- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Constraint-satisfying binary boson star initial data in the extended conformally flat condition formalism

Gabriele Palloni1,*, Nicolas Sanchis-Gual1, José A. Font1,2, Samuel Santos-Pérez3, Isabel Cordero-Carrión3, Pablo Cerdá-Durán1,2, and Claudio Lazarte1

  • 1Departamento de Astronomía y Astrofísica, Universitat de València, Avinguda Vicent Andrés Estellés 19, 46100, Burjassot (València), Spain
  • 2Observatori Astronòmic, Universitat de València, C/ Catedrático José Beltrán 2, 46980, Paterna (València), Spain
  • 3Departamento de Matemáticas, Universitat de València, Avinguda Vicent Andrés Estellés 19, Burjassot (València), Spain

  • *Contact author: gabriele.palloni@uv.es
PDF

Phys. Rev. D 114, 044011 – Published 5 August, 2026

DOI: https://doi.org/10.1103/hw4m-c7p2

Abstract

Numerical-relativity simulations with nontrivial matter configurations require initial data that satisfy the Hamiltonian and momentum constraints of the Einstein equations. We construct constraint-satisfying scalar-field initial data using the extended conformally flat condition (XCFC) formalism, in which the matter variables are conformally rescaled and an auxiliary vector field is introduced. In doing so, we overcome the issues of local uniqueness and convergence of the solutions that arise in the second-order elliptic equations associated with the constraints. Using an iterative solver method, we demonstrate the convergence of the XCFC approach to a solution for several scalar-field matter systems. Those include Gaussian-like profiles, topological torus configurations, and equal-mass boson star binaries. In particular, for the latter case, it is common to employ the superposition of two isolated boson star solutions in order to build the initial data. We show that our formalism significantly improves upon a superposition approach by generating genuinely constraint-satisfying initial data for boson star binaries.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. M. Alcubierre, Introduction to 3+1 Numerical Relativity (Oxford Academic, Oxford, 2008).
  2. E. Gourgoulhon, 3+1 Formalism and Bases of Numerical Relativity (Springer, Berlin, Heidelberg, 2007).
  3. T. W. Baumgarte and S. L. Shapiro, Numerical Relativity: Solving Einstein’s Equations on the Computer (Cambridge University Press, Cambridge, England, 2010).
  4. L. Andersson and V. Moncrief, Ann. Henri Poincare 4, 1 (2003).
  5. S. Bonazzola, E. Gourgoulhon, P. Grandclément, and J. Novak, Phys. Rev. D 70, 104007 (2004).
  6. J. W. York, Sources of Gravitational Radiation, edited by J. W. York (Cambridge University Press, Cambridge, England, 1979).
  7. G. B. Cook, Living Rev. Relativity 3, 5 (2000).
  8. H. P. Pfeiffer and J. W. York, Phys. Rev. D 67, 044022 (2003).
  9. J. W. York, Phys. Rev. Lett. 82, 1350 (1999).
  10. H. P. Pfeiffer, J. Hyperbol. Differ. Equations 02, 497 (2005).
  11. M. Boyle, D. A. Brown, L. E. Kidder, A. H. Mroué, H. P. Pfeiffer, M. A. Scheel, G. B. Cook, and S. A. Teukolsky, Phys. Rev. D 76, 124038 (2007).
  12. S. Ossokine, F. Foucart, H. P. Pfeiffer, M. Boyle, and B. Szilágyi, Classical Quantum Gravity 32, 245010 (2015).
  13. W. Tichy, Rep. Prog. Phys. 80, 026901 (2016).
  14. J. C. Aurrekoetxea, K. Clough, and E. A. Lim, Living Rev. Relativity 28, 5 (2025).
  15. M. Bezares and N. Sanchis-Gual, in New Frontiers in GRMHD Simulations (Springer, New York, 2025), pp. 619–661.
  16. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, Phys. Rev. D 81, 123530 (2010).
  17. A. Arvanitaki and S. Dubovsky, Phys. Rev. D 83, 044026 (2011).
  18. F. F. Freitas, C. A. Herdeiro, A. P. Morais, A. Onofre, R. Pasechnik, E. Radu, N. Sanchis-Gual, and R. Santos, J. Cosmol. Astropart. Phys. 12 (2021) 047.
  19. V. Cardoso and P. Pani, Living Rev. Relativity 22, 4 (2019).
  20. L. Barack et al., Classical Quantum Gravity 36, 143001 (2019).
  21. D. J. Kaup, Phys. Rev. 172, 1331 (1968).
  22. R. Ruffini and S. Bonazzola, Phys. Rev. 187, 1767 (1969).
  23. S. Yoshida and Y. Eriguchi, Phys. Rev. D 56, 762 (1997).
  24. E. Seidel and W.-M. Suen, Phys. Rev. D 42, 384 (1990).
  25. E. Seidel and W.-M. Suen, Phys. Rev. Lett. 66, 1659 (1991).
  26. N. Sanchis-Gual, C. Herdeiro, E. Radu, J. C. Degollado, and J. A. Font, Phys. Rev. D 95, 104028 (2017).
  27. N. Sanchis-Gual, F. Di Giovanni, M. Zilhão, C. Herdeiro, P. Cerdá-Durán, J. Font, and E. Radu, Phys. Rev. Lett. 123, 221101 (2019).
  28. C. Herdeiro, E. Radu, N. Sanchis-Gual, N. Santos, and E. dos Santos Costa Filho, Phys. Lett. B 852, 138595 (2024).
  29. F. E. Schunck and E. W. Mielke, Classical Quantum Gravity 20, R301 (2003).
  30. S. L. Liebling and C. Palenzuela, Living Rev. Relativity 15, 6 (2012).
  31. L. Visinelli, Int. J. Mod. Phys. D 30, 2130006 (2021).
  32. R. Brito, V. Cardoso, C. A. Herdeiro, and E. Radu, Phys. Lett. B 752, 291 (2016).
  33. C. Palenzuela, L. Lehner, and S. L. Liebling, Phys. Rev. D 77, 044036 (2008).
  34. J. Calderón Bustillo, N. Sanchis-Gual, A. Torres-Forné, J. A. Font, A. Vajpeyi, R. Smith, C. Herdeiro, E. Radu, and S. H. W. Leong, Phys. Rev. Lett. 126, 081101 (2021).
  35. N. Sanchis-Gual, J. C. Bustillo, C. Herdeiro, E. Radu, J. A. Font, S. H. W. Leong, and A. Torres-Forné, Phys. Rev. D 106, 124011 (2022).
  36. R. Croft, T. Helfer, B.-X. Ge, M. Radia, T. Evstafyeva, E. A. Lim, U. Sperhake, and K. Clough, Classical Quantum Gravity 40, 065001 (2023).
  37. B.-X. Ge, E. A. Lim, U. Sperhake, T. Evstafyeva, D. Cors, E. de Jong, R. Croft, and T. Helfer, Phys. Rev. D 112, 124080 (2025).
  38. C. Palenzuela, P. Pani, M. Bezares, V. Cardoso, L. Lehner, and S. Liebling, Phys. Rev. D 96, 104058 (2017).
  39. M. Bezares, C. Palenzuela, and C. Bona, Phys. Rev. D 95, 124005 (2017).
  40. C. Palenzuela, P. Pani, M. Bezares, V. Cardoso, L. Lehner, and S. Liebling, Phys. Rev. D 96, 104058 (2017).
  41. M. Bezares, M. Bošković, S. Liebling, C. Palenzuela, P. Pani, and E. Barausse, Phys. Rev. D 105, 064067 (2022).
  42. T. Evstafyeva, U. Sperhake, I. M. Romero-Shaw, and M. Agathos, Phys. Rev. Lett. 133, 131401 (2024).
  43. T. Evstafyeva, A. Seifert, U. Sperhake, C. J. Moore, and T. Jain, arXiv:2604.25582.
  44. N. Sanchis-Gual, M. Zilhão, C. Herdeiro, F. Di Giovanni, J. A. Font, and E. Radu, Phys. Rev. D 102, 101504 (2020).
  45. G. Palloni, N. Sanchis-Gual, J. A. Font, C. Herdeiro, and E. Radu, Phys. Rev. D 112, 104011 (2025).
  46. M. Bezares and C. Palenzuela, Classical Quantum Gravity 35, 234002 (2018).
  47. N. Sanchis-Gual, C. Herdeiro, J. A. Font, E. Radu, and F. Di Giovanni, Phys. Rev. D 99, 024017 (2019).
  48. V. Jaramillo, N. Sanchis-Gual, J. Barranco, A. Bernal, J. C. Degollado, C. Herdeiro, M. Megevand, and D. Núñez, Phys. Rev. D 105, 104057 (2022).
  49. R. Croft, T. Helfer, B.-X. Ge, M. Radia, T. Evstafyeva, E. A. Lim, U. Sperhake, and K. Clough, Classical Quantum Gravity 40, 065001 (2023).
  50. T. Helfer, E. A. Lim, M. A. G. Garcia, and M. A. Amin, Phys. Rev. D 99, 044046 (2019).
  51. T. Helfer, U. Sperhake, R. Croft, M. Radia, B.-X. Ge, and E. A. Lim, Classical Quantum Gravity 39, 074001 (2022).
  52. T. Evstafyeva, U. Sperhake, T. Helfer, R. Croft, M. Radia, B.-X. Ge, and E. A. Lim, Classical Quantum Gravity 40, 085009 (2023).
  53. Z. Ning, arXiv:2604.15240.
  54. F. Atteneder, H. R. Rüter, D. Cors, R. Rosca-Mead, D. Hilditch, and B. Brügmann, Phys. Rev. D 109, 044058 (2024).
  55. J. C. Aurrekoetxea, K. Clough, and E. A. Lim, Classical Quantum Gravity 40, 075003 (2023).
  56. N. Siemonsen and W. E. East, Phys. Rev. D 107, 124018 (2023).
  57. N. Siemonsen and W. E. East, Phys. Rev. D 108, 124015 (2023).
  58. J. C. Aurrekoetxea, S. E. Brady, L. Aresté-Saló, J. Bamber, L. Chung-Jukko, K. Clough, E. de Jong, M. Elley, P. Figueras, T. Helfer, E. A. Lim, M. Radia, A. Waeming, and Z. Wang, J. Open Source Softwaare 11, 9057 (2026).
  59. H. P. Pfeiffer, J. Hyperbol. Differ. Equations 02, 497 (2005).
  60. H. P. Pfeiffer and J. W. York, Phys. Rev. Lett. 95, 091101 (2005).
  61. T. W. Baumgarte, N. O. Murchadha, and H. P. Pfeiffer, Phys. Rev. D 75, 044009 (2007).
  62. I. Cordero-Carrión, P. Cerdá-Durán, H. Dimmelmeier, J. L. Jaramillo, J. Novak, and E. Gourgoulhon, Phys. Rev. D 79, 024017 (2009).
  63. J. R. Wilson, G. J. Mathews, and P. Marronetti, Phys. Rev. D 54, 1317 (1996).
  64. J. A. Isenberg, Int. J. Mod. Phys. D 17, 265 (2008).
  65. S. Bonazzola, E. Gourgoulhon, P. Grandclément, and J. Novak, Phys. Rev. D 70, 104007 (2004).
  66. I. Cordero-Carrión, J. M. Ibáñez, E. Gourgoulhon, J. L. Jaramillo, and J. Novak, Phys. Rev. D 77, 084007 (2008).
  67. O. Rinne, Classical Quantum Gravity 25, 135009 (2008).
  68. M. Taylor, Partial Differential Equations: Nonlinear Equations, Applied Mathematical Sciences No. v. 3 (Springer, New York, 1996).
  69. M. Protter and H. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall Partial Differential Equations Series (Prentice-Hall, NJ, 1967).
  70. L. Evans, Partial Differential Equations, Graduate Studies in Mathematics (American Mathematical Society, Providence, 1998).
  71. F. Di Giovanni, N. Sanchis-Gual, D. Guerra, M. Miravet-Tenés, P. Cerdá-Durán, and J. A. Font, Phys. Rev. D 106, 044008 (2022).
  72. J. Adsuara, I. Cordero-Carrión, P. Cerdá-Durán, and M. Aloy, J. Comput. Phys. 321, 369 (2016).
  73. J. Adsuara, I. Cordero-Carrión, P. Cerdá-Durán, V. Mewes, and M. Aloy, J. Comput. Phys. 332, 446 (2017).
  74. F. Banchelli, M. Garcia-Gasulla, F. Mantovani, J. Vinyals, J. Pocurull, D. Vicente, B. Eguzkitza, F. C. C. Galeazzo, M. C. Acosta, and S. Girona, arXiv:2503.09917.
  75. S. Santos-Pérez, I. Cordero-Carrión, and P. Cerdá-Durán, Phys. Rev. D 112, 024057 (2025).
  76. F. E. Schunck and E. W. Mielke, Classical Quantum Gravity 20, R301 (2003).
  77. C. Lazarte, Estrellas de ℓ-Proca: Generalización multicampo en simetría esférica de estrellas de Proca con momento angular, Master’s thesis, Universidad Nacional Autónoma de México, 2023.
  78. C. Lazarte and M. Alcubierre, Classical Quantum Gravity 41, 135003 (2024).
  79. J. Thornburg, Classical Quantum Gravity 4, 1119 (1987).
  80. S. R. Lau and R. H. Price, J. Comput. Phys. 227, 1126 (2007).

Outline

Information

Phys. Rev. D 114, 044011– Published 5 August, 2026
  • Received 25 May 2026
  • Accepted 10 July 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation