In this master's thesis, we investigate how the geometry of the black hole interior is reflected in the analytic structure of Green's functions and in the quasinormal spectrum. We first study bouncing geodesics in static, spherically symmetric Schwarzschild geometries with vanishing and positive cosmological constant. We determine their null limits and the associated complex bouncing times and, using the local Hadamard form and the propagation of singularities theorem, show that geodesics approaching the curvature singularity correspond to singularities of the analytically continued retarded Green's function. We then enclose the black hole in an ideal reflecting cavity and derive a thermal product formula for the boundary thermal correlator, expressing it in terms of its poles, or quasinormal frequencies. This yields the universal asymptotic relation, according to which the spacing between consecutive quasinormal frequencies is fixed by the complex bouncing time. The result applies to the scalar, electromagnetic, and gravitational perturbations considered here for black holes with vanishing, positive, and negative cosmological constant. We verify the prediction numerically and find that the spectrum often approaches it already at comparatively low quasinormal overtones. Finally, we replace the ideal wall by a partially transmitting spherical shell of accretion plasma. Our numerical results show that, over a finite frequency range, the plasma barrier can act as an effective reflecting wall, so that the spacings of trapped quasinormal modes continue to encode the geometry of the black-hole interior.
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