“Conserved charges” of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory -

[1]
B. P. Abbottet al. (Virgo, LIGO Scientific), Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837[gr-qc
[2]
B. P. Abbottet al. (Virgo, LIGO Scientific), Phys. Rev. Lett.116, 241103 (2016), arXiv:1606.04855[gr-qc
[3]
B. P. Abbottet al. (Virgo, LIGO Scientific), Phys. Rev. Lett.118, 221101 (2017), arXiv:1706.01812[gr-qc
[4]
B. P. Abbottet al. (Virgo, LIGO Scientific), Phys. Rev. Lett.119, 141101 (2017), arXiv:1709.09660[gr-qc
[5]
B. P. Abbottet al. (Virgo, LIGO Scientific), Phys. Rev. Lett.119, 161101 (2017), arXiv:1710.05832[gr-qc
[6]
B. P. Abbottet al. (Virgo and LIGO Scientific Collaborations), Astrophys. J.851, L35 (2017), arXiv:1711.05578[astro-ph.HE
[7]
B. P. Abbottet al. (Virgo and LIGO Scientific Collaborations), Phys. Rev. X9, 031040 (2019), arXiv:1811.12907[astro-ph.HE
[8]
B. P. Abbottet al. (Virgo and LIGO Scientific Collaborations), Astrophys. J. Lett.892, L3 (2020), arXiv:2001.01761[astro-ph.HE
[9]
R. Abbottet al. (LIGO Scientific, Virgo), Phys. Rev. D102, 043015 (2020), arXiv:2004.08342[astro-ph.HE
[10]
R. Abbottet al. (LIGO Scientific, Virgo), Astrophys. J. Lett.896, L44 (2020), arXiv:2006.12611[astro-ph.HE
[11]
R. Abbottet al. (LIGO Scientific, Virgo), Phys. Rev. Lett.125, 101102 (2020), arXiv:2009.01075[gr-qc
[12]
R. Abbottet al. (LIGO Scientific, Virgo), Astrophys. J. Lett.900, L13 (2020), arXiv:2009.01190[astro-ph.HE
[13]
R. Abbottet al. (LIGO Scientific, Virgo), (2020), arXiv: 2010.14527 [gr-qc]
[14]
A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.)1916, 688 (1916)
[15]
A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.)1918, 154 (1918)
[16]
C. M. Will, Living Rev. Rel.17, 4 (2014), arXiv:1403.7377[gr-qc
[17]
Y. Gong and S. Hou, Universe4, 85 (2018), arXiv:1806.04027[gr-qc
[18]
Y. B. Zel’dovich and A. G. Polnarev, Sov. Astron.18, 17 (1974)
[19]
V. Braginsky and L. Grishchuk, Sov. Phys. JETP62, 427 (1985)
[20]
D. Christodoulou, Phys. Rev. Lett.67, 1486 (1991)
[21]
H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Proc. Roy. Soc. Lond. A269, 21 (1962)
[22]
R. K. Sachs, Proc. Roy. Soc. Lond. A270, 103 (1962)
[23]
R. Sachs, Phys. Rev.128, 2851 (1962)
[24]
A. Strominger and A. Zhiboedov, JHEP01, 086 (2016), arXiv:1411.5745[hep-th
[25]
S. Pasterski, A. Strominger, and A. Zhiboedov, JHEP12, 053 (2016), arXiv:1502.06120[hep-th
[26]
D. A. Nichols, Phys. Rev. D98, 064032 (2018), arXiv:1807.08767[gr-qc
[27]
R. N. Lang, Phys. Rev. D89, 084014 (2014), arXiv:1310.3320[gr-qc
[28]
R. N. Lang, Phys. Rev. D91, 084027 (2015), arXiv:1411.3073[gr-qc
[29]
S. M. Du and A. Nishizawa, Phys. Rev. D94, 104063 (2016), arXiv:1609.09825[gr-qc
[30]
E. Kilicarslan and B. Tekin, Eur. Phys. J. C79, 114 (2019), arXiv:1805.02240[gr-qc
[31]
E. Kilicarslan, Phys. Rev. D98, 064048 (2018), arXiv:1808.00266[gr-qc
[32]
E. Kilicarslan, Turk. J. Phys.43, 126 (2019), arXiv:1811.00843[gr-qc
[33]
S. Hou, (2020), arXiv: 2011.02087[gr-qc]
[34]
S. Hou and Z.-H. Zhu, (2020), arXiv: 2005.01310[gr-qc]
[35]
C. Brans and R. Dicke, Phys. Rev.124, 925 (1961)
[36]
S. Tahura, D. A. Nichols, A. Saffeet al., (2020), arXiv: 2007.13799 [gr-qc]
[37]
R. Penrose, Phys. Rev. Lett.10, 66 (1963)
[38]
R. Penrose, Proc. Roy. Soc. Lond. A284, 159 (1965)
[39]
R. M. Wald and A. Zoupas, Phys. Rev. D61, 084027 (2000), arXiv:gr-qc/9911095[gr-qc
[40]
V. Chandrasekaran, E. E. Flanagan, and K. Prabhu, JHEP11, 125 (2018), arXiv:1807.11499[hep-th
[41]
B. Bonga, A. M. Grant, and K. Prabhu, Phys. Rev. D101, 044013 (2020), arXiv:1911.04514[gr-qc
[42]
K. Bhattacharya and B. R. Majhi, Phys. Rev. D95, 064026 (2017), arXiv:1702.07166[gr-qc
[43]
K. Bhattacharya, A. Das, and B. R. Majhi, Phys. Rev. D97, 124013 (2018), arXiv:1803.03771[gr-qc
[44]
C. Duval, G. Gibbons, and P. Horvathy, Class. Quant. Grav.31, 092001 (2014), arXiv:1402.5894[gr-qc
[45]
C. Duval, G. Gibbons, and P. Horvathy, J. Phys. A47, 335204 (2014), arXiv:1403.4213[hep-th
[46]
H. Godazgar, M. Godazgar, and M. J. Perry, Phys. Rev. Lett.125, 101301 (2020), arXiv:2007.01257[hep-th
[47]
H. Godazgar, M. Godazgar, and M. J. Perry, JHEP20, 084 (2020), arXiv:2007.07144[hep-th
[48]
R. Geroch,Asymptotic structure of space-time, inAsymptotic Structure of Space-Time, edited by F. P. Esposito and L. Witten (Springer US, Boston, MA, 1977) pp. 1–105
[49]
A. Ashtekar, J. Math. Phys.22, 2885 (1981)
[50]
A. Ashtekar and M. Streubel, Proc. Roy. Soc. Lond. A376, 585 (1981)
[51]
A. Ashtekar, (2014), arXiv: 1409.1800 [gr-qc]
[52]
R. M. Wald,General Relativity,(University of Chicago Press, Chicago, IL, 1984)
[53]
E. Poisson and C. M. Will,Gravity:Newtonian,Post-Newtonian,Relativistic(Cambridge University Press, 2014)
[54]
G. Barnich and C. Troessaert, JHEP05, 062 (2010), arXiv:1001.1541[hep-th
[55]
S. W. Hawking and G. F. R. Ellis,The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2011)
[56]
R. P. Geroch and J. Winicour, J. Math. Phys.22, 803 (1981)
[57]
Note that \begin{document}$ \bar{K} = \psi/2 $\end{document} defined in [34]
[58]
F. Alessio and M. Arzano, Phys. Rev. D100, 044028 (2019), arXiv:1906.05036[gr-qc
[59]
R. M. Wald, J. Math. Phys.31, 2378 (1990)
[60]
V. Iyer and R. M. Wald, Phys. Rev. D50, 846 (1994), arXiv:gr-qc/9403028[gr-qc
[61]
A. Ashtekar, M. Campiglia, and A. Laddha, Gen. Rel. Grav.50, 140 (2018), arXiv:1808.07093[gr-qc
[62]
In the terminology of Refs. [58, 61], \begin{document}$ {\cal{H}}_\alpha $\end{document} and \begin{document}$ {\cal{H}}_Y $\end{document} are both called charges, as they are given by the integrals over a 3-dimensional hypersurface, just like the electric charge: \begin{document}$ \int_\Sigma J^dn_d\epsilon_{abc} $\end{document} where \begin{document}$ J^a $\end{document} is the 4-current, \begin{document}$ \Sigma $\end{document} is a spacelike hypersurface with a unit normal \begin{document}$ n_a $\end{document} and the volume element \begin{document}$ \epsilon_{abc} $\end{document} . But we will call them fluxes because of Eq. (74)
[63]
E. E. Flanagan and D. A. Nichols, Phys. Rev. D95, 044002 (2017), arXiv:1510.03386[hep-th
[64]
P. J. McCarthy, Proc. Roy. Soc. Lond. A343, 489 (1975)
[65]
G. Barnich and B. Oblak, JHEP03, 033 (2015), arXiv:1502.00010[hep-th
[66]
A. Strominger, JHEP07, 152 (2014), arXiv:1312.2229[hep-th
[67]
G. Compère, A. Fiorucci, and R. Ruzziconi, JHEP11, 200 (2018), [Erratum: JHEP04, 172 (2020)], arXiv: 1810.00377[hep-th]
[68]
G. Compère, R. Oliveri, and A. Seraj, JHEP20, 116 (2020), arXiv:1912.03164[gr-qc
[69]
E. Newman and R. Penrose, J. Math. Phys.3, 566 (1962), [Errata: J. Math. Phys.4(7), 998 (1963)]
[70]
\begin{document}$ \bar\Psi_2 $\end{document} is the complex conjugate to \begin{document}$ \Psi_2 $\end{document}
[71]
L. Bieri and D. Garfinkle, Phys. Rev. D89, 084039 (2014), arXiv:1312.6871[gr-qc
[72]
E. E. Flanagan, A. M. Grant, A. I. Harteet al., Phys. Rev. D99, 084044 (2019), arXiv:1901.00021[gr-qc
[73]
R. Blumenhagen and E. Plauschinn, Lect. Notes Phys.779, 1 (2009)
[74]
A. Ashtekar and J. Winicour, J. Math. Phys.23, 2410 (1982)