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

TL;DR

This paper calculates the tidal Love numbers for a specific extremal Reissner-Nordstrom black hole configuration, revealing they are finite and non-zero, contrasting with the zero Love number of isolated black holes, thus advancing understanding of black hole responses to external fields.

Contribution

It provides an exact solution for the non-linear Einstein equations showing non-vanishing Love numbers for a particular extremal black hole configuration, extending previous zero Love number results.

Findings

Finite, non-zero Love number for the specific extremal black hole configuration.

Verification that isolated extremal Reissner-Nordstrom black holes have zero Love number.

Explicit calculation and matching of master functions with effective field theory.

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.