HOLOGRAPHY ON KERR-NEWMAN-UNTI- TAMBURINO-KISELEV-ADS IN RASTALL THEORY OF GRAVITY

• Main Author: Fitrah Alfian Rangga Sakti, M.
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/45723
• Institution: Institut Teknologi Bandung

Einstein's theory of gravity can be used to obtain black hole solutions in four dimensions which are in accordance with the dimensions of our universe. In addition, Einstein's field equations can also be used to formulate the black hole solutions for higher dimensions. One of the most common black hole solutions in four dimensions is the Plebanski-Demianski solution which has parameters of mass, angular momentum, electric charge, NUT charge, accel- eration, cosmological constant, and magnetic charge. When the acceleration vanishes, the solution will reduce to the Kerr-Newman-Unti-Tamburino-AdS solution. When all parameters disappear, except the mass, the Schwarzschild solution will be produced. The Schwarzschild solution is the black hole solution which was first discovered through Einstein's field equations. In this era, Einstein's theory of gravity has been heavily modified to generalize the black hole solutions to cover all existing physical theories. More general solutions can explain various solutions that are more specific due to several arbitrary circumstances as Plebanski-Demianski solution where each parameter represents a certain phenomenon. One of the modification of Einstein's theories which is quite promising is Rastall's theory of gravity. Rastall's theory of gravity uses the assumption that the law of conservation of matter tensor is not always zero but depends on a parameter known as the Rastall parameter. When this parameter is zero, the equation will reduce to an ordinary Einstein field equation. Einstein's theory of gravity is believed to be a condition in which the gravity is minimally coupled to the matter. Therefore, the Rastall formu- lation exists as a more general condition in which gravitational field and matter are non-minimally coupled. A black hole that is an object with a very strong gravitational field can also be a solution of the gravitational field equation in Rastall's theory of gravity. Within this dissertation, we look for a Kerr-Newman-Unti-Tamburino-AdS (KNUTAdS) black hole solution in which is extended in Rastall's theory of gravity and assumes that there is a quintessence field that is described by certain matter tensor. The interaction of quintessence with the black hole was firstly formulated by Kiselev. Solutions that have angular momentum and NUT charge can be generated by applying the Demianski-Newman-Janis algorithm. This algorithm is used to get the KNUTAdS solution. The physical properties of this black hole such as the horizon and ergosphere are studied in this disser- tation. The existence of the Rastall parameter and the quintessence equation of state can aect the number of horizons of the black hole. In addition, all parameters including the previous two parameters can aect the size of the ergosphere. Then thermodynamics of the black hole is also studied macroscop- ically or on the other hand, the calculation does not start from the formulation of the partition function. Then the thermodynamics of this black hole, especially the entropy, is also investigated microscopically with the help of the Kerr/CFT correspondence. The Kerr/CFT correspondence applies the holographic principle, i.e. there is a relation between the theory of gravity in N????dimension and the conformal field theory in (N ???? 1)????dimension, as we know that a hologram is a two- dimensional object that can describe three-dimensional object. There are two important conditions in using this correspondence, namely extremal and non- extremal conditions. The extremal condition occurs when a black hole only possesses exactly one horizon. While the non-extremal condition is the generic black hole solution. In extremal condition, a black hole has an AdS2 structure and there is a CFT on its boundary, so that the AdS/CFT correspondence can be used to study the thermodynamics and calculate the entropy of the black holes. Entropy is calculated using the Cardy entropy formula obtained from CFT2. Cardy formula is a function of central charge and conformal temperature of which have two parts, namely the right- and left-sectors. With the Kerr/CFT correspondence, it is found that this extreme black hole is holographically dual with the CFT. Furthermore, for non-extremal condition, we assume that the magnetic charge, quintessence field and Rastall parameter vanish to study the correspondence. This assumption is used to simplify the calculation. In this situation, the black hole is viewed as the background of a scalar field that can reveal the conformal symmetry in the quadratic Casimir operator. Furthermore, it can be seen that the scalar field equation of motion has the symmetry of the AdS3 space generated by the conformal generators. The conformal generators represent two sectors, right and left, so that they represent CFT2. Hence, the entropy of the black hole can be calculated using the Cardy formula. When a certain value of parameter is taken, the entropy is equal with the extremal entropy. Then the absorption cross section of this black hole is studied by applying this correspondence and it can be shown that the absorption cross-section agrees with that from the CFT by identifying several thermodynamic quantities. By using this correspondence, we conclude that the Kerr-Newman-Unti-Tamburino-Kiselev-AdS black hole in Rastall's theory of gravity is holographically dual with the CFT.