# Infinite quantum twisting at the Cauchy horizon of rotating black holes

February 22, 2024

We present a numerical calculation of the expectation value of the quantum
angular-momentum current flux density for a scalar field in the Unruh state
near the inner horizon of a Kerr-de Sitter black hole. Our results indicate
that this flux diverges as $V_-^{-1}$ in a suitable Kruskal coordinate such
that $V_-=0$ at the inner horizon. Depending on the parameter values of the
scalar field and black hole that we consider, and depending on the polar angle
(latitude), this flux can have different signs. In the near extremal cases
considered, the angle average of the expectation value of the quantum angular
momentum current flux is of the opposite sign as the angular momentum of the
background itself, suggesting that, in the cases considered, quantum effects
tend to decrease the total angular momentum of the spheres away from the
extremal value. We also numerically calculate the energy flux component, which
provides the leading order divergence of the quantum stress energy tensor,
dominant over the classical stress energy tensor, at the inner horizon. Taking
our expectation value of the quantum stress tensor as the source in the
semiclassical Einstein equation, our analysis suggests that the spheres
approaching the inner horizon can undergo an infinite twisting due to quantum
effects along latitudes separating regions of infinite expansion and
contraction.

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