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- Complex Quantum Tunneling, Picard-Lefschetz Theory, and the Decay of Black Holes

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17090071

Quantum effects render black holes unstable. In addition to Hawking radiation, which leads to the prediction of a long lifetime, there is the possibility of quantum tunneling of the black hole geometry itself. A robust possibility for treating the quantum tunneling of a spacetime geometry is through a complex path integral and Picard-Lefschetz theory. I will illustrate the semiclassical approximation of complex path integrals using these techniques with an analytically solvable 1D quantum potentialâ€”the inverse square barrierâ€”and describe the setup of the calculation for spherically symmetric black holes. While the black hole calculation is incomplete, I will be able to describe a surprising extension of this setup to the more astrophysical rotating Kerr black hole.

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