We present a method for generating exact interior solutions of Einstein’s equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well as the density and pressure of the seed solution. In the limiting vacuum case, it reduces to the Zipoy-Voorhees transformation that can be used to generate metrics with multipole moments. All the metric functions of the new solution can be calculated explicitly from the seed solution in a simple manner. The physical properties of the resulting new solutions are shown to be completely different from those of the seed solution.
REFERENCES
1.
R. P.
Kerr
, Phys. Rev. Lett.
11
, 237
(1963
).2.
H.
Stephani
, D.
Kramer
, M. A. H.
MacCallum
, C.
Hoenselaers
, and E.
Herlt
, Exact Solutions of Einstein’s Field Equations
(Cambridge University Press
, Cambridge, UK
, 2003
).3.
K.
Lake
, Phys. Rev. D
67
, 104015
(2003
).4.
S.
Rahman
and M.
Visser
, Classical Quantum Gravity
19
, 935
(2002
).5.
L.
Herrera
, J.
Ospino
, and A.
Di Prisco
, Phys. Rev. D
77
, 027502
(2008
).6.
I.
Semiz
, Rev. Math. Phys.
23
, 865
(2011
).7.
8.
D. M.
Zipoy
, J. Math. Phys.
7
, 1137
(1966
).9.
B.
Voorhees
, Phys. Rev. D
2
, 2119
(1970
).10.
11.
D.
Papadopoulos
, B.
Stewart
, and L.
Witten
, Phys. Rev. D
24
, 320
(1981
).12.
L.
Herrera
and J. L.
Hernandez-Pastora
, J. Math. Phys.
41
, 7544
(2000
).13.
L.
Herrera
, G.
Magli
, and D.
Malafarina
, Gen. Relativ. Gravitation
37
, 1371
(2005
).14.
N.
Dadhich
and G.
Date
“On a Peculiar Family of Static, Axisymmetric, Vacuum Solutions of the Einstein Equations,
” (2000); e-print arXiv:gr-qc/0012093.15.
H.
Kodama
and W.
Hikida
, Classical Quantum Gravity
20
, 5121
(2003
).16.
17.
H.
Quevedo
, Int. J. Mod. Phys.
20
, 1779
(2011
).18.
H. D.
Wahlquist
, Phys. Rev.
172
, 1291
(1968
).19.
P. C.
Vaidya
, Pramana
8
, 512
(1977
).20.
D.
Kramer
, Classical Quantum Gravity
1
, L3
(1984
).21.
J. M. M.
Senovilla
, Classical Quantum Gravity
4
, L115
(1987
).22.
M.
Mars
and J. M. M.
Senovilla
, Phys. Rev. D
54
, 6166
(1996
).23.
L.
Herrera
and J.
Jiménez
, J. Math. Phys.
23
, 2339
(1982
).24.
S.
Drake
and R.
Turolla
, Classical Quantum Gravity
14
, 1883
(1997
).25.
N.
Ibohal
, Gen. Relativ. Gravitation
37
, 19
(2005
).26.
T.
Papakostas
, J. Phys.: Conf. Ser.
8
, 22
(2005
).27.
T.
Papakostas
, J. Phys.: Conf. Ser.
189
, 012027
(2009
).28.
S.
Viaggiu
, Int. J. Mod. Phys. D
15
, 1441
(2006
).29.
S.
Viaggiu
, Int. J. Mod. Phys. D
19
, 1783
(2010
).30.
K.
Rosquist
, Classical Quantum Gravity
16
, 1755
(1999
).31.
C.
Lozanovski
and L.
Wylleman
, Classical Quantum Gravity
28
, 075015
(2011
).32.
R.
Ferraro
, Gen. Relativ. Gravitation
46
, 1705
(2014
).33.
G.
Lessner
, Gen. Relativ. Gravitation
40
, 2177
(2008
).34.
L.
Modesto
and P.
Nicolini
, Phys. Rev. D
82
, 104035
(2010
).35.
Y.
Miao
, Z.
Xue
, and S.
Zhang
, Int. J. Mod. Phys. D
21
, 1250017
(2012
).36.
F.
Caravelli
and L.
Modesto
, Classical Quantum Gravity
27
, 245022
(2010
).37.
M.
Azrag-Ainou
, Eur. Phys. J. C
74
, 2865
(2014
).38.
M.
Azrag-Ainou
, Phys. Rev. D
90
, 064041
(2014
).39.
A.
Larranaga
, A.
Cardenas-Avendano
, and D.
Torres
, Phys. Lett. B
743
, 492
(2015
).40.
H.
Erbin
, Gen. Relativ. Gravitation
47
, 19
(2015
).41.
L.
Herrera
, A.
Di Prisco
, J.
Ibáñez
, and J.
Ospino
, Phys. Rev. D
87
, 024014
(2013
).42.
S.
Toktarbay
and H.
Quevedo
, Gravitation Cosmol.
20
, 252
(2014
).43.
M.
Masood-ul-Alama
, Gen. Relativ. Gravitation
39
, 55
(2007
).© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
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