Love at the String Scale: Tidal Deformability Across the Black Hole-String Transition

Abstract

Tidal deformability provides a sensitive probe of the structure of compact objects, and black holes are exceptional in having vanishing static Love numbers in four-dimensional Einstein gravity. We ask what happens to this fine-tuned rigidity across the black hole-string transition, where the same states are expected to admit a weakly coupled description as a self-gravitating highly excited string, or "string star". We compute the static tidal Love numbers of the Horowitz-Polchinski (HP) string star for multipoles $\ell =2,3,4$ in $D=4,5,6$. The response is non-zero in all cases, as in the available ${\alpha }^{\prime }$-corrected black hole results, so the zero-Love structure of four-dimensional Einstein gravity does not survive on either side of the transition. On the string side, however, the response has a distinctive multipolar structure: the Love numbers grow rapidly with $\ell$, and we show analytically that this growth originates from the competition between the multipolar weight of the tidal field and the exponential tail of the winding condensate, with the result that the radial scale probed by the deformability grows linearly with $\ell$ at large multipole number. This provides a direct tidal signature of the extended, surface-less nature of the string star. We discuss the comparison with ${\alpha }^{\prime }$-corrected black holes and the limitations of the currently available perturbative results at large $\ell$.

32 pages, 3 figures