole, which possesses a noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Bekenstein-Smarr mass formula. In this paper, we first derive a new Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS superentropic black hole and then establish a set of very simple relations between thermodynamic quantities of the superentropic Kerr-Newman-AdS4 black hole and its usual counterparts. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS4 superentropic black hole can be obtained from those of the usual protype by taking the ultraspinning limit properly. Then these relations are extended to the singly rotating Kerr-AdS black holes in arbitrary dimensions and the double-rotating charged black hole in the five-dimensional minimal gauged supergravity. It can be inferred that the thermodynamic quantities of all superentropic black holes obey similar limiting relations to those of their corresponding conventional rotating AdS black holes and thus can be obtained by taking the ultraspinning limit appropriately.
By utilizing the ultraspinning limit we generate a new class of extremal vanishing horizon (EVH) black holes in odd dimensions ($d\geq5$). Starting from the general multi-spinning Kerr-AdS metrics, we show the EVH limit commutes with the ultraspinning limit, in which the resulting solutions possess a non-compact but finite area manifold for all $(t,r\neq r_+)=const.$ slices. We also demonstrate the near horizon geometries of obtained ultraspinning EVH solutions contain an AdS$_3$ throats, where it would be a BTZ black hole in the near EVH cases. The commutativity of the ultraspinning and near horizon limits for EVH solutions is confirmed as well. Furthermore, we discuss only five-dimensional case near the EVH point can be viewed as a super-entropic black hole. We also show that the thermodynamics of the obtained solutions agree with the BTZ black hole. Moreover we investigate the EVH/CFT proposal, demonstrating the entropy of $2$d dual CFT and Bekenstein-Hawking entropy are equivalent.
