Non-vanishing non-linear Static Love Number of a Class of Extremal Reissner-Nordstrom Black Holes

Abstract: We compute the tidal Love numbers for a particular axially symmetric configuration of extremal Reissner-Nordstrom geometry. By exactly solving the non-linear Einstein equations, we investigate the tidal response of extremal Reissner-Nordstrom black holes in four-dimensional spacetimes under external gravitational fields. We show that, for the specific geometry considered, the static tidal Love number remains finite and non-vanishing to all orders in the external tidal field. By contrast, we verify that the Love number of an isolated extremal Reissner-Nordstrom black hole remains zero, in agreement with previous expectations. Furthermore, we explicitly calculate the Zerilli-Moncrief master functions and match them with the effective field theory description.