2009

Higher-dimensional numerical relativity: Formulation and code tests

Yoshino, Hirotaka, Shibata, Masaru

Understand

We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time.

First, the Baumgarte-Shapiro-Shibata-Nakamura formalism is extended for arbitrary spacetime dimensions $D \ge 4$, and then, the so-called cartoon method, which was originally proposed as a robust method for simulating axisymmetric 4D spacetimes, is described for 5D spacetimes of several types of symmetries.
Implementing 5D numerical relativity codes with the cartoon methods, we perform test simulations by evolving a 5D Schwarzschild spacetime and a 5D spacetime composed of a gravitational-wave packet of small amplitude.
The numerical simulations are stably performed for a sufficiently long time, as done in the 4D case, and the obtained numerical results agree well with the analytic solutions: The numerical solutions are shown to converge at the correct order.

Built on

L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields
1962
Earlier work this paper cites.
I. Novikov, Ph.D. thesis, Shternberg Astronomical Institute, Moscow, 1963
1963
Earlier work this paper cites.
P. C. Aichelburg and R. U. Sexl, Gen. Rel. Grav. 2
1971
Earlier work this paper cites.
C. Misner, K. Thorne, and J. Wheeler, Gravitation
1973
Earlier work this paper cites.
F. Estabrook, H. Wahlquist, S. Christensen, B. DeWitt, L. Smarr and E. Tsiang, Phys. Rev. D 7
1973
Earlier work this paper cites.
K. S. Thorne, Rev. Mod. Phys. 52
1980
Earlier work this paper cites.
R. Wald, General Relativity
1984
Earlier work this paper cites.
R. C. Myers and M. J. Perry, Annals Phys. 172
1986
Earlier work this paper cites.
M. Shibata and T. Nakamura, Phys. Rev. D 52
1995
Earlier work this paper cites.
N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 429
1998
Earlier work this paper cites.
T. W. Baumgarte and S. L. Shapiro, Phys. Rev. D 59
1998
Earlier work this paper cites.
L. Randall and R. Sundrum, Phys. Rev. Lett. 83
1999
Earlier work this paper cites.
M. Shibata, Prog. Theor. Phys. 104
2000
Earlier work this paper cites.
S. Dimopoulos and G. Landsberg, Phys. Rev. Lett. 87
2001
Earlier work this paper cites.
M. Alcubierre, S. Brandt, B. Brügmann, D. Holz, E. Seidel, R. Takahashi and J. Thornburg, Int. J. Mod. Phys. D 10
2001
Earlier work this paper cites.

Similar

S. B. Giddings and S. Thomas, Phys. Rev. D 65
2002
Cited alongside, same era.
D. M. Eardley and S. B. Giddings, Phys. Rev. D 66
2002
Cited alongside, same era.
R. Emparan, A. Fabbri and N. Kaloper, JHEP 0208
2002
Cited alongside, same era.
M. Choptuik, L. Lehner, I. I. Olabarrieta, R. Petryk, F. Pretorius and H. Villegas, Phys. Rev. D 68
2003
Cited alongside, same era.
H. Yoshino and Y. Nambu, Phys. Rev. D 67
2003
Cited alongside, same era.
R. Emparan and R. C. Myers, JHEP 0309
2003
Cited alongside, same era.
H. Kudoh, T. Tanaka and T. Nakamura, Phys. Rev. D 68
2003
Cited alongside, same era.
T. Tanaka, Prog. Theor. Phys. Suppl. 148
2003
Cited alongside, same era.
M. Shibata, Phys. Rev. D 67
2003
Cited alongside, same era.
M. Alcubierre, B. Brügmann, P. Diener, M. Koppitz, D. Pollney, E. Seidel and R. Takahashi, Phys. Rev. D 67
2003
Cited alongside, same era.
H. Kodama and A. Ishibashi, Prog. Theor. Phys. 110
Original
2003
Cited alongside, same era.
F. Pretorius, Phys. Rev. Lett. 95
2005
Cited alongside, same era.

Then

M. Campanelli, C. O. Lousto, P. Marronetti and Y. Zlochower, Phys. Rev. Lett. 96
2006
Later among the works it cites.
J. G. Baker, J. Centrella, D. I. Choi, M. Koppitz and J. van Meter, Phys. Rev. Lett. 96
2006
Later among the works it cites.
P. Diener et al
2006
Later among the works it cites.
M. Boyle, D. A. Brown, L. E. Kidder, A. H. Mroue, H. P. Pfeiffer, M. A. Scheel, G. B. Cook, and S. A. Teukolsky, Phys. Rev. D 76
Original
2007
Later among the works it cites.
M. Hannam, S. Husa, D. Pollney, B. Brügmann and N. Ó Murchadha, Phys. Rev. Lett. 99
2007
Later among the works it cites.
M. Hannam, S. Husa, B. Brügmann, J. A. González, U. Sperhake and N. Ó. Murchadha, J. Phys. Conf. Ser. 66
2007
Later among the works it cites.
T. W. Baumgarte and S. G. Naculich, Phys. Rev. D 75
2007
Later among the works it cites.
U. Sperhake, V. Cardoso, F. Pretorius, E. Berti and J. A. González, Phys. Rev. Lett. 101
Original
2008
Later among the works it cites.
M. Shibata, H. Okawa and T. Yamamoto, Phys. Rev. D 78
Original
2008
Later among the works it cites.
K. Murata and J. Soda, Prog. Theor. Phys. 120
Original
2008
Later among the works it cites.
B. Brügmann, J. A. González, M. Hannam, S. Husa, U. Sperhake and W. Tichy, Phys. Rev. D 77
2008
Later among the works it cites.
T. Yamamoto, M. Shibata and K. Taniguchi, Phys. Rev. D 78
Original
2008
Later among the works it cites.
P. Kanti, Lect. Notes Phys. 769
Original
2009
Closest in time.
H. Yoshino, JHEP 0901
Original
2009
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…