Maxwell quasinormal modes on a global monopole Schwarzschild-anti-de Sitter black hole with Robin boundary conditions

Abstract

We generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge–Wheeler–Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existence of the monopole parameter. In the small black hole and low frequency approximations, the Maxwell quasinormal modes are solved perturbatively on top of normal modes by using an asymptotic matching method, while beyond the aforementioned approximation, the Maxwell quasinormal modes are obtained numerically. We analyze the Maxwell quasinormal spectrum by varying the angular momentum quantum number $$\ell $$ ℓ , the overtone number N, and in particular, the monopole parameter $$8\pi \eta ^2$$ 8 π η 2 . We show explicitly, through calculating quasinormal frequencies with both boundary conditions, that the global monopole produces the repulsive force.

Electromagnetic quasinormal modes of Schwarzschild-anti-de Sitter black holes: bifurcations, spectral similarity, and exact solutions in the large black hole limit

“…The description of the splitting of two pairs satisfying (2) into two purely imaginary modes as 'bifurcations' was given very recently [23,24]. (In the earlier Ref.…”

“…The Dirichlet boundary condition (43) corresponding to a total internal reflection at spatial infinity does not support the zero mode, since the corresponding eigenfunction vanishes. However, other boundary conditions may support the zero mode [23,24], whenever the boundary conditions permit a constant non-zero solution.…”

“…and the boundary condition at spatial infinity that supports a constant solution. As a sample calculation, let us consider the Robin boundary condition corresponding to a conservation of energy condition at spatial infinity [23,24],…”

“…Historically, the first investigation of its quasinormal mode spectrum was conducted in [9], while its implications in CFT were first described in [10]. Since then, a wealth of papers has been written for different dimensions, coupled perturbing fields, boundary conditions and using different numerical and analytical methods [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

“…1. As the dimensionless parameter ρ is varied, a bifurcation in the spectrum occurs [23,24]. This happens whenever a pair of quasinormal modes satisfying…”