Evolution of linear gravitational and electromagnetic perturbations inside a Kerr black hole

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 61, Issue 2, 2000, Pages

  Ori, Amos ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044410531     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.61.024001     Document Type: Article

References (49)

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21. See the oscillations in (Formula presented) in Eq. (5) of Ref. 20. Note, however, that since the analysis in Ref. 20 does not tell which of the coefficients vanishes and which does not, it does not exclude the possibility that all oscillatory terms decay faster than the nonoscillatory ones, which would lead to an overall nonoscillatory behavior at the CH.
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26. The local approach used in Refs. 22232425 (unlike the global approach used in Ref. 20 and also in the present paper) cannot tell whether the CH singularity is oscillatory or not, because this completely depends on whether the local initial data assumed are oscillatory or monotonic. All the local analyses 22232425 explicitly assumed nonoscillatory local initial data for simplicity. However, Brady et al. 22 argue that their analysis can be generalized to include oscillations.
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41. In S. Hod, Phys. Rev. D 58, 104022 (1998), there is an attempt to analyze the late-time behavior for both (Formula presented) and (Formula presented) in the frequency domain, to the leading order in the frequency ω. This analysis, however, yields an incorrect description of the late-time behavior (it yields the standard Schwarzschild index (Formula presented) at fixed r for all multipoles l), primarily because the approximation (Formula presented) is used there out of its domain of validity, leading to an incorrect description of the coupling between different multipoles.
42. S. Hod, gr-qc/9902073.
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45. The analyses of external perturbations 2938 clearly indicate the presence of the higher-order terms (Formula presented) at the EH. So far, however, these analyses have not excluded the possibility of additional broken-power terms like (Formula presented) etc., or extra logarithmic factors in the higher-order terms (Formula presented) Such subdominant broken-power or logarithmic terms will not affect the results of our analysis, which are restricted to the leading order in (Formula presented) and (Formula presented) Since the present analyses do not give positive indication for such extra terms, we do not include them in Eq. (15).
46. In Ref. 41 Hod’s analysis led to the result (Formula presented) in all cases. This result followed from an invalid assumption about the asymptotic behavior of the (Formula presented) radial functions at the EH, as explained in Ref. 43.
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