Higher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the Brans–Dicke theory are presented. We show that for a negative cosmological constant and for specific values of the parameters, a particular subclass of these solutions includes higher dimensional topological black hole-type solutions with a flat horizon topology. We briefly extend our discussion to stationary vacuum and -vacuum solutions.
REFERENCES
1.
O.
Klein
, Z. Phys.
37
, 895
(1926
).2.
M. B.
Green
, J. H.
Schwarz
, and E.
Witten
, Superstring Theory
(Cambridge University Press
, London
, 1987
).3.
C. H.
Brans
and R. H.
Dicke
, Phys. Rev.
124
, 925
(1961
).4.
V.
Faraoni
, Cosmology in Scalar Tensor Gravity
(Kluwer Academic
, Dordrecht
, 2004
).5.
C. H.
Brans
, e-print arXiv:gr-qc/9705069;e-print arXiv:gr-qc/0506063.
6.
B.
Bertotti
, L.
Iess
, and P.
Tortora
, Nature (London)
425
, 374
(2003
).7.
T. P.
Sotiriou
and V.
Faraoni
, Rev. Mod. Phys.
82
, 451
(2010
);e-print arXiv:0805.1726.
8.
H.
Stephani
, D.
Kramer
, M.
MacCallum
, and C.
Hoenselaers
, Exact Solutions of Einstein’s Field Equations
, 2nd ed. (Cambridge University Press
, Cambridge
, 2003
).9.
10.
A. Z.
Wang
, M. F. A.
da Silva
, and N. O.
Santos
, Class. Quantum Grav.
14
, 2417
(1997
).11.
A.
Vilenkin
, Phys. Rev. D
23
, 852
(1981
).12.
A.
Vilenkin
and E. P. S.
Shellard
, Cosmic Strings and Other Topological Defects
(Cambridge University Press
, Cambridge
, 1994
).13.
M. B.
Hindmarsh
and T. W. B.
Kibble
, Rep. Prog. Phys.
58
, 477
(1995
).14.
F.
Dahia
and C.
Romero
, Phys. Rev. D
60
, 104019
(1999
).15.
A.
Arazi
and C.
Simeone
, Gen. Relativ. Gravit.
32
, 2259
(2000
).16.
J.
Ponce de Leon
, Mod. Phys. Lett. A
24
, 1659
(2009
).17.
B.
Linet
, J. Math. Phys.
27
, 1817
(1986
).18.
Q.
Tian
, Phys. Rev. D
33
, 3549
(1986
).19.
M. F. A.
da Silva
, A.
Wang
, F. M.
Paiva
, and N. O.
Santos
, Phys. Rev. D
61
, 044003
(2000
).20.
J. P. S.
Lemos
, Phys. Lett. B
353
, 46
(1995
);e-print arXiv:gr-qc/9404041.
21.
R. -G.
Cai
and Y. -Z.
Zhang
, Phys. Rev. D
54
, 4891
(1996
).22.
D.
Birmingham
, Class. Quantum Grav.
16
, 1197
(1999
).23.
M.
Žofka
and J.
Bičák
, Class. Quantum Grav.
25
, 015011
(2008
).24.
O.
Delice
, Phys. Rev. D
74
, 067703
(2006
).25.
O.
Delice
, Phys. Rev. D
74
, 124001
(2006
).26.
O.
Sarıoğlu
and B.
Tekin
, Class. Quantum Grav.
26
, 048001
(2009
).27.
O.
Sarıoğlu
and B.
Tekin
, Phys. Rev. D
79
, 087502
(2009
).28.
D.
Lorenz-Petzold
, Phys. Rev. D
29
, 2399
(1984
).29.
M.
Arık
and O.
Delice
, Int. J. Mod. Phys. D
12
, 1095
(2003
).30.
M. H.
Dehghani
and N.
Farhangkhah
, Phys. Rev. D
71
, 044008
(2005
).31.
R. -G.
Cai
, J. -Y.
Ji
, and K. -S.
Soh
, Phys. Rev. D
57
, 6547
(1998
).32.
A. M.
Awad
, Class. Quantum Grav.
20
, 2827
(2003
).33.
G. T.
Horowitz
and R. C.
Myers
, Phys. Rev. D
59
, 026005
(1998
).34.
T.
Lewis
, Proc. R. Soc. London, Ser. A
136
, 176
(1932
).35.
A.
Krasinski
, Class. Quantum Grav.
11
, 1373
(1994
).36.
N. O.
Santos
, Class. Quantum Grav.
10
, 2401
(1993
).37.
J.
Stachel
, Phys. Rev. D
26
, 1281
(1982
);J.
Stachel
, J. Math. Phys.
25
, 338
(1984
);M. A. H.
MacCallum
and N. O.
Santos
, Class. Quantum Grav.
15
, 1627
(1998
);M. A. H.
MacCallum
, Gen. Relativ. Gravit.
30
, 131
(1998
).© 2010 American Institute of Physics.
2010
American Institute of Physics
You do not currently have access to this content.