Marginally stable Schwarzschild-black-hole-non-minimally-coupled-Proca-field bound-state configurations
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2025
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| author | Hod, Shahar |
| author_facet | Hod, Shahar |
| contents | It has recently been revealed that, in curved black-hole spacetimes, non-minimally coupled massive Proca fields may be characterized by the existence of poles in their linearized perturbation equations and may therefore develop exponentially growing instabilities. Interestingly, recent numerical computations [H. W. Chiang, S. Garcia-Saenz, and A. Sang, arXiv:2504.04779] have provided compelling evidence that the onset of monopole instabilities in the composed black-hole-field system is controlled by the dimensionless physical parameter $μr_-$, where $μ$ is the proper mass of the non-minimally coupled Proca field and $r_-\equiv (-2α)^{1/3}r_{\text{H}}$ is the radial location of the pole [here $α$ is the non-minimal coupling parameter of the Einstein-Proca theory and $r_{\text{H}}$ is the radius of the black-hole horizon]. In the present paper we use {\it analytical} techniques in order to explore the physical properties of critical (marginally-stable) composed Schwarzschild-black-hole-nonminimally-coupled-monopole-Proca-field configurations. In particular, we derive a remarkably compact analytical formula for the discrete spectrum $\{μ(r_{\text{H}},r_-;n) \}^{n=\infty}_{n=1}$ of Proca field masses which characterize the critical black-hole-monopole-Proca-field configurations in the dimensionless regime ${r_- -r_{\text{H}}\over{r_{\text{H}}}}\ll1$ of near-horizon poles. The physical significance of the analytically derived resonance spectrum stems from the fact that the critical field mass $μ_{\text{c}}\equivμ(r_{\text{H}},r_-;n=1)$ marks the onset of instabilities in the Schwarzschild-black-hole-nonminimally-coupled-monopole-Proca-field system. In particular, composed black-hole-linearized-Proca-field configurations in the small-mass regime $μ\leqμ_{\text{c}}$ of the Proca field are stable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_19849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marginally stable Schwarzschild-black-hole-non-minimally-coupled-Proca-field bound-state configurations Hod, Shahar General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory It has recently been revealed that, in curved black-hole spacetimes, non-minimally coupled massive Proca fields may be characterized by the existence of poles in their linearized perturbation equations and may therefore develop exponentially growing instabilities. Interestingly, recent numerical computations [H. W. Chiang, S. Garcia-Saenz, and A. Sang, arXiv:2504.04779] have provided compelling evidence that the onset of monopole instabilities in the composed black-hole-field system is controlled by the dimensionless physical parameter $μr_-$, where $μ$ is the proper mass of the non-minimally coupled Proca field and $r_-\equiv (-2α)^{1/3}r_{\text{H}}$ is the radial location of the pole [here $α$ is the non-minimal coupling parameter of the Einstein-Proca theory and $r_{\text{H}}$ is the radius of the black-hole horizon]. In the present paper we use {\it analytical} techniques in order to explore the physical properties of critical (marginally-stable) composed Schwarzschild-black-hole-nonminimally-coupled-monopole-Proca-field configurations. In particular, we derive a remarkably compact analytical formula for the discrete spectrum $\{μ(r_{\text{H}},r_-;n) \}^{n=\infty}_{n=1}$ of Proca field masses which characterize the critical black-hole-monopole-Proca-field configurations in the dimensionless regime ${r_- -r_{\text{H}}\over{r_{\text{H}}}}\ll1$ of near-horizon poles. The physical significance of the analytically derived resonance spectrum stems from the fact that the critical field mass $μ_{\text{c}}\equivμ(r_{\text{H}},r_-;n=1)$ marks the onset of instabilities in the Schwarzschild-black-hole-nonminimally-coupled-monopole-Proca-field system. In particular, composed black-hole-linearized-Proca-field configurations in the small-mass regime $μ\leqμ_{\text{c}}$ of the Proca field are stable. |
| title | Marginally stable Schwarzschild-black-hole-non-minimally-coupled-Proca-field bound-state configurations |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.19849 |