Kerr–Newman–NUT–Kiselev black holes in Rastall theory of gravity and Kerr/CFT correspondence

Abstract

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...

Rotating black holes and exotic compact objects in the Kerr/CFT correspondence within Rastall gravity

“…The KNUTK black holes are the exact solution to Einstein-Maxwell-perfect fluid equations with nonvanishing NUT charge in Rastall gravity for a nonvanishing Rastall coupling constant. These black hole solutions are obtained in [63] by using Demiański-Newman-Janis algorithm to the Reissner-Nordström-Kiselev black holes in Rastall gravity. The solutions portray the spacetime for a rotating electrically and magnetically charged massive object with a twisting NUT charge surrounded by a quintessential field.…”

“…Kiselev first derived the quintessential field in the black hole solutions [75], so that it is common to say the quintessential black holes as Kiselev black holes. The line element of KNUTK spacetime in Rastall gravity reads as [63]…”

“…It is clearly seen that for a = 0, e = 0, g = 0, n = 0, α = 0, it reduces to Schwarzschild space-time in Rastall gravity. The electromagnetic potential is given by [63] A…”

“…Hence, this theory is still feasible as the generalization of general relativity. Rastall theory has also been applied to several astrophysical objects [63][64][65][66][67][68][69] and cosmology [70][71][72] in different aspects. In a gravitational system, quantum effects may give rise to the violation of the conservation of the matter tensor.…”

“…Firstly, we investigate the hidden conformal symmetry of rotating black holes in Rastall gravity. We choose the Kerr-Newman-NUT-Kiselev (KNUTK) black hole solutions in Rastall gravity obtained in [63]. These solutions portray the charged rotating and twisting black holes environed by the quintessential field with a non-vanishing Rastall coupling constant.…”