Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation
Rotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale M set by the geometric size (mass...
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| Format: | Article |
| Language: | English |
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Elsevier
2015-10-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269315005912 |
| _version_ | 1818611474848808960 |
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| author | Shahar Hod |
| author_facet | Shahar Hod |
| author_sort | Shahar Hod |
| collection | DOAJ |
| description | Rotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale M set by the geometric size (mass) of the central black hole. It is well-known that, in the small-mass limit α≡Mμ≪1 (here μ is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic oscillation spectrum: ωR/μ=1−α2/2n¯02, where the integer n¯0(l,n;α→0)=l+n+1 is the principal quantum number of the bound-state resonance (here the integers l=1,2,3,… and n=0,1,2,… are the spheroidal harmonic index and the resonance parameter of the field mode, respectively). As it depends only on the principal resonance parameter n¯0, this small-mass (α≪1) hydrogenic spectrum is obviously degenerate. In this paper we go beyond the small-mass approximation and analyze the quasi-stationary bound-state resonances of massive scalar fields in rapidly-spinning Kerr black-hole spacetimes in the regime α=O(1). In particular, we derive the non-hydrogenic (and, in general, non-degenerate) resonance oscillation spectrum ωR/μ=1−(α/n¯)2, where n¯(l,n;α)=(l+1/2)2−2mα+2α2+1/2+n is the generalized principal quantum number of the quasi-stationary resonances. This analytically derived formula for the characteristic oscillation frequencies of the composed black-hole-massive-scalar-field system is shown to agree with direct numerical computations of the quasi-stationary bound-state resonances. |
| first_indexed | 2024-12-16T15:30:55Z |
| format | Article |
| id | doaj.art-51f54df3ced5450a9315bf4bf2247c11 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 1873-2445 |
| language | English |
| last_indexed | 2024-12-16T15:30:55Z |
| publishDate | 2015-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-51f54df3ced5450a9315bf4bf2247c112022-12-21T22:26:21ZengElsevierPhysics Letters B0370-26931873-24452015-10-01749C16717110.1016/j.physletb.2015.07.071Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximationShahar Hod0The Ruppin Academic Center, Emeq Hefer 40250, IsraelRotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale M set by the geometric size (mass) of the central black hole. It is well-known that, in the small-mass limit α≡Mμ≪1 (here μ is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic oscillation spectrum: ωR/μ=1−α2/2n¯02, where the integer n¯0(l,n;α→0)=l+n+1 is the principal quantum number of the bound-state resonance (here the integers l=1,2,3,… and n=0,1,2,… are the spheroidal harmonic index and the resonance parameter of the field mode, respectively). As it depends only on the principal resonance parameter n¯0, this small-mass (α≪1) hydrogenic spectrum is obviously degenerate. In this paper we go beyond the small-mass approximation and analyze the quasi-stationary bound-state resonances of massive scalar fields in rapidly-spinning Kerr black-hole spacetimes in the regime α=O(1). In particular, we derive the non-hydrogenic (and, in general, non-degenerate) resonance oscillation spectrum ωR/μ=1−(α/n¯)2, where n¯(l,n;α)=(l+1/2)2−2mα+2α2+1/2+n is the generalized principal quantum number of the quasi-stationary resonances. This analytically derived formula for the characteristic oscillation frequencies of the composed black-hole-massive-scalar-field system is shown to agree with direct numerical computations of the quasi-stationary bound-state resonances.http://www.sciencedirect.com/science/article/pii/S0370269315005912 |
| spellingShingle | Shahar Hod Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation Physics Letters B |
| title | Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation |
| title_full | Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation |
| title_fullStr | Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation |
| title_full_unstemmed | Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation |
| title_short | Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation |
| title_sort | quasi bound states of massive scalar fields in the kerr black hole spacetime beyond the hydrogenic approximation |
| url | http://www.sciencedirect.com/science/article/pii/S0370269315005912 |
| work_keys_str_mv | AT shaharhod quasiboundstatesofmassivescalarfieldsinthekerrblackholespacetimebeyondthehydrogenicapproximation |