We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild-(A)dS background in arbitrary dimensions. We then use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers — in particular that they vanish for all types of perturbation in four spacetime dimensions — but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory.
Hui, Lam, et al. "Static response and Love numbers of Schwarzschild black holes." Journal of Cosmology and Astroparticle Physics, vol. 2021, no. 04, Apr. 2021. https://doi.org/10.1088/1475-7516/2021/04/052
Hui, Lam, Joyce, Austin, Penco, Riccardo, Santoni, Luca, & Solomon, Adam R. (2021). Static response and Love numbers of Schwarzschild black holes. Journal of Cosmology and Astroparticle Physics, 2021(04). https://doi.org/10.1088/1475-7516/2021/04/052
Hui, Lam, Joyce, Austin, Penco, Riccardo, et al., "Static response and Love numbers of Schwarzschild black holes," Journal of Cosmology and Astroparticle Physics 2021, no. 04 (2021), https://doi.org/10.1088/1475-7516/2021/04/052
@article{osti_1849522,
author = {Hui, Lam and Joyce, Austin and Penco, Riccardo and Santoni, Luca and Solomon, Adam R.},
title = {Static response and Love numbers of Schwarzschild black holes},
annote = {Abstract We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild-(A)dS background in arbitrary dimensions. We then use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers — in particular that they vanish for all types of perturbation in four spacetime dimensions — but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory.},
doi = {10.1088/1475-7516/2021/04/052},
url = {https://www.osti.gov/biblio/1849522},
journal = {Journal of Cosmology and Astroparticle Physics},
issn = {ISSN 1475-7516},
number = {04},
volume = {2021},
place = {United States},
publisher = {Institute of Physics (IOP)},
year = {2021},
month = {04}}
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 344, Issue 1639, p. 441-452https://doi.org/10.1098/rspa.1975.0112