We study the OPE coefficients c ∆,J for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension ∆ L in an AdS black hole. We verify that the OPE coefficient c d,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energymomentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer ∆ L , although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients γ ∆,J of the log(zz) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for γ ∆,J . We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with ∆ L = d − 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient c d−2,0 . Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how c d,0 can be nonzero with exchanging scalar operators in these backgrounds.The AdS/CFT correspondence establishes an insightful routine to investigate a strongly coupled conformal field theory (CFT) by using appropriate weakly coupled gravity in antide Sitter (AdS) spacetime and vice versa [1]. Originally, the AdS/CFT correspondence is typically referred to as the duality between type IIB superstring in AdS 5 × S 5 and N = 4, d = 4 super Yang-Mills theory. The holographic principle is expected to be more general and can apply to a variety of gravity theories even without supersymmetry, and indeed it has passed a large amount of tests at the AdS scale, i.e. the locality holds at the scale that is never shorter than the AdS radius ℓ [2]. The results include the correct structures of two-point functions, three-point functions [3,4], conformal anomalies [5,6] in CFTs that are fixed by the virtue of conformal symmetry. Typically, even though the structures are the same, different gravity theories may lead to different CFT data. Thus gravities can be served as effective CFTs. By finding relations and bounds from the holographic CFT data that follow exactly the same pattern regardless of the specific details of a gravity theory, some universal properties of CFTs can be revealed. Known examples include the controlling pattern of shear-viscosity/entropy ratio and entanglement entropy by central charges [7-10], central charge relations [11-13].Below the AdS scale where the higher-point correlation functions (≥ 4) come out to be visible, the generality of AdS/CFT becomes highly nontrivial. Fortunately, it was argued that...

We show that there exists a critical point for the coupling constants in Einsteinian cubic gravity where the linearized equations on the maximally-symmetric vacuum vanish identically. We construct an exact isotropic bounce universe in the critical theory in four dimensions. The comoving time runs from minus infinity to plus infinity, yielding a smooth universe bouncing between two de Sitter vacua. In five dimensions we adopt numerical approach to construct a bounce solution, where a singularity occurred before the bounce takes place. We then construct exact anisotropic bounces that connect two isotropic de Sitter spacetimes with flat spatial sections. We further construct exact AdS black holes in the critical theory in four and five dimensions and obtain an exact AdS wormbrane in four dimensions. *

We consider massless higher-order gravities in general D = d + 1 dimensions, which are Einstein gravity extended with higher-order curvature invariants in such a way that the linearized spectrum around the AdS vacua involves only the massless graviton. We derive the covariant holographic two-point functions and find that they have a universal structure.In particular, the theory-dependent overall coefficient factor C T can be universally expressed by (d − 1)C T = ℓ(∂a/∂ℓ), where a is the holographic a-charge and ℓ is the AdS radius. We verify this relation in quasi-topological Ricci polynomial, Einstein-Gauss-Bonnet, Einstein-Lovelock and Einstein cubic gravities. In d = 4, we also find an intriguing relation between the holographic c and a charges, namely c = 1 3 ℓ(∂a/∂ℓ), which also implies C T = c. †

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The superradiant stability is investigated for non-extremal Reissner-Nordström black holes. We use an algebraic method to demonstrate that all non-extremal Reissner-Nordström black holes are superradiantly stable against a charged massive scalar perturbation. This improves the results obtained before for non-extremal ReissnerNordström black holes.The stability problem of black hole is an important topic in black hole physics. Regge and Wheeler [1] proved that the spherically symmetric Schwarzschild black hole is stable under perturbations. The stability problems of rotating or charged black holes are complicated due to the significant effect of superradiance. The superradiance effect can occur in both classical and quantum scattering processes [2][3][4][5]. When a charged bosonic wave is impinging on a charged rotating black hole, the wave reflected by the event horizon will be amplified if the wave frequency ω lies in the following superradiant regime:where m and e are the azimuthal harmonic number and charge of the incoming charged wave, is the angular velocity of black hole horizon, and = Q/r H is the electric potential of the black hole [6][7][8][9][10][11][12]. This means that when the incoming wave is scattered, the wave extracts rotational energy from the rotating black hole and electric energy from charged black hole. According to the black hole bomb mechanism proposed by Press and Teukolsky [13], if there is a mirror between the black hole horizon and spatial infinity, the amplified wave can be reflected back and forth between the mirror and the black After this paper was completed, Ref.[31] appeared which addresses the same issue with a different method and gets the same conclusion.a e-mail: huangjh@m.scnu.edu.cn hole and grows exponentially. This leads to the superradiant instability of the black hole. The superradiant mechanism has been studied by many authors for the (in)stability problem of black holes [14][15][16][17][18][19][20][21][22][23][24][25][26]. Recently, for a Kerr black hole under massive scalar perturbation, Hod has proposed a stronger stability regime than before [27]. The extremal and non-extremal charged Reissner-Nordström (RN) black holes have been proved to be stable against a charged massive perturbation [28,29]. Similarly, the analog of the charged RN black hole in string theory has also been proved to be stable under a charged massive scalar perturbation [30].In fact, up to now, the non-extremal charged RN black hole is proved to be superradiantly stable when the mass M and charge Q of the black hole satisfy (Q/M) 2 ≤ 8/9 [28,29]. In this paper, we demonstrate that the all non-extremal charged RN black hole is stable against a massive charged scalar perturbation. We find that there is no trapping well outside the black hole, which is separated from the horizon by a potential barrier. As a result, there is no bound state in the superradiant regime, that can lead to the instability of the charged RN black hole.The metric of the RN black hole (in natural unit G = c = h = 1...

We introduce the quasi-topological electromagnetism which is defined to be the squared norm of the topological 4-form F ∧F . A salient property is that its energy-momentum tensor is of the isotropic perfect fluid with the pressure being precisely the opposite to its energy density. It can thus provide a model for dark energy. We study its application in both black hole physics and cosmology. The quasi-topological term has no effect on the purely electric or magnetic Reissner-Nordström black holes, the dyonic solution is however completely modified. We find that the dyonic black holes can have four real horizons. For suitable parameters, the black hole can admit as many as three photon spheres, with one being stable. Another intriguing property is that although the quasi-topological term breaks the electromagnetic duality, the symmetry emerges in the on-shell action in the Wheeler-DeWitt patch. In cosmology, we demonstrate that the quasi-topological term alone is equivalent to a cosmological constant, but the model provides a mechanism for the dark energy to couple with other types of matter. We present a concrete example of the quasi-topological electromagnetism coupled to a scalar field that admits the standard FLRW cosmological solutions.

We study the superradiant stability of the system of a Kerr black hole and a massive scalar perturbation. It was proved previously that this system is superradiantly stable when µ ≥ √ 2mΩH , where µ is the proper mass of the scalar, m is the azimuthal number of the scalar mode, and ΩH is the angular velocity of the Kerr black hole horizon. Our study is a complementary work of this result. We analytically prove that in the complementary parameter region µ < √ 2mΩH , when the parameters of scalar perturbation and Kerr black hole satisfy two simple inequalities, ω < µ √ 2 , r − r + < 0.802, the system is also superradiantly stable.

By choosing an appropriate vielbein basis, we obtain a class of spherically-symmetric solutions in f (T ) gravities. The solutions are asymptotic to Minkowski spacetimes with leading falloffs the same as those of the Schwarzschild black hole. In general, these solutions have branch-cut singularities in the middle. For appropriately chosen f (T ) functions, extremal black holes can also emerge. Furthermore, we obtain wormhole configurations whose spatial section is analogous to an Ellis wormhole, but −g tt runs from 0 to 1 as the proper radial coordinate runs from −∞ to +∞. Thus a signal sent from −∞ to +∞ through the wormhole will be infinitely red-shifted. We call such a spacetime configuration a dark wormhole. By introducing a bare cosmological constant Λ 0 , we construct smooth solitons that are asymptotic to local AdS with an effective Λ eff . In the middle of bulk, the soliton metric behaves like the AdS of bare Λ 0 in global coordinates. We also embed AdS planar and Lifshitz black holes in f (T ) gravities. Finally we couple the Maxwell field to the f (T ) theories and construct electrically-charged solutions. *