Chern-Simons caps for rotating black holes

We study the dynamical Chern-Simons gravity as an effective quantum field theory, and discuss a broad range of its parameter space where the theory is valid. Within that validity range, we show that slowly rotating black holes acquire novel geometric structures due to the gravitational dynamical Chern-Simons term. In particular, the rotating black-hole solutions get endowed with two caplike domains, emanating from the north and south poles in the standard Boyer-Lindquist coordinates. The domains extend out to a distance that is approximately a few percent of the black hole's size. The caplike domains have an unusual equation of state, pointing to nonstandard dynamics within the caps. In particular, the focusing condition for geodesics is violated in those domains. This in turn implies that the Hawking-Penrose singularity theorem cannot be straightforwardly applied to hypothetical probe matter placed within the Chern-Simons caps.