Gravitational Memory Effects at the Event Horizon

We discuss the memory effect at the horizon of a non-extremal black hole arising from a burst of gravitational radiation. We show that, generically, the burst of radiation induces a change in all the mass and angular momentum multipoles of the horizon, but only the changes in the quadrupole and higher-order multipoles are necessary to fully characterise the memory effect: permanent shifts of the velocity of massless particles travelling along the horizon induced by the burst of radiation. We argue that the quadrupole and higher-order horizon multipoles are not intrinsic degrees of freedom of the horizon, instead they should be understood as distortions induced by the presence of matter and radiation external to the black hole. We conclude that these memory effects on the horizon cannot “store holographically” the information about the state of particles falling to the black hole, as proposed by S. Hawking in arXiv:1509.01147.