Recently, an interesting inflationary scenario, named Gauss-Bonnet inflation, is proposed by Kanti et al. [1,2]. In the model, there is no inflaton potential but the inflaton couples to the Guass-Bonnet term. In the case of quadratic coupling, they find inflation occurs with graceful exit. The scenario is attractive because of the natural set-up. However, we show there exists the gradient instability in the tensor perturbations in this inflationary model. We further prove the no-go theorem for the Gauss-Bonnet inflation without an inflaton potential.
We investigate the Kerr-Newman-NUT black hole solution obtained from Plebański-Demiański solutions with several assumptions. The origin of the microscopic entropy of this black hole is studied using the conjectured Kerr/CFT correspondence which is first proposed for extremal Kerr black holes. The isometry of the near-horizon extremal Kerr-Newman-NUT black hole shows that the asymptotic symmetry group may be applied to compute the central charge of the Virasoro algebra. Furthermore, by assuming Frolov-Thorne vacuum, the temperatures can be obtained which then using Cardy formula, the microscopic entropy is obtained and agrees with the Bekenstein-Hawking entropy. We also assume the case when the lowest eigenvalue of the conformal operator L 0 is non-zero to find the logarithmic correction of the entropy of NHEKNUT black hole. At the limit J → 0, the extremal Reissner-Nordström-NUT solution is produced and by adding the fibered coordinate we find the 5D solution. The second dual CFT is used to find the entropy and it still produces the area law of 5D black hole solution. So, the extremal Reissner-Nordström-NUT solution is also holographically dual to the CFT.
In this article, we consider a special case of Metric-Affine f (R)-gravity for f (R) = R, i.e. the Metric-Affine General Relativity (MAGR). As a companion to the first article in the series, we perform the (3+1) decomposition to the hypermomentum equation, obtained from the minimization of the MAGR action S [g, ω] with respect to the connection ω. Moreover, we show that the hypermomentum tensor H could be constructed completely from 10 hypersurfaces variables that arise from its dilation, shear, and rotational (spin) parts. The (3+1) hypermomentum equations consists of 1 scalar, 3 vector, 3 matrix, and 1 tensor equation of order -21 . Together with the (3+1) decomposition of the traceless torsion constraint, consisting of 1 scalar and 1 vector equation, we obtain 10 hypersurface equations, which are the main result in this article. Finally, we consider some special cases of MAGR, namely, the zero hypermomentum, metric, and torsionless cases. For vanishing hypermomentum, we could retrieve the metric compatibility and torsionless condition in the (3+1) framework, hence forcing the affine connection to be Levi-Civita as in the standard General Relativity.withn * ∈ T * p M is the covariant vector ton, satisfyingn * = g (n, •) = g (n) (the label p is omitted for simplicity).The Adapted Coordinate, Lapse Function, and Shift Vector Let x µ = x 0 , x i be a local coordinate on M, with x 0 and x i are, respectively, the temporal and spatial part of x µ . The corresponding coordinate vector basis on T p M is ∂ µ = {∂ 0 , ∂ i }. Any vector V ∈ T p M could be decomposed as follows:
We present a new twisted rotating black hole solution by performing Demiański-Newman-Janis algorithm to the electrically and dyonically charged black hole with quintessence in Rastall theory of gravity. Using our black hole solution, we argue that Rastall gravity is not equivalent with Einstein gravity. For further explanation, the black hole properties such as the horizon and ergosphere are studied for which there are some different properties for those theories. Some thermodynamic properties of the black hole solution are also discussed. At the end, considering the Kerr/CFT correspondence is valid for our black hole solution, the central charge from the CFT of this extremal solution is derived. spacetime. It is considered a non-minimal coupling of the matter field to space-time geometry with the coupling constant κλ or Rastall parameter. This quantity quantifies the deviation from the Einstein theory of gravity. When Rastall parameter vanishes, it produces the Einstein theory of gravity. Furthermore, in [3,4] it is argued that Rastall gravity is a special case of f (R, T ) gravity.Rastall theory of gravity might be interpreted as a direct accomplishment of the Mach principle which suggests that the inertial properties of a mass distribution are determined by the distribution of mass-energy in the external space-time [5]. Thus, the source of gravitation, either mass-density or the elements of energy-momentum tensor, depends on the gravitational tensor. We can find also some recent research work that use this gravitational theory to explain the cosmological aspects such as the accelerating expansion of the universe and the inflationary problems [6,7,8,9,10,11,12,13,14,15,16]. In the smaller scale, some astrophysical configurations are investigated by performing this theory. For instance, the investigation of perfect fluid spheres, compact stars, neutron stars, black holes, and wormholes is done in the context of Rastall gravity [17,18,19,20,21,22,23,24,25]. Corresponding to black hole solutions in Rastall gravity, a fascinating non-commutative inspired black hole solution is obtained in [26]. In addition, the black hole solution with the source of a Gaussian matter distribution is obtained in [27]. Several extensions of black hole solution in Rastall gravity are further investigated in [28,29,30,31,32]. Besides that, the thermodynamic properties of black hole solutions in the Rastall gravity are discussed in [33].Recently, it is claimed by Visser [34] that Rastall theory of gravity is equivalent with Einstein theory. However, Darabi et al. [35] compare these two gravitational theories and summarize that Visser's conclusion is not correct. The argument in [35], indeed, supports Rastall theory of gravity for which this theory is still an open theory comparing to the usual general relativity. Henceforth, this theory may face the challenges of cosmological observations as the general relativity.In recent years, it is found that our universe experiences accelerated expansion due to the existence of dark energy that fi...
We show the generic non-extremal Kerr-Newman-NUT-AdS black holes are holographically dual to the hidden conformal field theories in two different pictures. The two pictures can be merged together to the dual CFTs in general picture, that are generated by the SL(2, Z) modular group. We also extend the calculation to the extremal limit and find the corresponding quantities. Using the extended central charges from the Kerr/CFT correspondence, we also find agreement between the macroscopic and microscopic entropies. We also find the absorption cross-section of the scalar probes for the generic and extremal Kerr-Newman-NUT-AdS black holes, to further support the different dual CFTs to the black holes.
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