- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Charges, conserved quantities, and fluxes in de Sitter spacetime

Aaron Poole, Kostas Skenderis, and Marika Taylor

  • STAG Research Centre & Mathematical Sciences, Highfield, University of Southampton, SO17 1BJ Southampton, United Kingdom

PDF

Phys. Rev. D 106, L061901 – Published 8 September, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L061901

Abstract

We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analog of holographic charges at future and past infinity and at other Cauchy surfaces It as integrals over the intersection of timelike surfaces C and the Cauchy surface It. In general, the charges Qt defined on the Cauchy surface It depend on C, but if gravitational flux is absent the charges are independent of C. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by C1, C2 and two Cauchy surfaces then ΔQt(C1,C2)=Qt(C1)−Qt(C2) changes by the same amount.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (69)

  1. F. A. E. Pirani, Invariant formulation of gravitational radiation theory, Phys. Rev. 105, 1089 (1957).
  2. A. Trautman, Radiation and boundary conditions in the theory of gravitation, Bull. Acad. Pol.. Sci., Ser. Sci., Math., Astron. Phys. 6, 407 (1958), https://arxiv.org/pdf/1604.03145.pdf.
  3. R. L. Arnowitt, S. Deser, and C. W. Misner, Dynamical structure and definition of energy in general relativity, Phys. Rev. 116, 1322 (1959).
  4. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. R. Soc. A 269, 21 (1962).
  5. R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962).
  6. S. de Haro, S. N. Solodukhin, and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217, 595 (2001).
  7. C. Fefferman and C. Graham, Conformal invariants, in Elie Cartan et les Math ematiques d’aujourd’hui, Asterisque 95 (1985), https://smf.emath.fr/en/publications/asterisque.
  8. M. Henningson and K. Skenderis, The holographic Weyl anomaly, J. High Energy Phys. 07 (1998) 023.
  9. I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes, J. High Energy Phys. 08 (2005) 004.
  10. V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208, 413 (1999).
  11. K. Skenderis, Asymptotically anti-de Sitter space-times and their stress energy tensor, Int. J. Mod. Phys. A 16, 740 (2001).
  12. E. Witten and S.-T. Yau, Connectedness of the boundary in the AdS/CFT correspondence, Adv. Theor. Math. Phys. 3, 1635 (1999).
  13. K. Skenderis, Lecture notes on holographic renormalization, Classical Quantum Gravity 19, 5849 (2002).
  14. A. A. Starobinsky, Isotropization of arbitrary cosmological expansion given an effective cosmological constant, JETP Lett. 37, 66 (1983), https://ui.adsabs.harvard.edu/abs/1983ZhPmR..37...55S/abstract.
  15. L. F. Abbott and S. Deser, Stability of gravity with a cosmological constant, Nucl. Phys. B195, 76 (1982).
  16. A. Ashtekar, B. Bonga, and A. Kesavan, Asymptotics with a positive cosmological constant: I. Basic framework, Classical Quantum Gravity 32, 025004 (2015).
  17. A. Ashtekar, B. Bonga, and A. Kesavan, Asymptotics with a positive cosmological constant. II. Linear fields on de Sitter spacetime, Phys. Rev. D 92, 044011 (2015).
  18. A. Ashtekar, B. Bonga, and A. Kesavan, Asymptotics with a positive cosmological constant: III. The quadrupole formula, Phys. Rev. D 92, 104032 (2015).
  19. A. Ashtekar, B. Bonga, and A. Kesavan, Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant, Phys. Rev. Lett. 116, 051101 (2016).
  20. A. Ashtekar, Implications of a positive cosmological constant for general relativity, Rep. Prog. Phys. 80, 102901 (2017).
  21. A. Ashtekar and S. Bahrami, Asymptotics with a positive cosmological constant. IV. The no-incoming radiation condition, Phys. Rev. D 100, 024042 (2019).
  22. P. Krtous, J. Podolsky, and J. Bicak, Gravitational and Electromagnetic Fields near a de Sitter—Like Infinity, Phys. Rev. Lett. 91, 061101 (2003).
  23. R. Penrose, On cosmological mass with positive Lambda, Gen. Relativ. Gravit. 43, 3355 (2011).
  24. P. T. Chruściel and L. Ifsits, The cosmological constant and the energy of gravitational radiation, Phys. Rev. D 93, 124075 (2016).
  25. P. T. Chruściel, S. J. Hoque, and T. Smołka, Energy of weak gravitational waves in spacetimes with a positive cosmological constant, Phys. Rev. D 103, 064008 (2021).
  26. P. T. Chruściel, S. J. Hoque, M. Maliborski, and T. Smołka, On the canonical energy of weak gravitational fields with a cosmological constant Λ∈R, Eur. Phys. J. C 81, 696 (2021).
  27. N. T. Bishop, Gravitational waves in a de Sitter universe, Phys. Rev. D 93, 044025 (2016).
  28. G. Date and S. J. Hoque, Gravitational waves from compact sources in a de Sitter background, Phys. Rev. D 94, 064039 (2016).
  29. G. Date and S. J. Hoque, Cosmological horizon and the quadrupole formula in de Sitter background, Phys. Rev. D 96, 044026 (2017).
  30. S. J. Hoque and A. Virmani, On propagation of energy flux in de Sitter spacetime, Gen. Relativ. Gravit. 50, 40 (2018).
  31. M. Kolanowski and J. Lewandowski, Energy of gravitational radiation in the de Sitter universe at I+ and at a horizon, Phys. Rev. D 102, 124052 (2020).
  32. L. B. Szabados and P. Tod, A positive Bondi–type mass in asymptotically de Sitter spacetimes, Classical Quantum Gravity 32, 205011 (2015).
  33. V.-L. Saw, Mass loss due to gravitational waves with Λ>0, Mod. Phys. Lett. A 32, 1730020 (2017).
  34. V.-L. Saw, Bondi mass with a cosmological constant, Phys. Rev. D 97, 084017 (2018).
  35. L. B. Szabados and P. Tod, A review of total energy–momenta in GR with a positive cosmological constant, Int. J. Mod. Phys. D 28, 1930003 (2018).
  36. F. Fernández-Álvarez and J. M. M. Senovilla, Gravitational radiation condition at infinity with a positive cosmological constant, Phys. Rev. D 102, 101502(R) (2020).
  37. F. Fernández-Álvarez and J. M. M. Senovilla, Asymptotic structure with a positive cosmological constant, Classical Quantum Gravity 39, 165012 (2022).
  38. V. Balasubramanian, J. de Boer, and D. Minic, Mass, entropy and holography in asymptotically de Sitter spaces, Phys. Rev. D 65, 123508 (2002).
  39. D. Anninos, G. S. Ng, and A. Strominger, Asymptotic symmetries and charges in de Sitter space, Classical Quantum Gravity 28, 175019 (2011).
  40. D. Anninos, G. S. Ng, and A. Strominger, Future boundary conditions in de Sitter space, J. High Energy Phys. 02 (2012) 032.
  41. W. R. Kelly and D. Marolf, Phase spaces for asymptotically de Sitter cosmologies, Classical Quantum Gravity 29, 205013 (2012).
  42. A. Prema Balakrishnan, S. J. Hoque, and A. Virmani, Conserved charges in asymptotically de Sitter spacetimes, Classical Quantum Gravity 36, 205008 (2019).
  43. M. Kolanowski and J. Lewandowski, Hamiltonian charges in the asymptotically de Sitter spacetimes, J. High Energy Phys. 05 (2021) 063.
  44. G. Compère, A. Fiorucci, and R. Ruzziconi, The Λ−BMS4 group of dS4 and new boundary conditions for AdS4, Classical Quantum Gravity 36, 195017 (2019).
  45. G. Compère, A. Fiorucci, and R. Ruzziconi, The Λ−BMS4 charge algebra, J. High Energy Phys. 10 (2020) 205.
  46. A. Fiorucci and R. Ruzziconi, Charge algebra in Al(A)dSn spacetimes, J. High Energy Phys. 05 (2021) 210.
  47. C. Crnković and E. Witten, Covariant description of canonical formalism in geometrical theories, in Three Hundred Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987).
  48. J. Lee and R. M. Wald, Local symmetries and constraints, J. Math. Phys. (N.Y.) 31, 725 (1990).
  49. R. M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48, R3427 (1993).
  50. V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50, 846 (1994).
  51. V. Iyer and R. M. Wald, A comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes, Phys. Rev. D 52, 4430 (1995).
  52. R. M. Wald and A. Zoupas, A general definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D 61, 084027 (2000).
  53. D. Harlow and J.-Q. Wu, Covariant phase space with boundaries, J. High Energy Phys. 10 (2020) 146.
  54. V. Chandrasekaran, E. E. Flanagan, I. Shehzad, and A. J. Speranza, A general framework for gravitational charges and holographic renormalization, Int. J. Mod. Phys. A 37, 2250105 (2022).
  55. G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B633, 3 (2002).
  56. A. Poole, K. Skenderis, and M. Taylor, (A)dS4 in Bondi gauge, Classical Quantum Gravity 36, 095005 (2019).
  57. I. Robinson and A. Trautman, Spherical Gravitational Waves, Phys. Rev. Lett. 4, 431 (1960).
  58. I. Bakas and K. Skenderis, Non-equilibrium dynamics and AdS4 Robinson-Trautman, J. High Energy Phys. 08 (2014) 056.
  59. R. F. Aranha, I. Damiao Soares, and E. V. Tonini, The Bondi-Sachs 4-momentum in non-axisymmetric Robinson-Trautman spacetimes, Classical Quantum Gravity 30, 025014 (2013).
  60. P. Chruściel, Semiglobal existence and convergence of solutions of the Robinson-Trautman (two-dimensional Calabi) equation, Commun. Math. Phys. 137, 289 (1991).
  61. P. T. Chrusciel, On the global structure of Robinson-Trautman space-times, Proc. R. Soc. A 436, 299 (1992).
  62. Y.-Z. Chu, Transverse traceless gravitational waves in a spatially flat FLRW universe: Causal structure from dimensional reduction, Phys. Rev. D 92, 124038 (2015).
  63. L. Bieri, D. Garfinkle, and S.-T. Yau, Gravitational wave memory in de Sitter spacetime, Phys. Rev. D 94, 064040 (2016).
  64. A. Kehagias and A. Riotto, BMS in cosmology, J. Cosmol. Astropart. Phys. 05 (2016) 059.
  65. Y.-Z. Chu, Gravitational wave memory In dS4+2n and 4D cosmology, Classical Quantum Gravity 34, 035009 (2017).
  66. A. Tolish and R. M. Wald, Cosmological memory effect, Phys. Rev. D 94, 044009 (2016).
  67. Y.-Z. Chu, More on cosmological gravitational waves and their memories, Classical Quantum Gravity 34, 194001 (2017).
  68. Y. Hamada, M.-S. Seo, and G. Shiu, Memory in de Sitter space and Bondi-Metzner-Sachs-like supertranslations, Phys. Rev. D 96, 023509 (2017).
  69. L. Bieri, D. Garfinkle, and N. Yunes, Gravitational wave memory in ΛCDM cosmology, Classical Quantum Gravity 34, 215002 (2017).

Outline

Information

Phys. Rev. D 106, L061901– Published 8 September, 2022
  • Received 17 February 2022
  • Accepted 20 August 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation