Birkhoff’s theorem in Lovelock gravity for general base manifolds - INSPIRE

DataBETA

Birkhoff’s theorem in Lovelock gravity for general base manifolds

Sourya Ray
(
- Chile Austral U., Valdivia
)

May 14, 2015

7 pages

Published in:

Class.Quant.Grav. 32 (2015) 19, 195022

Published: Sep 17, 2015

e-Print:

1505.03830 [gr-qc]

DOI:

10.1088/0264-9381/32/19/195022

View in:

reference search36 citations

Citations per year

Abstract: (IOP)

We extend the Birkhoff’s theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.

Note:

minor corrections, matches the published version

Lovelock gravity
Birkhoff's theorem
black holes
gravitation: Lovelock
Birkhoff theorem
space: warped
space-time: static
coupling

References(20)

Figures(0)

[1]

C. Böhm

- Invent.Math. 134 (1998) 145

[2]

Uniqueness and nonuniqueness of static vacuum black holes in higher dimensions

Gary W. Gibbons
(
- Cambridge U., DAMTP
)
,
Daisuke Ida
(
- Tokyo U., RESCEU
)
,
Tetsuya Shiromizu
(
- Tokyo U., RESCEU
)

- Prog.Theor.Phys.Suppl. 148 (2003) 284-290
•
e-Print:
- gr-qc/0203004
•
DOI:
- 10.1143/PTPS.148.284

[3]

Uniqueness and nonuniqueness of static black holes in higher dimensions

Gary W. Gibbons
(
- Cambridge U., DAMTP
)
,
Daisuke Ida
(
- Tokyo U., RESCEU
)
,
Tetsuya Shiromizu
(
- Tokyo U., RESCEU
)

- Phys.Rev.Lett. 89 (2002) 041101
•
e-Print:
- hep-th/0206049
•
DOI:
- 10.1103/PhysRevLett.89.041101

[4]

Birkhoff's theorem in Lovelock gravity

Robin Zegers
(
- Orsay, LPT and
- APC, Paris
)

- J.Math.Phys. 46 (2005) 072502
•
e-Print:
- gr-qc/0505016
•
DOI:
- 10.1063/1.1960798

[5]

Birkhoff for Lovelock redux

Stanley Deser
(
- Brandeis U.
)
,
J. Franklin
(
- MIT, MKI
)

- Class.Quant.Grav. 22 (2005) L103-L106
•
e-Print:
- gr-qc/0506014
•
DOI:
- 10.1088/0264-9381/22/16/L03

[6]

The Einstein tensor and its generalizations

D. Lovelock
(
- Waterloo U.
)

- J.Math.Phys. 12 (1971) 498-501
•
DOI:
- 10.1063/1.1665613

[7]

Stacking a 4-D geometry into an Einstein-Gauss-Bonnet bulk

Carlos Barcelo
(
- Portsmouth U., ICG
)
,
Roy Maartens
(
- Portsmouth U., ICG
)
,
Carlos F. Sopuerta
(
- Portsmouth U., ICG
)
,
Fermin Viniegra
(
- Portsmouth U., ICG
)

- Phys.Rev.D 67 (2003) 064023
•
e-Print:
- hep-th/0211013
•
DOI:
- 10.1103/PhysRevD.67.064023

[8]

Obstructions on the horizon geometry from string theory corrections to Einstein gravity

Gustavo Dotti
(
- Cordoba U.
)
,
Reinaldo J. Gleiser
(
- Cordoba U.
)

- Phys.Lett.B 627 (2005) 174-179
•
e-Print:
- hep-th/0508118
•
DOI:
- 10.1016/j.physletb.2005.08.110

[9]

Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory

- Int.J.Mod.Phys.A 24 (2009) 1690-1694
•
e-Print:
- 0809.4378
•
DOI:
- 10.1142/S0217751X09045248

[10]

Einstein-Gauss-Bonnet metrics: Black holes, black strings and a staticity theorem

C. Bogdanos
(
- Orsay, LPT
)
,
C. Charmousis
(
- Orsay, LPT and
- Fed. Denis Poisson, Tours
)
,
B. Gouteraux
(
- Orsay, LPT
)
,
R. Zegers
(
- Durham U., Dept. of Math.
)

- JHEP 10 (2009) 037
•
e-Print:
- 0906.4953
•
DOI:
- 10.1088/1126-6708/2009/10/037

[11]

Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

Gustavo Dotti
(
- Cordoba U. and
- Buenos Aires, CONICET
)
,
Julio Oliva
(
- Chile Austral U., Valdivia
)
,
Ricardo Troncoso
(
- CECS, Valdivia
)

- Phys.Rev.D 82 (2010) 024002
•
e-Print:
- 1004.5287
•
DOI:
- 10.1103/PhysRevD.82.024002

[12]

Extensions of Birkhoff's theorem in 6D Gauss-Bonnet gravity

Charalampos Bogdanos
(
- Orsay, LPT
)

- AIP Conf.Proc. 1241 (2010) 1, 521-527
•
DOI:
- 10.1063/1.3462680

[13]

Gauss-Bonnet black holes with non-constant curvature horizons

Hideki Maeda
(
- CECS, Valdivia
)

- Phys.Rev.D 81 (2010) 124007
•
e-Print:
- 1004.0917
•
DOI:
- 10.1103/PhysRevD.81.124007

[14]

All the solutions of the form M2(warped)x\Sigma(d-2) for Lovelock gravity in vacuum in the Chern-Simons case

Julio Oliva
(
- Chile Austral U., Valdivia and
- Buenos Aires U.
)

- J.Math.Phys. 54 (2013) 042501
•
e-Print:
- 1210.4123
•
DOI:
- 10.1063/1.4795258

[15]

On static black holes solutions in Einstein and Einstein–Gauss–Bonnet gravity with topology $\mathbf{S^{n} \times S^{n}}$

Josep M. Pons
(
- Barcelona U., ECM and
- ICC, Barcelona U.
)
,
Naresh Dadhich
(
- Jamia Millia Islamia and
- IUCAA, Pune
)

- Eur.Phys.J.C 75 (2015) 6, 280
•
e-Print:
- 1408.6754
•
DOI:
- 10.1140/epjc/s10052-015-3481-y

[16]

Lovelock black holes with nonmaximally symmetric horizons

N. Farhangkhah
(
- Azad U., Marvdasht
)
,
M. H. Dehghani
(
- RIAAM, Maragha and
- Shiraz U.
)

- Phys.Rev.D 90 (2014) 4, 044014
•
e-Print:
- 1409.1410
•
DOI:
- 10.1103/PhysRevD.90.044014

[17]

Static pure Lovelock black hole solutions with horizon topology S $^{(n)}\times$ S $^{(n)}$

Naresh Dadhich
(
- Jamia Millia Islamia
)
,
Josep M. Pons
(
- Barcelona U., ECM and
- ICC, Barcelona U.
)

- JHEP 05 (2015) 067
•
e-Print:
- 1503.00974
•
DOI:
- 10.1007/JHEP05(2015)067

[18]

Symmetric Solutions to the Maximally {Gauss-Bonnet} Extended Einstein Equations

James T. Wheeler
(
- Chicago U. and
- Chicago U., EFI
)

- Nucl.Phys.B 273 (1986) 732-748
•
DOI:
- 10.1016/0550-3213(86)90388-3

[19]

Lectures on Functional Equations and Their Applications

J. Aczél

[20]

O. Sutô

- Tohoku Math.J. 6 (1914) 1