Built on

O. J. C. Dias, P. Figueras, R. Monteiro and J. E. Santos, “Ultraspinning instability of rotating black holes,” Phys. Rev. D 82
Original
1904
Earlier work this paper cites.
P. M. Morse and H. Feshbach, “Methods of theoretical physics,” McGraw-Hill, U.S.A. (1953)
1953
Earlier work this paper cites.
D. G. B. Edelen “Helmholtz equation on the surface of the unit ( N + 1 ) (N+1) -sphere,” J. Math. Anal. Appl. 23
1968
Earlier work this paper cites.
P. G. O. Freund and M. A. Rubin, “Dynamics of dimensional reduction,” Phys. Lett. B 97
1980
Earlier work this paper cites.
S. S. Gubser and I. Mitra, “The Evolution of unstable black holes in anti-de Sitter space,” JHEP 0108
2001
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O. DeWolfe, D. Z. Freedman, S. S. Gubser, G. T. Horowitz and I. Mitra, “Stability of A d S p × M q AdS_{p}\times M_{q} compactifications without supersymmetry,” Phys. Rev. D 65
2002
Earlier work this paper cites.
S. S. Gubser “On non-uniform black branes” Class. Quant. Grav. 19
2002
Earlier work this paper cites.
K. R. Riley, M. P. Hobson and J. J. Bence “Mathematical methods for physics and engineering,” Cambridge, U.K. (2002)
2002
Earlier work this paper cites.

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Then

I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, series and products 7ed.” Elsevier, U.K. (2007)
2007
Later among the works it cites.
S. M. Carroll, M. C. Johnson and L. Randall, “Dynamical compactification from de Sitter space,” JHEP 0911
Original
2009
Later among the works it cites.
O. J. C. Dias, P. Figueras, R. Monteiro, J. E. Santos and R. Emparan, “Instability and new phases of higher-dimensional rotating black holes,” Phys. Rev. D 80
Original
2009
Later among the works it cites.
S. Kinoshita and S. Mukohyama, “Thermodynamic and dynamical stability of Freund-Rubin compactification,” JCAP 0906
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2009
Later among the works it cites.
R. Emparan and P. Figueras, “Multi-black rings and the phase diagram of higher-dimensional black holes,” JHEP 1011
Original

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2012

Warped branches of flux compactifications

Lim, Yen-Kheng

Understand

We consider Freund-Rubin-type compactifications which are described by (p+q)-dimensional Einstein gravity with a positive cosmological constant and a q-form flux.

Using perturbative expansions of Kinoshita's ansatz for warped dS_pxS^q and AdS_pxS^q spacetimes, we obtain analytical solutions describing the warped branches and their respective phase spaces.
These equations are given by inhomogeneous Gegenbauer differential equations which can be solved by the Green's function method.
The requirement that the Green's functions are regular provides constraints which determine the structure of the phase space of the warped branches.

Built on

O. J. C. Dias, P. Figueras, R. Monteiro and J. E. Santos, “Ultraspinning instability of rotating black holes,” Phys. Rev. D 82
Original
1904
Earlier work this paper cites.
P. M. Morse and H. Feshbach, “Methods of theoretical physics,” McGraw-Hill, U.S.A. (1953)
1953
Earlier work this paper cites.
D. G. B. Edelen “Helmholtz equation on the surface of the unit ( N + 1 ) (N+1) -sphere,” J. Math. Anal. Appl. 23
1968
Earlier work this paper cites.
P. G. O. Freund and M. A. Rubin, “Dynamics of dimensional reduction,” Phys. Lett. B 97
1980
Earlier work this paper cites.
S. S. Gubser and I. Mitra, “The Evolution of unstable black holes in anti-de Sitter space,” JHEP 0108
2001
Earlier work this paper cites.
O. DeWolfe, D. Z. Freedman, S. S. Gubser, G. T. Horowitz and I. Mitra, “Stability of A d S p × M q AdS_{p}\times M_{q} compactifications without supersymmetry,” Phys. Rev. D 65
2002
Earlier work this paper cites.
S. S. Gubser “On non-uniform black branes” Class. Quant. Grav. 19
2002
Earlier work this paper cites.
K. R. Riley, M. P. Hobson and J. J. Bence “Mathematical methods for physics and engineering,” Cambridge, U.K. (2002)
2002
Earlier work this paper cites.

Similar

R. Bousso, O. DeWolfe and R. C. Myers, “Unbounded entropy in space-times with positive cosmological constant,” Found. Phys. 33
2003
Cited alongside, same era.
R. Emparan and R. C. Myers, “Instability of ultra-spinning black holes,” JHEP 0309
2003
Cited alongside, same era.
C. R. Contaldi, L. Kofman and M. Peloso, “Gravitational instability of de Sitter compactifications,” JCAP 0408
2004
Cited alongside, same era.
A. V. Frolov and L. Kofman, “Can inflating brane worlds be stabilized?,” Phys. Rev. D 69
2004
Cited alongside, same era.
J. U. Martin, “Cosmological perturbations in flux compactifications,” JCAP 0504
2005
Cited alongside, same era.
S. Kinoshita, “New branch of Kaluza-Klein compactification,” Phys. Rev. D 76