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Quasinormal Modes and Universality of the Penrose Limit of Black Hole Photon Rings
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We study the physics of photon rings in a wide range of axisymmetric black holes admitting a separable Hamilton-Jacobi equation for the geodesics. Utilizing the Killing-Yano tensor, we derive the Penrose limit of the black holes, which describes the physics near the photon ring. The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation, as well as the instabilities and Lyapunov exponents of the null geodesics. Consequently, the Lyapunov exponents and frequencies of the photon geodesics, along with the quasinormal modes, can be all extracted from a Hamiltonian in the Penrose limit plane wave metric. Additionally, we explore potential bounds on the Lyapunov exponent, the orbital and precession frequencies, in connection with the corresponding inverted harmonic oscillators and we discuss the possibility of photon rings serving as holographic horizons in a holographic duality framework for astrophysical black holes. Our formalism is applicable to spacetimes encompassing various types of black holes, including stationary ones like Kerr, Kerr-Newman, as well as static black holes such as Schwarzschild, Reissner-Nordstr\"om, among others.
Forward citations
Cited by 4 Pith papers
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Thermal Origin of Black Hole Quasinormal Modes
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Black Hole Mergers as the Fastest Photon Ring Scramblers
Merger remnant mass and spin are claimed to maximize the average Lyapunov exponent of the photon shell of an effective Kerr black hole, matching numerical relativity fits within a few percent for q ≲ 20.
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Bounds for Lyapunov exponent of circular light orbits in black holes
For any static, spherically symmetric black hole obeying Einstein's equations and the dominant energy condition, the circular photon orbit's Lyapunov exponent is bounded by the photon-sphere surface gravity, the Unruh...
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