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arXiv · 2503.01029

Finding quasinormal modes directly from the boundary conditions in a Schwarzschild black hole

Jeff Steinhauer
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Abstract

We present a conceptually simple method for finding quasinormal modes (QNMs) in a Schwarzschild black hole. QNMs are defined by their boundary conditions at infinity and at the horizon. These include the intuitively satisfying assertion that the QNM should be purely outgoing at infinity, with no incoming wave coming from infinity and scattering off the black hole. One applies this condition at past null infinity by demanding that the incoming wave there vanish, despite the infinite outgoing wave at the same point in spacetime. We search for QNMs by minimizing the incoming wave, but we are forced to work at a finite distance rather than past null infinity, to avoid the infinite outgoing wave. This technique lets us find the fundamental QNM, but we do not succeed in finding the overtones since the incoming waves always vanish due to damping. The technique is inherently approximate due to the boundary condition at a finite distance.

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Jeff Steinhauer. 2025-03-02. Finding quasinormal modes directly from the boundary conditions in a Schwarzschild black hole. https://doi.org/10.1103/hhmn-xh31

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