It was reported that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. These stationary massive charged scalar fields can form bound states, which are called stationary scalar clouds. In this paper, we show that Kerr-Sen black holes can also support stationary massive charged scalar clouds by matching the nearand far-region solutions of the radial part of the Klein-Gordon wave equation. We also review stationary scalar clouds within the background of static electrically charged black hole solutions in the low-energy limit of heterotic string field theory, namely, the GibbonsMaeda-Garfinkle-Horowitz-Strominger black holes.

It is reported that Kerr-Newman and Kerr-Sen black holes are unstable to perturbations of charged massive scalar field. In this paper, we study analytically the complex frequencies which characterize charged massive scalar fields in a near-extremal Kerr-Sen black hole. For near-extremal Kerr-Sen black holes and for charged massive scalar fields in the eikonal large-mass M ≫ µ regime, where M is the mass of the black hole, and µ is the mass of the charged scalar field, we have obtained a simple expression for the dimensionless ratio ω I / (ω R − ω c ), where ω I and ω R are, respectively, the imaginary and real parts of the frequency of the modes, and ω c is the critical frequency for the onset of super-radiance. We have also found our expression is consistent with the result of Hod [1] for the case of a near-extremal Kerr-Newman black hole and the result of Zouros and Eardly [2] for the case of neutral scalar fields in the background of a near-extremal Kerr black hole.

The nonextremal Kerr black holes have been considered to be holographically dual to twodimensional (2D) conformal field theories (CFTs). In this paper, we extend the holography to the case of an asymptotically anti-de Sitter (AdS) rotating charged black holes in f (T ) gravity, where f (T ) = T + αT 2 , where α is a constant. We find that the scalar wave radial equation at the near-horizon region implies the existence of the 2D conformal symmetries. We note that the 2π identification of the azimuthal angle φ in the black hole line element, corresponds to a spontaneous breaking of the conformal symmetry by left and right temperatures TL and TR, respectively. We show that choosing proper central charges for the dual CFT, we produce exactly the macroscopic Bekenstein-Hawking entropy from the microscopic Cardy entropy for the dual CFT. These observations suggest that the rotating charged AdS black hole in f (T ) gravity is dual to a 2D CFT at finite temperatures TL and TR for a specific value of mass M , rotational, charge, and f (T ) parameters, Ω, Q, and |α|, respectively.

IntisariDalam makalah ini akan ditinjau kembali bahwa persamaan medan gravitasi Einstein mempunyai solusi yaitu solusi Reissner-Nordström dengan menghitung seluruh komponen dari tensor Einstein dan tensor energimomentum dengan adanya interaksi elektromagnetik. Solusi Reissner-Nordström adalah solusi yang menggambarkan ruangwaktu di luar sebuah bola pejal statik bermassa M dan bermuatan listrik Q. Solusi ReissnerNordström juga merupakan solusi lubang hitam statik bermuatan listrik dalam teori Einstein-Maxwell. ABSTRACTIn this paper, we review that Reissner-Nordström metric is the solution of Einstein gravitational field equation. Reissner-Nordström solution describes spacetime outside a static spherically symmetric charged mass. To solve the field equation, we calculate all the non-zero components of Einstein tensor and energy-momentum tensor of the electromagnetic field of the charged object. One finds that the Reissner-Nordström metric is also a charged static black hole solution in Einstein-Maxwell theory.KATA KUNCI: Persamaan medan Einstein, metrik Reissner-Nordström, lubang hitam http://dx