In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies ω and angular quantum numbers λ, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate as well as efficient method for investigating quasinormal modes. Black holes constitute an intriguing topic in astrophysics and theoretical physics, where the gravitational force is so strong that nothing can escape from inside of its event horizon. The study of the properties of black holes might lead to insightful perspectives on quantum gravity. The observation of many astronomical phenomena, as, for instance, gravitational lensing, become more accessible when associated to very compact stellar objects such as black holes. Among others, one of the most important tools in the study of black holes is the analysis of its quasinormal mode (QNM) oscillations, which describe the late time dynamics of black holes or black hole binaries, and therefore provide valuable information on the inherent properties of the black hole spacetime as well as its stability. Recently, such signal was observed in the LIGO's first direct detection of gravitational wave [1,2].
KeywordsGenerally, the QNM problem can be reformulated in terms of a Schrödinger-type equation. Due to mathematical difficulties, an exact analytic solution is not always attainable. Therefore, semi-analytical approximate and numerical methods have been proposed to calculate the quasinormal frequency (QNF) [3][4][5][6][7], for example, the Pöschl-Teller potential method [8], continued fractions method [9,10], the Horowitz-Hubeny method (HH) for anti-de Sitter spacetime [11], the WKB approximation [12][13][14], the finite difference method [15][16][17][18][19][20] and the asymptotic iteration method [21][22][23][24] among others [25][26][27].In this letter, we make use of a matrix method [28] to calculate the scalar QNF's for rotating Kerr and Kerr-Sen black hole spacetimes. By using the method of separation of variables, the radial and angular parts of the linearized perturbation equation of the scalar fields are given by [29,30] (whereHere, a ∈ [0,] gives the angular momentum per unit mass. When b = 0, it is the Kerr-Sen black hole case, which reduces to the Kerr black hole spacetime at b = 0. For the case of Kerr black hole, in order to compare our results with those from the continuous fraction method, the mass of the black hole is taken to be M = 1/2. On the other hand, for the case of Kerr-Sen black hole, the mass M = (2b + r 0 + r i )/2 and angular momentum a = √ r i r 0 can be expressed in terms of the event horizon r 0 and the inner horizon r i . m represents the magnetic quantum number and u = cos θ ∈ [−1, 1]. It...
