arXiv subjects

Shuang-Qing Wu

Publications and source records attributed to Shuang-Qing Wu.

At least 19 recordsLinked to original sources

arXiv2026

Two-horizon sector thermodynamics and NUT bi-hair in Kerr-Newman-NUT spacetimes

First law consistency alone does not determine the black hole state space of NUT-charged spacetimes, because several inequivalent macroscopic formulations can yield consistent thermodynamics. We develop a two-horizon sector diagnostic for the electrically charged Kerr-Newman-NUT family by organizing the inner- and outer-horizon entropies and inverse temperatures into sum ($Σ$) and difference ($Δ$) sectors. The charged rotating geometry gives a more stringent test of the uncharged Taub-NUT sector result, since the mass $M$, ordinary electric charge $Q$, ordinary angular momentum $J$, NUT charge $N$, and the NUT secondary hair $J_N=MN$ all enter the same two-horizon thermodynamics. For the physically anchored minimal homogeneous state spaces defined and tested here, we find a clear sector separation: the $Σ$ sector closes with the charge-like variables $Q$ and $N$, whereas the $Δ$ sector additionally requires the rotation-like variables $J$ and $J_N$. Natural reductions that eliminate either $J_N$ or $N$ fail to reproduce the first law coefficient fixed by the sector temperature, and their associated Bekenstein-Smarr relations do not close with the assigned scaling weights. Within this class, electric charge and ordinary rotation therefore do not absorb the NUT secondary response, and the charged rotating family supports the NUT bi-hair organization: $N$ has a charge-like sector role, while $J_N=MN$ is a rotation-like thermodynamic secondary hair. The latter is defined off shell in the homogeneous equation of state, not as a new metric parameter or asymptotic conserved charge.

gr-qc↗

arXiv2026

Multihair thermodynamics of Kerr-Newman-NUT-AdS$_4$ spacetimes

In this paper, we develop a multihair thermodynamic description of Lorentzian Kerr-Newman-NUT-AdS$_4$ spacetime in which rotation, electric charge, AdS pressure and polar conical tensions enter a homogeneous Christodoulou-Ruffini-type squared-mass formula. The NUT contribution is described by a rotation-like secondary hair $J_n=mn/K^2$ and a charge-like secondary hair $N=n/\sqrt K$. Both depend on the metric parameters of the physical solution family but are varied independently in the enlarged thermodynamic state space. The mass formula yields the first law and Smarr relation in a single enthalpy representation, with the area entropy and Hawking temperature. The Kerr-Newman-AdS, asymptotically flat Kerr-Newman-NUT and nonrotating RN-NUT-AdS limits check the angular normalization and the NUT and pressure contributions. We also consider alternative NUT variables, including the conformal dual mass, and derive the corresponding changes in thermodynamic volume and conical-defect lengths. This description applies to the chosen homogeneous state space and does not require the secondary hairs to be independent asymptotic or Misner-string surface charges.

hep-th↗

arXiv2026

Two-Horizon Sector Thermodynamics as a Diagnostic for the Bi-Hair Organization of NUT Charge

After decades without a fully self-consistent thermodynamic formulation, recent proposals for Lorentzian Taub-NUT spacetime have yielded several inequivalent descriptions, each satisfying its own first law and Smarr relation, leaving unresolved which formulation is physically preferred. In this Letter we introduce a two-horizon diagnostic whose sector temperatures are fixed by harmonic mean relations before the thermodynamic variables are chosen. For uncharged Taub-NUT, the sum sector closes with the mass and NUT charge, whereas, within the restricted homogeneous class examined here, the difference sector requires the thermodynamic secondary hair $J_n=mn$. This result supports a bi-hair thermodynamic organization of the NUT parameter through $N=n$ and $J_n=mn$. Furthermore, this two-horizon framework offers a new route toward addressing similar thermodynamic nonuniqueness in other two-horizon systems when the first law and Smarr relation alone do not identify a physically preferred formulation.

gr-qc↗

arXiv2026

Static four-charge squashed black hole in five-dimensional $STU-W^2U$ supergravity and its thermodynamics

In this paper, we present a remarkably simple expression for the exact solution to the $D = 5$, $\mathcal{N} = 2$ supergravity coupled to three vector multiplets with the prepotential $\mathcal{V} = STU -W^2U \equiv 1$, which represents a five-dimensional static Kaluza-Klein black hole with squashed $S^3$ horizons and four independent electric charges. It is asymptotically locally flat and has a spatial infinity $R \times S^1 \hookrightarrow S^2$. We compute its conserved charges via the counterterm method and demonstrate that the thermodynamic quantities satisfy both the first law and Bekenstein-Smarr mass formula, provided the length of the compact extra dimension is treated as a thermodynamic variable.

hep-th↗

arXiv2026

Thermodynamics and topological classifications of static non-extremal four-charge AdS black hole in the five-dimensional $\mathcal{N} = 2$, $STU-W^2U$ gauged supergravity

In this paper, we investigate thermodynamical aspects of a novel static non-extremal black hole solution in the five-dimensional anti-de Sitter (AdS) space carrying four independent electric charge parameters and with a negative cosmological constant, within the framework of $D=5$, $\mathcal{N} = 2$ gauged supergravity coupled to three vector multiplets specified by the pre-potential $\mathcal{V} = STU -W^2U \equiv 1$. A central outcome of our work is the demonstration that the thermodynamics of this solution consistently satisfies both the differential and integral forms of the mass formulae of black hole thermodynamics. When the fourth charge is set to zero, our configuration reduces to the known three-charge static non-extremal AdS$_5$ black hole within the gauged $STU$ model, and its thermodynamic behavior connects smoothly to that limit. Finally, we also provide a brief discussion about topological classifications of its thermodynamics.

hep-th↗

arXiv2026

Four-charge static non-extremal black holes in the five-dimensional $\mathcal{N}=2$, $STU-W^2U$ supergravity

We construct, for the first time, new static non-extremal five-dimensional black hole solutions (without or with squashed horizons) endowing with four different electric charge parameters in the $D = 5$, $\mathcal{N} = 2$ supergravity coupled to three vector multiplets with a specific pre-potential $\mathcal{V} = STU -W^2U \equiv 1$. When the fourth charge parameter disappears, the solution simplify reduces to the three-charge static black hole solution previously presented in ref. [1], which belongs to the solution to the $D = 5$, $\mathcal{N} = 2$ supergravity coupled to two vector multiplets (also notably known as the $STU$ model). We parameterize the model in such a simple fashion that not only can one easily recover the static three-charge solution but also it is very convenient to study their thermodynamical properties of the obtained black hole solutions in the case without a squashing horizon. We then show that the thermodynamical quantities perfectly obey both the differential first law and integral Smarr formula of thermodynamics. Finally, we also extend to present its generalizations with squashed horizons or including a nonzero cosmological constant.

hep-th↗

arXiv2025

Novel topological classes in black hole thermodynamics

By viewing black hole solutions as topological defects in thermodynamic parameter space, we unveil a novel topological class and two new topological subclasses, respectively denoted $W^{0-\leftrightarrow 1+}$, $\overline{W}^{1+}$, and $\hat{W}^{1+}$, that extend beyond the four established categories proposed by Wei et al. [Phys. Rev. D 110, L081501 (2024)]. Within the newly identified class and these two novel subclasses, the innermost small black hole states exhibit a distinct sequence of unstable, stable, and stable behaviours, while the outermost large black hole states display a uniform pattern of stable behaviours. These classifications indicate thermodynamic properties in both the low and high Hawking temperature regimes that are strikingly different from the previously known four topological classes. In particular, we demonstrate that static charged AdS black holes in gauged supergravity exhibit an intricate thermodynamic evolution that is notably distinct from that of the Reissner-Nordström anti-de Sitter (RN-AdS) black hole. From a topological perspective, we emphasize the advantages and potential of investigating thermodynamic phase transitions in these black hole spacetimes, an area that has been rarely explored in previous research. Our findings not only enrich and sharpen the framework of topological classifications in black hole thermodynamics, but also represent a significant stride toward unraveling the fundamental nature of black holes and gravity.

hep-th↗

arXiv2024

Is the type-D NUT C-metric really "missing" from the most general Plebański-Demiański solution?

It remains a long-standing problem, unsettled for almost two decades in the general relativity community, ever since Griffiths and Podolsky demonstrated in Ref. [J.B. Griffiths and J. Podolsky, Class. Quant. Grav. 22, 3467 (2005)] that the type-D NUT C-metric seems to be absent from the most general family of the type-D Plebański-Demiański (P-D) solution. However, Astorino [Phys. Rev. D 109, 084038 (2024)] presented a different form of rotating and accelerating black holes and showed that all known four-dimensional type-D accelerating black holes (without the NUT charge) can be recovered via various different limits in a definitive fashion. In particular, he provided, for the first time, the correct expressions for the type-D static accelerating black holes with a nonzero NUT charge, which was previously impossible using the traditional parametrization of the familiar P-D solution. Nevertheless, it still remains elusive how these two different forms of the four-dimensional rotating and accelerating solutions are related. In this paper, we aim to fill this gap by finding the obvious coordinate transformations and parameter identifications between the vacuum metrics after two different parametrizations of the generated solution via the inverse scattering method from the seed metric -- the Rindler vacuum background. We then resolve this ``missing" puzzle by providing another Möbius transformation and linear combinations of the Killing coordinates, which clearly cast the type-D NUT C-metric into the familiar form of the P-D solution. Additionally, we propose an alternative new routine for the normalization of the obtained metric derived via the inverse scattering method from the vacuum seed solution, which could be potentially useful for the construction of higher-dimensional solutions using the trivial vacuum background as the seed metric.

gr-qc↗

arXiv2023

Revisiting mass formulas of the four-dimensional Reissner-Nordström-NUT-AdS solutions in a different metric form

Recently, the so-called ``consistent thermodynamics'' of the Lorentzian Reissner-Nordström (RN)-NUT-AdS$_4$ spacetimes has been pursued by a lot of efforts via different means. Among these attempts, we had proposed a novel idea that ``The NUT charge is a thermodynamical multihair" to successfully tackle with the subject. In this paper, we will adopt this strategy to reconsider the mass formulas of the RN-NUT-AdS$_4$ solutions but written in an alternative form, which had not been studied before in any existing literature and might be a most appropriate ansatz for the higher dimensional multiply NUTty-charged AdS spacetimes without any constraint condition. Here, we shall discuss the Christodoulou-Ruffini-like squared mass formula and the first law as well as the Bekenstein-Smarr mass formula by introducing the secondary hair $J_n = Mn$. For the sake of generality, we have introduced a dimensionless constant $w$ into the constant factor $Ξ$ in the solution expression so that when $w = 1$, all obtained results can reproduce those delivered in our previous work.

gr-qc↗

arXiv2023

Consistent mass formulas for higher even-dimensional Taub-NUT spacetimes and their AdS counterparts

Currently, there is a great deal of interest in the seeking of consistent thermodynamics of the Lorentzian Taub-NUT spacetimes. Despite a lot of ``satisfactory'' efforts have been made, all of these activities have been restricted to the four-dimensional cases, with the higher even-dimensional cases remaining unexplored. The aim of this article is to fill the gap, for the first time. To the end of this subject, we first adopt our own idea that ``The NUT charge is a thermodynamical multi-hair" to investigate the consistent thermodynamics of $D = 6, 8, 10$ Lorentzian Taub-NUT spacetimes without a cosmological constant. Similarly to the $D = 4$ cases as did in our previous works, we find that the first law and Bekenstein-Smarr mass formulas are perfectly satisfied if we still assign the secondary hair: $J_n = Mn$ as a conserved charge in both mass formulae. Turning to the cases with a nonzero cosmological constant, our treatment continues to work very well and all the results can be fairly generalized to the corresponding Taub-NUT AdS spacetimes in higher even-dimensions, although we do not know how to define and introduce a similar higher-dimensional version of the dual (magnetic) mass that is well known in four dimensions. Based upon the preceding results, we will also derive the reduced version of the mass formulae when the secondary hair $J_n$ is viewed as a redundant thermodynamic variable.

hep-th↗

arXiv2023

Consistent mass formulas for higher even-dimensional Reissner-Nordström-NUT-AdS spacetimes

In our previous work [D. Wu and S.-Q. Wu, Phys. Rev. D 108, 064034 (2023)], we have formulated consistent thermodynamic first law and Bekenstein-Smarr mass formulae for all higher even-dimensional uncharged Taub-NUT (AdS) spacetimes through the inclusion of a secondary hair $J_n = Mn$ as did in the four-dimensional NUT-charged cases [S.-Q. Wu and D. Wu, Phys. Rev. D 100, 101501(R) (2019)]. In this article, we will show that the corresponding Reissner-Nordström(RN)-NUT (AdS) cases in all higher even-dimensions can be coherently treated just like the uncharged cases if another secondary hair $Q_n \propto qn$ is further introduced as did in the four-dimensional dyonic NUT-charged case [D. Wu and S.-Q. Wu, Phys. Rev. D 105, 124013 (2022)]. As a by-product of our consequence, it is also demonstrated that there is no need to introduce the secondary hair $Q_n$ in the mass formulae for the four-dimensional purely electric-charged RN-NUT (AdS) spacetimes.

gr-qc↗

arXiv2023

Topological classes of thermodynamics of rotating AdS black holes

In this paper, we extend our previous work [Phys. Rev. D 107, 024024 (2023)] to the more general cases with a negative cosmological constant, and investigate the topological numbers for the singly rotating Kerr-AdS black holes in all dimensions and the four-dimensional Kerr-Newman-AdS black hole as well as the three-dimensional Bañados-Teitelboim-Zanelli black hole. We find that the topological numbers of black holes are remarkably influenced by the cosmological constant. In addition, we also demonstrate that the dimension of spacetimes has an important effect on the topological number for rotating AdS black holes. Furthermore, it is interesting to observe that the difference between the topological number of the AdS black hole and that of its corresponding asymptotically flat black hole is always unity. This new observation leads us to conjure that it might be valid also for other black holes. Of course, this novel conjecture needs to be further verified by examining the topological numbers of many other black holes and their AdS counterparts in the future work.

hep-th↗

arXiv2022

Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes

In our previous work, a novel idea that the NUT charge can be thought of as a thermodynamical multi-hair has been advocated to describe perfectly the thermodynamical character of the generic four-dimensional Taub-NUT spacetimes. According to this scheme, the Komar mass M, the gravito-magnetic charge and/or the dual (magnetic) mass N, together with a new secondary hair J_N=MN, namely, a Kerr-like conserved angular momentum, enter into the standard forms of the first law and Bekenstein-Smarr mass formula. Distinguished from other recent attempts, our consistent thermodynamic differential and integral mass formulae are both obtainable from a meaningful Christodoulou-Ruffini-type squared mass formula of almost all of the four-dimensional NUT-charged spacetimes. As an excellent consequence, the famous Bekenstein-Hawking one-quarter area-entropy relation can be naturally restored not only in the Lorentzian sector and but also in the Euclidian counterpart of the generic Taub-NUT-type spacetimes without imposing any constraint condition. However, only purely electric-charged cases in the four-dimensional Einstein-Maxwell gravity theory with a NUT charge have been addressed there. In this paper, we shall follow the simple, systematic way proposed in that article to further investigate the dyonic NUT-charged case. It is shown that the standard thermodynamic relations continue to hold true provided that no new secondary charge is added, however, the so-obtained electrostatic and magneto-static potentials are not coincident with those computed via the standard method. To rectify this inconsistence, a simple strategy is provided by further introducing two additional secondary hairs: Q_N=QN and P_N=PN, together with their thermodynamical conjugate potentials, so that the first law and Bekenstein-Smarr mass formula are still satisfied.

gr-qc↗

arXiv2021

Ultra-spinning Chow's black holes in six-dimensional gauged supergravity and their properties

By taking the ultra-spinning limit as a simple solution-generating trick, a novel class of ultra-spinning charged black hole solutions has been constructed from Chow's rotating charged black hole with two equal-charge parameters in six-dimensional $\mathcal{N} = 4$ gauged supergravity theory. We investigate their thermodynamical properties and then demonstrate that all thermodynamical quantities completely obey both the differential first law and the Bekenstein-Smarr mass formula. For the six-dimensional ultra-spinning Chow's black hole with only one rotation parameter, we show that it does not always obey the reverse isoperimetric inequality, thus it can be either sub-entropic or super-entropic, depending upon the ranges of the mass parameter and especially the charge parameter. This property is obviously different from that of the six-dimensional singly-rotating Kerr-AdS super-entropic black hole, which always strictly violates the RII. For the six-dimensional doubly-rotating Chow's black hole but ultra-spinning only along one spatial axis, we point out that it may also obey or violate the RII, and can be either super-entropic or sub-entropic in general.

hep-th↗

arXiv2020

Aspects of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning version

We explore some (especially, thermodynamical) properties of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning counterpart, and check whether or not both black holes satisfy the first law and Bekenstein-Smarr mass formulas. To this end, new Christodoulou-Ruffini-like squared-mass formulae for the usual dyonic Kerr-Sen-AdS$_4$ solution and its ultraspinning cousin are deduced. Similar to the ultraspinning Kerr-Sen-AdS$_4$ black hole case, we demonstrate that the ultraspinning dyonic Kerr-Sen-AdS$_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since the value of the isoperimetric ratio can either be larger/smaller than, or equal to unity, depending upon the range of the solution parameters, as is the case only with an electric charge. This property is apparently distinct from that of the superentropic dyonic Kerr-Newman-AdS$_4$ black hole, which always strictly violates the RII, although both of them have some similar properties in other aspects, such as the horizon geometry and conformal boundary.

gr-qc↗

arXiv2020

Are ultra-spinning Kerr-Sen-AdS$_4$ black holes always super-entropic ?

We study thermodynamics of the four-dimensional Kerr-Sen-AdS black hole and its ultra-spinning counterpart, and verify that both black holes fullfil the first law and Bekenstein-Smarr mass formulae of black hole thermodynamics. Furthermore, we derive new Christodoulou-Ruffini-like squared-mass formulae for the usual and ultra-spinning Kerr-Sen-AdS$_4$ solutions. We show that this ultra-spinning Kerr-Sen-AdS$_4$ black hole does not always violate the Reverse Isoperimetric Inequality (RII) since the value of the isoperimetric ratio can be larger/smaller than, or equal to unity, depending upon where the solution parameters lie in the parameters space. This property is obviously different from that of the Kerr-Newman-AdS$_4$ super-entropic black hole, which always strictly violates the RII, although both of them have some similar properties in other aspects, such as horizon geometry and conformal boundary. In addition, it is found that while there exists the same lower bound on mass ($m_e \geqslant 8l/\sqrt{27}$ with $l$ being the cosmological scale) both for the extremal ultra-spinning Kerr-Sen-AdS$_4$ black hole and for the extremal super-entropic Kerr-Newman-AdS$_4$ case, the former has a maximal horizon radius: $r_{\rm\, HP} = l/\sqrt{3}$ which is the minimum of the latter. Therefore, these two different kinds of four-dimensional ultra-spinning charged AdS black holes exhibit some significant physical differences .

gr-qc↗

arXiv2020

Notes on thermodynamics of super-entropic AdS black holes

The super-entropic 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 super-entropic black hole, and then establish a set of very simple relations between thermodynamic quantities of the super-entropic Kerr-Newman-AdS$_4$ black hole and its usual counterparts. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS$_4$ super-entropic black hole can be obtained from those of the usual pro-type by taking the ultra-spinning 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 super-entropic black holes obey similar limiting relations to those of their corresponding conventional rotating AdS black holes, and thus can be obtained by taking the ultra-spinning limit appropriately.

gr-qc↗

arXiv2019

Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes

It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass ($M = m$), the "angular momentum" ($J_n = mn$), the gravitomagnetic charge ($N = n$), and/or the dual (magnetic) mass ($\widetilde{M} = n$). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physical feature, or that it is purely a single solution parameter. To arrive at this novel result, we put forward a simple, systematic way to investigate the consistent thermodynamic first law and Bekenstein-Smarr mass formulas of all four-dimensional spacetimes that contain a nonzero NUT charge, facilitated by first deriving a meaningful Christodoulou-Ruffini-type squared-mass formula. In this way, not only can the elegant Bekenstein-Hawking one-quarter area-entropy relation be naturally restored in the Lorentzian and Euclidian sectors of generic Taub-NUT-type spacetimes without imposing any constraint condition, but also the physical meaning of the NUT parameter as a poly-facet can be completely clarified in the thermodynamic sense for the first time.

hep-th↗