On the numerical integration of Einstein's field equations - INSPIRE

DataBETA

On the numerical integration of Einstein's field equations

Oct, 1998

7 pages

Published in:

Phys.Rev.D 59 (1998) 024007

Published: Dec 7, 1998

e-Print:

gr-qc/9810065 [gr-qc]

DOI:

10.1103/PhysRevD.59.024007

View in:

reference search1,186 citations

Citations per year

Abstract: (arXiv)

Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura, we modify these equations by factoring out the conformal factor and introducing three ``connection functions''. The evolution equations can then be reduced to wave equations for the conformal metric components, which are coupled to evolution equations for the connection functions. We evolve small amplitude gravitational waves and make a direct comparison of the numerical performance of the modified equations with the standard ADM equations. We find that the modified form exhibits much improved stability.

Einstein equation: solution
boundary condition
numerical calculations

References(23)

Figures(0)

Correlation between energy spectral states and fast time variability and further evidence for the marginally stable orbit in 4u 1820-30

- Astrophys.J.Lett. 500 (1998) L171
•
e-Print:
- astro-ph/9804228
•
DOI:
- 10.1086/311418

Instabilities in Close Neutron Star Binaries

J.R. Wilson
(
- LLNL, Livermore
)
,
G.J. Mathews
(
- LLNL, Livermore
)

- Phys.Rev.Lett. 75 (1995) 4161-4164
•
DOI:
- 10.1103/PhysRevLett.75.4161

Relativistic numerical model for close neutron star binaries

- Phys.Rev.D 54 (1996) 1317-1331
•
e-Print:
- gr-qc/9601017
•
DOI:
- 10.1103/PhysRevD.54.1317

On the Newtonian limit of general relativity

Simonetta Frittelli
(
- Cordoba U.
)
,
Oscar Reula
(
- Cordoba U.
)

- Commun.Math.Phys. 166 (1994) 221
•
e-Print:
- gr-qc/9506077
•
DOI:
- 10.1007/BF02112314

A New formalism for numerical relativity

Carles Bona
(
- Balearic Islands U.
)
,
Joan Masso
(
- Balearic Islands U. and
- NCSA, Urbana
)
,
Edward Seidel
(
- NCSA, Urbana and
- Illinois U., Urbana
)
,
Joan Stela
(
- Balearic Islands U.
)

- Phys.Rev.Lett. 75 (1995) 600-603
•
e-Print:
- gr-qc/9412071
•
DOI:
- 10.1103/PhysRevLett.75.600

Einstein and Yang-Mills theories in hyperbolic form without gauge fixing

Andrew Abrahams
(
- North Carolina U.
)
,
Arlen Anderson
(
- North Carolina U.
)
,
Yvonne Choquet-Bruhat
(
- North Carolina U.
)
,
James W. York, Jr.
(
- North Carolina U.
)

- Phys.Rev.Lett. 75 (1995) 3377-3381
•
e-Print:
- gr-qc/9506072
•
DOI:
- 10.1103/PhysRevLett.75.3377

Nonlinear wave equations for relativity

- Phys.Rev.D 53 (1996) 3056-3063
•
e-Print:
- gr-qc/9505023
•
DOI:
- 10.1103/PhysRevD.53.3056

Hyperbolic reductions for Einstein's equations

H. Friedrich
(
- Potsdam, Max Planck Inst.
)

- Class.Quant.Grav. 13 (1996) 1451-1469
•
DOI:
- 10.1088/0264-9381/13/6/014

Evolution of three-dimensional gravitational waves: Harmonic slicing case

Masaru Shibata
(
- Osaka U.
)
,
Takashi Nakamura
(
- Kyoto U., FIHS
)

- Phys.Rev.D 52 (1995) 5428-5444
•
DOI:
- 10.1103/PhysRevD.52.5428

- J.Math.Pure.Appl. 23 37

Gravitational degrees of freedom and the initial-value problem

James W. York, Jr.
(
- Princeton U.
)

- Phys.Rev.Lett. 26 (1971) 1656-1658
•
DOI:
- 10.1103/PhysRevLett.26.1656

Gravitational wave extraction and outer boundary conditions by perturbative matching

Binary Black Hole Grand Challenge Alliance

Collaboration

•

A.M. Abrahams
(
- Illinois U., Urbana and
- J.P. Morgan, N.Y. and
- North Carolina U.
)

et al.

- Phys.Rev.Lett. 80 (1998) 1812-1815
•
e-Print:
- gr-qc/9709082
•
DOI:
- 10.1103/PhysRevLett.80.1812

Boosted three-dimensional black hole evolutions with singularity excision

Binary Black Hole Challenge Alliance

Collaboration

•

G.B. Cook
(
- Cornell U., LNS
)

et al.

- Phys.Rev.Lett. 80 (1998) 2512-2516
•
e-Print:
- gr-qc/9711078
•
DOI:
- 10.1103/PhysRevLett.80.2512

- Phys.Rept. 96 205

Reading Off Gravitational Radiation Wave Forms in Numerical Relativity Calculations: Matching to Linearized Gravity

A.M. Abrahams
(
- Illinois U., Urbana
)
,
C.R. Evans
(
- Caltech
)

- Phys.Rev.D 37 (1988) 318-332
•
DOI:
- 10.1103/PhysRevD.37.318

Solving Einstein's equations for rotating space-times: Evolution of relativistic star clusters

- Phys.Rev.D 49 (1994) 5153-5164
•
DOI:
- 10.1103/PhysRevD.49.5153

- Phys.Z. 23 537

- Commun.Math.Phys. 28 1

Radiation gauge in general relativity

Larry Smarr
(
- Harvard U.
)
,
James W. York, Jr.
(
- North Carolina U.
)

- Phys.Rev.D 17 (1978) 8, 1945-1956
•
DOI:
- 10.1103/PhysRevD.17.1945

LINEARIZED QUADRUPOLE WAVES IN GENERAL RELATIVITY AND THE MOTION OF TEST PARTICLES

S.A. Teukolsky
(
- Cornell U., LNS and
- Harvard-Smithsonian Ctr. Astrophys.
)

- Phys.Rev.D 26 (1982) 745-750,
- Phys. Rev. D26 ( 1982) 745-750
•
DOI:
- 10.1103/PhysRevD.26.745

Cauchy perturbative matching and outer boundary conditions. 1. Methods and tests

M.E. Rupright
(
- North Carolina U.
)
,
A.M. Abrahams
(
- Illinois U., Urbana and
- NCSA, Urbana and
- JP Morgan, Zurich
)
,
L. Rezzolla
(
- Illinois U., Urbana and
- NCSA, Urbana
)

- Phys.Rev.D 58 (1998) 044005
•
e-Print:
- gr-qc/9802011
•
DOI:
- 10.1103/PhysRevD.58.044005

- Phys.Rev.Lett. 76 4303

A Method for calculating the structure of (singular) space-times in the large

Peter Hubner
(
- Garching, Max Planck Inst.
)

- Phys.Rev.D 53 (1996) 701-721
•
e-Print:
- gr-qc/9409029
•
DOI:
- 10.1103/PhysRevD.53.701