Dirac perturbations on Schwarzschild–anti–de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

We study Dirac quasinormal modes of Schwarzschild–anti–de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015).]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

Figure 1

Left: comparison of the imaginary part of quasinormal frequencies for the fundamental modes of each branch of solutions, between the analytic matching approximation for small BHs (dashed lines) and the numerical data (solid lines). Right: effects of the angular momentum quantum number $\ell$ on the quasinormal frequencies for intermediate BHs with $r_{+}=1$, and $N=0$.