مشخصات پژوهش

We study the propagation of massless fermionic fields, implementing a family of special functions: Heun functions, in solving the wave equation in three three- dimensional backgrounds, including the BTZ black hole in string theory and Lifshitz black hole solutions in conformal gravity and Hu–Sawicki F(R) theory. The main properties of the selected black hole solutions is that their line elements are Weyl related to that of a homogeneous spacetime, whose spa- tial part possesses Lie symmetry, described by Lobachevsky- type geometry with arbitrary negative Gaussian curvature. Using the Weyl symmetry of massless Dirac action, we con- sider the perturbation equations of fermionic fields in rela- tion to those of the homogeneous background, which having definite singularities, are transformed into Heun’s equation. We point out the existence of quasinormal modes labeled by the accessory parameter of the Heun function. The distribu- tion of the quasinormal modes has been clarified to satisfy the boundary conditions that require ingoing and decaying waves at the event horizon and conformal infinity, respec- tively. It turned out that the procedure based on the Heun function, beside reproducing the previously known results obtained via hypergeometric function for the BTZ and Lif- shitz black hole solution in conformal gravity, brings up new families of quasinormal frequencies, which can also contain purely imaginary modes. Also, the analysis of the quasinor- mal modes shows that with the negative imaginary part of complex frequencies ω = ωRe + iωI m , the fermionic pertur- bations are stable in this background.