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Physical Effects of the Gravitational $Θ$-Parameter

We describe the effect of the gravitational $Θ$-parameter on the behavior of the stretched horizon of a black hole in $(3+1)$-dimensions. The gravitational $Θ$-term is a total derivative, however, it affects the transport properties of the horizon. In particular, the horizon acquires a third order parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the horizon. In the context of the gauge/gravity duality, the $Θ$-term induces a non-trivial contact term in the energy-momentum tensor of a $(2+1)-$dimensional large-N gauge theory, which admits a dual gravity description. As a consequence, the dual gauge theory in the presence of the $Θ$-term acquires the same third order parity violating transport coefficient.