Abstract
Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub ‘highly-damped’ modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.
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Acknowledgments
We acknowledge fruitful scientific exchange with I. Bah, E. Berti, I. Bena, V. Bevilacqua, G. Bonelli, G. Bossard, V. Cardoso, A. Cipriani, D. Consoli, V. Cuozzo, A. De Santis, C. Di Benedetto, G. Dibitetto, A. Evangelista, G. Frittoli, F. Fucito, C. Gasbarra, B. Giambenedetti, C. Iossa, P. Heidmann, M. Marzi, D. Mayerson, P. Pani, L. Pirelli, A. Salvio, R. Savelli, N. Speeney, L. Tabarroni, A. Tanzini, and F. Tombesi. M. B., G. D. R. and J. F. M. would like to thank GGI Arcetri (FI) for the kind hospitality during completion of this work. We thank the MIUR PRIN contract 2020KR4KN2 “String Theory as a bridge between Gauge Theories and Quantum Gravity” and the INFN project ST&FI “String Theory and Fundamental Interactions” for partial support.
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Bianchi, M., Di Russo, G., Grillo, A. et al. On the stability and deformability of top stars. J. High Energ. Phys. 2023, 121 (2023). https://doi.org/10.1007/JHEP12(2023)121
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DOI: https://doi.org/10.1007/JHEP12(2023)121