Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity

Hideki Asada

Banach Center Publications (1997)

  • Volume: 41, Issue: 2, page 85-93
  • ISSN: 0137-6934

Abstract

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The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful for numerical computations providing an initial data for the final merging phase of coalescing binary neutron stars which can be treated only by fully general relativistic simulations.

How to cite

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Asada, Hideki. "Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity." Banach Center Publications 41.2 (1997): 85-93. <http://eudml.org/doc/252235>.

@article{Asada1997,
abstract = {The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful for numerical computations providing an initial data for the final merging phase of coalescing binary neutron stars which can be treated only by fully general relativistic simulations.},
author = {Asada, Hideki},
journal = {Banach Center Publications},
keywords = {post-Newtonian hydrodynamic equations; quadrupole gravitational radiation; (3+1) formalism},
language = {eng},
number = {2},
pages = {85-93},
title = {Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity},
url = {http://eudml.org/doc/252235},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Asada, Hideki
TI - Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 2
SP - 85
EP - 93
AB - The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful for numerical computations providing an initial data for the final merging phase of coalescing binary neutron stars which can be treated only by fully general relativistic simulations.
LA - eng
KW - post-Newtonian hydrodynamic equations; quadrupole gravitational radiation; (3+1) formalism
UR - http://eudml.org/doc/252235
ER -

References

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  1. [1] A. Abramovici et al., Science, 256 (1992), 325; 
  2. K. S. Thorne, in proceedings of the eighth Nishinomiya-Yukawa memorial symposium on Relativistic Cosmology, edited by M. Sasaki (Universal Academy Press, Tokyo, 1994), pp.67. 
  3. [2] C. Bradaschia et al., Nucl. Instrum. Method Phys. Res. Sect. A289 (1990), 518. 
  4. [3] D. Lai, F. Rasio and S. L. Shapiro, Astrophys. J. 420 (1994), 811; Astrophys. J. supplement 88 (1993), 205. 
  5. [4] T. Nakamura, in the proceedings of the eighth Nishinomiya-Yukawa memorial symposium on Relativistic Cosmology (ref.1), pp. 155. 
  6. [5] S. Chandrasekhar and F. P. Esposito, Astrophys. J. 160 (1970), 153; see their series of papers cited therein. 
  7. [6] L. Blanchet, T. Damour and G. Schäfer, Mon. Not. R. Astr. Soc. 242 (1990), 289. 
  8. [7] K. Oohara and T. Nakamura, Prog. Theor. Phys. 83 (1990), 906; 86 (1991), 73; 88 (1992), 307; 
  9. M. Shibata, T. Nakamura and K. Oohara, Prog. Theor. Phys. 88 (1992), 1079; 89 (1993), 809. 
  10. [8] H. Asada, M. Shibata and T. Futamase, Prog. Theor. Phys. 96 (1996), 81. 
  11. [9] T. Ohta, H. Okamura, T. Kimura and K. Hiida, Prog. Thor. Phys. 51 (1974), 1598. 
  12. [10] J. R. Wilson and G. J. Mathews, Phys. Rev. Lett. 75 (1995), 4161. 

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