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Numerical relativity simulations in the era of the Einstein Telescope

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Abstract

Numerical-relativity (NR) simulations of compact binaries are expected to be an invaluable tool in gravitational-wave astronomy. The sensitivity of future detectors such as the Einstein Telescope (ET) will place much higher demands on NR simulations than first- and second-generation ground-based detectors. We discuss the issues facing compact-object simulations over the next decade, with an emphasis on estimating where the accuracy and parameter space coverage will be sufficient for ET and where significant work is needed.

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References

  1. Abbott B. et al.: Rept. Prog. Phys. 72, 076901 (2009)

    Article  ADS  Google Scholar 

  2. Acernese F. et al.: Class. Quantum Grav. 23, S635 (2006)

    Article  MATH  ADS  Google Scholar 

  3. Hild S.: (for the LIGO Scientific Collaboration): Class. Quantum Grav. 23, S643 (2006)

    Article  MATH  Google Scholar 

  4. Sathyaprakash B.S., Schutz B.F.: Living Rev. Relativ. 12, 2 (2009)

    ADS  Google Scholar 

  5. Pretorius F.: Phys. Rev. Lett. 95, 121101 (2005). doi:10.1103/PhysRevLett.95.121101

    Article  MathSciNet  ADS  Google Scholar 

  6. Campanelli M., Lousto C.O., Marronetti P., Zlochower Y.: Phys. Rev. Lett. 96, 111101 (2006)

    Article  ADS  Google Scholar 

  7. Baker J.G., Centrella J., Choi D.I., Koppitz M., Meter J.: Phys. Rev. Lett. 96, 111102 (2006)

    Article  ADS  Google Scholar 

  8. Hannam M.: Class. Quantum Grav. 26, 114001 (2009). doi:10.1088/0264-9381/26/11/114001

    Article  MathSciNet  ADS  Google Scholar 

  9. Shibata M., Uryu K.: Phys. Rev. D61, 064001 (2000). doi:10.1103/PhysRevD.61.064001

    ADS  Google Scholar 

  10. Faber, J.: Class. Quantum Grav. 26(11), 114004 (2009) (18 pp). http://stacks.iop.org/0264-9381/26/114004

  11. Pfeiffer H.P. et al.: Class. Quantum Grav. 24, S59 (2007). doi:10.1088/0264-9381/24/12/S06

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Husa S., Hannam M., Gonzalez J.A., Sperhake U., Brügmann B.: Phys. Rev. D77, 044037 (2008). doi:10.1103/PhysRevD.77.044037

    ADS  Google Scholar 

  13. Campanelli M., Lousto C.O., Nakano H., Zlochower Y.: Phys. Rev. D79, 084010 (2009)

    ADS  Google Scholar 

  14. Alcubierre M.: Introduction to 3 + 1 Numerical Relativity. Oxford University Press, USA (2008)

    Book  MATH  Google Scholar 

  15. Cook G.B.: Living Rev. Relativ. 3, 5 (2000)

    ADS  Google Scholar 

  16. Pretorius, F.: In: Colpi, M., Casella, P., Gorini, V., Moschella, U., Possenti, A. (eds.) Physics of Relativistic Objects in Compact Binaries: from Birth to Coalescence, vol. 359, pp. 269–305. Springer-Verlag, New York (2009). arXiv:0710.1338

  17. Husa S.: Eur. Phys. J. ST 152, 183 (2007)

    Google Scholar 

  18. Palenzuela, C., Anderson, M., Lehner, L., Liebling, S.L., Neilsen, D.: (2009). arXiv:0905.1121

  19. van Meter J.R. et al.: ApJL 711, 89 (2010)

    Article  ADS  Google Scholar 

  20. Lindblom L., Owen B.J., Brown D.A.: Phys. Rev. D78, 124020 (2008). doi:10.1103/PhysRevD.78.124020

    ADS  Google Scholar 

  21. Hannam M. et al.: Phys. Rev. D79, 084025 (2009)

    ADS  Google Scholar 

  22. Reisswig, C., Bishop, N.T., Pollney, D., Szilagyi, B.: (2009). arXiv:0907.2637

  23. Scheel M.A. et al.: Phys. Rev. D79, 024003 (2009). doi:10.1103/PhysRevD.79.024003

    MathSciNet  ADS  Google Scholar 

  24. Sintes, A.M., Vecchio, A.: (1999). gr-qc/0005058

  25. Van Den Broeck C., Sengupta A.S.: Class. Quantum Grav. 24, 1089 (2007). doi:10.1088/0264-9381/24/5/005

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Babak, S., Hannam, M., Husa, S., Schutz, B.: (2008). arXiv:0806.1591

  27. Thorpe J.I. et al.: CQG 26, 094026 (2009)

    Article  ADS  Google Scholar 

  28. Boyle M. et al.: Phys. Rev. D78, 104020 (2008). doi:10.1103/PhysRevD.78.104020

    ADS  Google Scholar 

  29. Pollney, D.: Talk given at NRDA2009, AEI-Potsdam, 6–9 July 2009

  30. Buonanno A., Damour T.: Phys. Rev. D 59, 084006 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  31. Buonanno A., Damour T.: Phys. Rev. D 62, 064015 (2000)

    Article  ADS  Google Scholar 

  32. Damour T., Jaranowski P., Schäfer G.: Phys. Rev. D 62, 084011 (2000)

    Article  ADS  Google Scholar 

  33. Damour T.: Phys. Rev. D 64, 124013 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  34. Buonanno A., Chen Y., Damour T.: Phys. Rev. D 74, 104005 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  35. Buonanno A. et al.: Phys. Rev. D 76, 104049 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  36. Damour T., Nagar A.: Phys. Rev. D77, 024043 (2008). doi:10.1103/PhysRevD.77.024043

    ADS  Google Scholar 

  37. Damour T., Nagar A., Dorband E.N., Pollney D., Rezzolla L.: Phys. Rev. D77, 084017 (2008). doi:10.1103/PhysRevD.77.084017

    ADS  Google Scholar 

  38. Damour T., Nagar A., Hannam M., Husa S., Brügmann B.: Phys. Rev. D 78, 044039 (2008). doi:10.1103/PhysRevD.78.044039

    Article  ADS  Google Scholar 

  39. Baker J.G. et al.: Phys. Rev. D78, 044046 (2008). doi:10.1103/PhysRevD.78.044046

    ADS  Google Scholar 

  40. Mroue A.H., Kidder L.E., Teukolsky S.A.: Phys. Rev. D78, 044004 (2008). doi:10.1103/PhysRevD.78.044004

    ADS  Google Scholar 

  41. Damour T., Nagar A.: PRD 79, 081503 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  42. Buonanno A. et al.: PRD 79, 124028 (2009)

    Article  ADS  Google Scholar 

  43. Pan Y. et al.: PRD 81, 084041 (2009)

    Article  ADS  Google Scholar 

  44. Buonanno A., Cook G.B., Pretorius F.: Phys. Rev. D75, 124018 (2007). doi:10.1103/PhysRevD.75.124018

    MathSciNet  ADS  Google Scholar 

  45. Ajith P. et al.: Class. Quantum Grav. 24, S689 (2007). doi:10.1088/0264-9381/24/19/S31

    Article  MATH  MathSciNet  ADS  Google Scholar 

  46. Ajith P. et al.: Phys. Rev. D77, 104017 (2008). doi:10.1103/PhysRevD.77.104017

    MathSciNet  ADS  Google Scholar 

  47. Ajith P.: Class. Quantum Grav. 25, 114033 (2008). doi:10.1088/0264-9381/25/11/114033

    Article  ADS  Google Scholar 

  48. Ajith, P., et al.: (2009). arXiv:0909.2867

  49. Shibata M., Kyutoku K., Yamamoto T., Taniguchi K.: Phys. Rev. D 79, 044030 (2009). doi:10.1103/PhysRevD.79.044030

    Article  Google Scholar 

  50. Baker J.G., van Meter J.R., McWilliams S.T., Centrella J., Kelly B.J.: Phys. Rev. Lett. 99, 181101 (2007). doi:10.1103/PhysRevLett.99.181101

    Article  ADS  Google Scholar 

  51. Hannam M., Husa S., Sperhake U., Brügmann B., Gonzalez J.A.: Phys. Rev. D77, 044020 (2008). doi:10.1103/PhysRevD.77.044020

    ADS  Google Scholar 

  52. Gopakumar A., Hannam M., Husa S., Bruegmann B.: Phys. Rev. D 78, 064026 (2008). doi:10.1103/PhysRevD.78.064026

    Article  ADS  Google Scholar 

  53. Boyle M. et al.: Phys. Rev. D76, 124038 (2007). doi:10.1103/PhysRevD.76.124038

    MathSciNet  ADS  Google Scholar 

  54. Hannam M., Husa S., Bruegmann B., Gopakumar A.: Phys. Rev. D 78, 104007 (2008). doi:10.1103/PhysRevD.78.104007

    Article  ADS  Google Scholar 

  55. Hinder, I., Herrmann, F., Laguna, P., Shoemaker, D.: (2008)

  56. Hannam, M., et al.: (2009) (in preparation)

  57. Buonanno, A., Iyer, B., Ochsner, E., Pan, Y., Sathyaprakash, B.S.: (2009)

  58. Ajith, P., et al.: (2009) (in preparation)

  59. Boyle L., Kesden M., Nissanke S.: Phys. Rev. Lett. 100, 151101 (2008). doi:10.1103/PhysRevLett.100.151101

    Article  MathSciNet  ADS  Google Scholar 

  60. Boyle L., Kesden M.: Phys. Rev. D78, 024017 (2008). doi:10.1103/PhysRevD.78.024017

    ADS  Google Scholar 

  61. Dain S., Lousto C.O., Zlochower Y.: Phys. Rev. D78, 024039 (2008). doi:10.1103/PhysRevD.78.024039

    ADS  Google Scholar 

  62. Volonteri M., Madau P., Quataert E., Rees M.J.: Astrophys. J. 620, 69 (2005). doi:10.1086/426858

    Article  ADS  Google Scholar 

  63. Gammie C.F., Shapiro S.L., McKinney J.C.: Astrophys. J. 602, 312 (2004)

    Article  ADS  Google Scholar 

  64. Shapiro S.L.: Astrophys. J. 620, 59 (2005)

    Article  ADS  Google Scholar 

  65. Lovelace G., Owen R., Pfeiffer H.P., Chu T.: Phys. Rev. D78, 084017 (2008). doi:10.1103/PhysRevD.78.084017

    ADS  Google Scholar 

  66. Lovelace G.: Class. Quantum Grav. 26, 114002 (2009). doi:10.1088/0264-9381/26/11/114002

    Article  MathSciNet  ADS  Google Scholar 

  67. Hannam M., Husa S., Brügmann B., Gonzalez J.A., Sperhake U.: Class. Quantum Grav. 24, S15 (2007)

    Article  MATH  ADS  Google Scholar 

  68. Gonzalez J.A., Sperhake U., Brugmann B.: Phys. Rev. D79, 124006 (2009). doi:10.1103/PhysRevD.79.124006

    ADS  Google Scholar 

  69. Husa S., Gonzalez J.A., Hannam M., Brügmann B., Sperhake U.: Class. Quantum Grav. 25, 105006 (2008). doi:10.1088/0264-9381/25/10/105006

    Article  ADS  Google Scholar 

  70. Lousto C.O., Zlochower Y.: Phys. Rev. D77, 024034 (2008). doi:10.1103/PhysRevD.77.024034

    MathSciNet  ADS  Google Scholar 

  71. Pazos, E., Tiglio, M., Duez, M.D., Kidder, L.E., Teukolsky, S.A.: (2009). arXiv:0904.0493

  72. Winicour, J.: Living Rev. Relativ. 12(3) (2009). http://www.livingreviews.org/lrr-2009-3

  73. Pretorius F.: Class. Quantum Grav. 22, 425 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  74. Pretorius F.: Class. Quantum Grav. 23, S529 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  75. Lindblom L., Scheel M.A., Kidder L.E., Owen R., Rinne O.: Class. Quantum Grav. 23, S447 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  76. Lau, S.R., Pfeiffer, H.P., Hesthaven, J.S.: Comput Commun Phys 6, 1063 (2009)

    Google Scholar 

  77. Brown J.D.: Phys. Rev. D 73, 024001 (2006). doi:10.1103/PhysRevD.73.024001

    Article  ADS  Google Scholar 

  78. Richter R., Lubich C.: Class. Quantum Grav. 25, 225018 (2008). doi:10.1088/0264-9381/25/22/225018

    Article  MathSciNet  ADS  Google Scholar 

  79. Richter R.: Class. Quantum Grav. 26, 145017 (2009). doi:10.1088/0264-9381/26/14/145017

    Article  ADS  Google Scholar 

  80. Frauendiener J.: J Phys A 41, 382005 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  81. Ohme F., Hannam M., Husa S., Murchadha N.O.: CQG 26, 175014 (2009)

    Article  ADS  Google Scholar 

  82. Buchman L.T., Pfeiffer H.P., Bardeen J.M.: PRD 80, 084024 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  83. Zenginoglu A., Nunez D., Husa S.: Class. Quantum Grav. 26, 035009 (2009). doi:10.1088/0264-9381/26/3/035009

    Article  MathSciNet  ADS  Google Scholar 

  84. Zenginoglu A., Tiglio M.: Phys. Rev. D80, 024044 (2009). doi:10.1103/PhysRevD.80.024044

    MathSciNet  ADS  Google Scholar 

  85. Moncrief V., Rinne O.: Class. Quantum Grav. 26, 125010 (2009). doi:10.1088/0264-9381/26/12/125010

    Article  MathSciNet  ADS  Google Scholar 

  86. Rinne O.: Class. Quantum Grav. 27, 035014 (2010). doi:10.1088/0264-9381/27/3/035014

    Article  MathSciNet  ADS  Google Scholar 

  87. Hannam M., Husa S., Pollney D., Bruegmann B., O’Murchadha N.: Phys. Rev. Lett. 99, 241102 (2007). doi:10.1103/PhysRevLett.99.241102

    Article  MathSciNet  ADS  Google Scholar 

  88. Hannam M., Husa S., Ohme F., Bruegmann B., O’Murchadha N.: Phys. Rev. D78, 064020 (2008). doi:10.1103/PhysRevD.78.064020

    ADS  Google Scholar 

  89. Hannam M., Husa S., Murchadha N.O.: PRD 80, 124007 (2009)

    Article  ADS  Google Scholar 

  90. Detweiler, S.: Talk given at 7th Lisa Symposium, Barcelona, 16–20 June 2008

  91. Ott C.D.: Class. Quantum Grav. 26, 063001 (2009). doi:10.1088/0264-9381/26/6/063001

    Article  ADS  Google Scholar 

  92. Oechslin R., Janka H.T.: Phys. Rev. Lett. 99, 121102 (2007). doi:10.1103/PhysRevLett.99.121102

    Article  ADS  Google Scholar 

  93. Barnes A.P., Lefloch P.G., Schmidt B.G., Stewart J.M.: Class. Quantum Grav. 21, 5043 (2004). doi:10.1088/0264-9381/21/22/003

    Article  MATH  MathSciNet  ADS  Google Scholar 

  94. Banyuls F., Font J.A., Ibáñez J.M., Martí J.M., Miralles J.A.: Astrophys. J. 476, 221 (1997)

    Article  ADS  Google Scholar 

  95. Kiuchi K., Sekiguchi Y., Shibata M., Taniguchi K.: PRD 80, 064037 (2009)

    Article  ADS  Google Scholar 

  96. Baiotti L., Giacomazzo B., Rezzolla L.: Phys. Rev. D78, 084033 (2008). doi:10.1103/PhysRevD.78.084033

    ADS  Google Scholar 

  97. Read J.S., Lackey B.D., Owen B.J., Friedman J.L.: Phys. Rev. D79, 124032 (2009). doi:10.1103/PhysRevD.79.124032

    ADS  Google Scholar 

  98. Read J.S. et al.: Phys. Rev. D79, 124033 (2009). doi:10.1103/PhysRevD.79.124033

    ADS  Google Scholar 

  99. Font, J.A.: Living Rev. Relativ. 11(7) (2008). http://www.livingreviews.org/lrr-2008-7

  100. Martí, J.M., Müller, E.: Living Rev. Relativ. 6(7) (2003). http://www.livingreviews.org/lrr-2003-7

  101. Godunov S.K.: Mat. Sb. 47, 271 (1959)

    MathSciNet  Google Scholar 

  102. Dimmelmeier H., Novak J., Font J.A., Ibanez J.M., Muller E.: Phys. Rev. D71, 064023 (2005). doi:10.1103/PhysRevD.71.064023

    ADS  Google Scholar 

  103. Duez M.D. et al.: Phys. Rev. D78, 104015 (2008). doi:10.1103/PhysRevD.78.104015

    ADS  Google Scholar 

  104. Zink B., Schnetter E., Tiglio M.: Phys. Rev. D77, 103015 (2008). doi:10.1103/PhysRevD.77.103015

    ADS  Google Scholar 

  105. Baiotti L., Hawke I., Rezzolla L., Schnetter E.: Phys. Rev. Lett. 94, 131101 (2005). doi:10.1103/PhysRevLett.94.131101

    Article  ADS  Google Scholar 

  106. Yamamoto T., Shibata M., Taniguchi K.: Phys. Rev. D78, 064054 (2008). doi:10.1103/PhysRevD.78.064054

    ADS  Google Scholar 

  107. Anderson M. et al.: Phys. Rev. Lett. 100, 191101 (2008). doi:10.1103/PhysRevLett.100.191101

    Article  ADS  Google Scholar 

  108. Baiotti L., Giacomazzo B., Rezzolla L.: Class. Quantum Grav. 26, 114005 (2009). doi:10.1088/0264-9381/26/11/114005

    Article  MathSciNet  ADS  Google Scholar 

  109. Baker J.G., Centrella J., Choi D.I., Koppitz M., van Meter J.: Phys. Rev. D73, 104002 (2006). doi:10.1103/PhysRevD.73.104002

    ADS  Google Scholar 

  110. Tchekhovskoy A., McKinney J.C., Narayan R.: Mon. Not. R. Astron. Soc. 379, 469 (2007). doi:10.1111/j.1365-2966.2007.11876.x

    Article  ADS  Google Scholar 

  111. Palenzuela C., Lehner L., Reula O., Rezzolla L.: MNRAS 394, 1727 (2009)

    Article  ADS  Google Scholar 

  112. Dumbser M., Zanotti O.: JCP 228, 6991 (2009)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  113. Neilsen D., Hirschmann E.W., Millward R.S.: Class. Quantum Grav. 23, S505 (2006). doi:10.1088/0264-9381/23/16/S12

    Article  MATH  MathSciNet  ADS  Google Scholar 

  114. Anderson M., Hirschmann E., Liebling S.L., Neilsen D.: Class. Quantum Grav. 23, 6503 (2006). doi:10.1088/0264-9381/23/22/025

    Article  MATH  MathSciNet  ADS  Google Scholar 

  115. Oechslin R., Rosswog S., Thielemann F.: Phys. Rev. D65, 103005 (2002)

    ADS  Google Scholar 

  116. Price D.J., Rosswog S.: Science 312(5774), 719 (2006). doi:10.1126/science.1125201

    Article  ADS  Google Scholar 

  117. Rosswog, S.: (2009). arXiv:0907.4890

  118. Bonazzola S., Villain L., Bejger M.: Class. Quantum Grav. 24, S221 (2007). doi:10.1088/0264-9381/24/12/S15

    Article  MATH  MathSciNet  ADS  Google Scholar 

  119. Costa B., Don W.S.: J. Comput. Appl. Math. 204(2), 209 (2007). doi:10.1016/j.cam.2006.01.039

    Article  MATH  MathSciNet  ADS  Google Scholar 

  120. Costa B., Don W.S.: J. Comput. Phys. 224(2), 970 (2007). doi:10.1016/j.jcp.2006.11.002

    Article  MATH  MathSciNet  ADS  Google Scholar 

  121. Kastaun W.: Phys. Rev. D74, 124024 (2006). doi:10.1103/PhysRevD.74.124024

    MathSciNet  ADS  Google Scholar 

  122. Duez M.D., Marronetti P., Shapiro S.L., Baumgarte T.W.: Phys. Rev. D 67, 024004 (2003). doi:10.1103/PhysRevD.67.024004

    Article  MathSciNet  ADS  Google Scholar 

  123. Liu Y.T., Shapiro S.L., Etienne Z.B., Taniguchi K.: Phys. Rev. D78, 024012 (2008). doi:10.1103/PhysRevD.78.024012

    ADS  Google Scholar 

  124. Giacomazzo B., Rezzolla L., Baiotti L.: MNRAS 299, L164 (2009)

    ADS  Google Scholar 

  125. Kiuchi K., Shibata M., Yoshida S.: Phys. Rev. D78, 024029 (2008). doi:10.1103/PhysRevD.78.024029

    ADS  Google Scholar 

  126. Braithwaite J., Nordlund A.: A&A 450(3), 1077 (2006). doi:10.1051/0004-6361:20041980

    Article  MATH  ADS  Google Scholar 

  127. Braithwaite J.: MNRAS 386, 1947 (2008)

    Article  ADS  Google Scholar 

  128. Braithwaite J.: MNRAS 397, 763 (2009)

    Article  ADS  Google Scholar 

  129. Toth G.: J. Comput. Phys. 161, 605 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  130. Schnetter, E., Ott, C.D., Allen, G., Diener, P., Goodale, T., Radke, T., Seidel, E., Shalf, J.: In: Bader, D.A. (ed.) Petascale Computing: Algorithms and Applications. Computational Science Series, chap. 24. Chapman & Hall/CRC, London/Boco Raton (2007)

  131. Zink, B.: (2008). arXiv:0810.5349

  132. Farris B.D., Li T.K., Liu Y.T., Shapiro S.L.: Phys. Rev. D78, 024023 (2008). doi:10.1103/PhysRevD.78.024023

    ADS  Google Scholar 

  133. Duez M.D., Liu Y.T., Shapiro S.L., Stephens B.C.: Phys. Rev. D69, 104030 (2004). doi:10.1103/PhysRevD.69.104030

    ADS  Google Scholar 

  134. Andersson N., Comer G.L.: Living Rev. Relativ. 10, 1 (2005)

    ADS  Google Scholar 

  135. Numerial INJection Analysis project. http://www.ninja-project.org

  136. Aylott B. et al.: Class. Quantum Grav. 26, 165008 (2009). doi:10.1088/0264-9381/26/16/165008

    Article  ADS  Google Scholar 

  137. Danzmann, K., Rüdiger, A.: Class. Quantum Grav. 20, S1 (2003). http://stacks.iop.org/CQG/20/S2

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Authors and Affiliations

  1. Physics Department, University College Cork, Cork, Ireland

    Mark Hannam

  2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    Mark Hannam

  3. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    Ian Hawke

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  1. Mark Hannam
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Hannam, M., Hawke, I. Numerical relativity simulations in the era of the Einstein Telescope. Gen Relativ Gravit 43, 465–483 (2011). https://doi.org/10.1007/s10714-010-1008-2

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