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Volumn 74, Issue 26, 1995, Pages 5170-5173

Critical behavior in gravitational collapse of radiation fluid: A renormalization group (linear perturbation) analysis

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Indexed keywords

EID: 0000360396 PISSN: 00319007 EISSN: None Source Type: Journal
DOI: 10.1103/PhysRevLett.74.5170 Document Type: Article

Times cited : (272)

References (10)

3
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- (1994) Phys. Rev. Lett. , vol.72 , pp. 1782
- Evans, C.R.¹ Coleman, J.S.²

4
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- Phys. Rep., For more recent exposition see, e.g., Addison-Wesley, Reading
- (1974) Lectures on Critical Phenomena and the Renormalization Group , vol.12 C , pp. 75
- Wilson, K.¹ Kogut, J.²

5
- 84990739185
- Renormalization group and asymptotics of solutions of nonlinear parabolic equations
- (1994) Communications on Pure and Applied Mathematics , vol.47 , pp. 893
- Bricmont, J.¹ Kupiainen, A.² Lin, G.³

6
- 84927840061
- If there is more than one relevant mode, the stable manifold of Hss will have a codimension of more than one; a generic family of initial data will not intersect the stable manifold, thus no sharp critical behavior will be seen. Fixed points with more than one relevant mode are responsible for the so-called multicritical behavior.

7
- 84927840060
- An alert reader will notice a gap between the first and second lines of Eq. 10: T^ on the second line, which is defined as the tangent map at the fixed point Hss, should in fact be the tangent map at Hc. The maneuver, however, can in general be justified because of Eq. 8. More precisely, what matters most in controlling the critical behavior is the part of the RGT flow in the vicinity of the fixed point (between P and Q of Fig. 1), where Hinit(s) spends most of its time during its journey from Hinit to Hinit(s0). For the part from P to Q, we can justify the use of T^ above. The parts Hinit→P and Q→Hinit(s0) are supposed to be regular. For this reason, it is expected that our conclusion, Eq. 15, is an exact relation.

9
- 4243425478
- (1990) Phys. Rev. D , vol.42 , pp. 1068-1090
- Ori, A.¹ Piran, T.²

10
- 0000574080
- On the Equations Governing the Perturbations of the Schwarzschild Black Hole
- (1975) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , vol.343 , pp. 289-298
- Chandrasekhar, S.¹

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