Abstract
Covariant conserved 2-form currents for linearised gravity are constructed by contracting the linearised curvature with conformal Killing-Yano tensors. The corresponding conserved charges were originally introduced by Penrose and have recently been interpreted as the generators of generalised symmetries of the graviton. We introduce an off-shell refinement of these charges and find the relation between these improved Penrose charges and the linearised version of the ADM momentum and angular momentum. If the graviton field is globally well-defined on a background Minkowski space then some of the Penrose charges give the momentum and angular momentum while the remainder vanish. We consider the generalisation in which the graviton has Dirac string singularities or is defined locally in patches, in which case the conventional ADM expressions are not invariant under the graviton gauge symmetry in general. We modify them to render them gauge-invariant and show that the Penrose charges give these modified charges plus certain magnetic gravitational charges. We discuss properties of the Penrose charges, generalise to toroidal Kaluza-Klein compactifications and check our results in a number of examples.
Article PDF
Avoid common mistakes on your manuscript.
References
R. Penrose, Quasilocal mass and angular momentum in general relativity, Proc. Roy. Soc. Lond. A 381 (1982) 53 [INSPIRE].
S.-i. Tachibana, On conformal Killing tensor in a Riemannian space, Tohoku Math. J. 21 (1969) 56.
T. Kashiwada, On conformal Killing tensor, Nat. Sci. Rep. Ochanomizu Univ. 19 (1968) 67 [INSPIRE].
J. Jezierski, CYK tensors, Maxwell field and conserved quantities for the spin-2 field, Class. Quant. Grav. 19 (2002) 4405 [gr-qc/0211039] [INSPIRE].
J. Jezierski and S. Migacz, The 3 + 1 decomposition of conformal Yano-Killing tensors and ‘momentary charges for the spin-2 field, Class. Quant. Grav. 32 (2015) 035016 [ar**v:1404.6629] [INSPIRE].
K. Hinterbichler, D.M. Hofman, A. Joyce and G. Mathys, Gravity as a gapless phase and biform symmetries, JHEP 02 (2023) 151 [ar**v:2205.12272] [INSPIRE].
V. Benedetti, H. Casini and J.M. Magán, Generalized symmetries of the graviton, JHEP 05 (2022) 045 [ar**v:2111.12089] [INSPIRE].
V. Benedetti, P. Bueno and J.M. Magán, Generalized Symmetries for Generalized Gravitons, Phys. Rev. Lett. 131 (2023) 111603 [ar**v:2305.13361] [INSPIRE].
V. Benedetti, H. Casini and J.M. Magán, Generalized symmetries and Noether’s theorem in QFT, JHEP 08 (2022) 304 [ar**v:2205.03412] [INSPIRE].
C. Gómez-Fayrén, P. Meessen and T. Ortín, Covariant generalized conserved charges of General Relativity, JHEP 09 (2023) 174 [ar**v:2307.04041] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [ar**v:1412.5148] [INSPIRE].
C.M. Hull, Magnetic charges for the graviton, JHEP 05 (2024) 257 [ar**v:2310.18441] [INSPIRE].
D. Kastor and J. Traschen, Conserved gravitational charges from Yano tensors, JHEP 08 (2004) 045 [hep-th/0406052] [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, Dynamical Structure and Definition of Energy in General Relativity, Phys. Rev. 116 (1959) 1322 [INSPIRE].
L.F. Abbott and S. Deser, Stability of Gravity with a Cosmological Constant, Nucl. Phys. B 195 (1982) 76 [INSPIRE].
C.M. Hull, Strongly coupled gravity and duality, Nucl. Phys. B 583 (2000) 237 [hep-th/0004195] [INSPIRE].
S. Ramaswamy and A. Sen, Dual-mass in general relativity, J. Math. Phys. 22 (1981) 2612.
A. Ashtekar and A. Sen, NUT 4-momenta are forever, J. Math. Phys. 23 (1982) 2168.
R. Penrose and W. Rindler, Spinors and space-time. Vol. 2: Spinor and twistor methods in space-time geometry, Cambridge University Press (1988) [https://doi.org/10.1017/CBO9780511524486] [INSPIRE].
U. Lindström and Ö. Sarıoğlu, Killing-Yano Cotton currents, JHEP 03 (2022) 029 [ar**v:2110.03470] [INSPIRE].
V.P. Frolov and D. Kubizňák, Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables, Class. Quant. Grav. 25 (2008) 154005 [ar**v:0802.0322] [INSPIRE].
P.S. Howe and U. Lindström, Some remarks on (super)-conformal Killing-Yano tensors, JHEP 11 (2018) 049 [ar**v:1808.00583] [INSPIRE].
U. Lindström and Ö. Sarıoğlu, Geometry, conformal Killing-Yano tensors and conserved “currents”, JHEP 05 (2023) 176 [ar**v:2206.08037] [INSPIRE].
U. Lindström and Ö. Sarıoğlu, New currents with Killing-Yano tensors, Class. Quant. Grav. 38 (2021) 195011 [ar**v:2104.12451] [INSPIRE].
H. Casini and J.M. Magán, On completeness and generalized symmetries in quantum field theory, Mod. Phys. Lett. A 36 (2021) 2130025 [ar**v:2110.11358] [INSPIRE].
C.M. Hull, Gravitational duality, branes and charges, Nucl. Phys. B 509 (1998) 216 [hep-th/9705162] [INSPIRE].
S. Deser and M. Soldate, Gravitational Energy in Spaces With Compactified Dimensions, Nucl. Phys. B 311 (1989) 739 [INSPIRE].
E. Newman, L. Tamburino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].
A.H. Taub, Empty space-times admitting a three parameter group of motions, Annals Math. 53 (1951) 472 [INSPIRE].
C.W. Misner, Taub-Nut Space as a Counterexample to almost anything, in Relativity Theory and Astrophysics. Vol.1: Relativity and Cosmology, J. Ehlers ed., vol. 8 (1967), p. 160 [INSPIRE].
C.W. Bunster, S. Cnockaert, M. Henneaux and R. Portugues, Monopoles for gravitation and for higher spin fields, Phys. Rev. D 73 (2006) 105014 [hep-th/0601222] [INSPIRE].
W. Dietz and R. Rüdiger, Space-Times Admitting Killing-Yano Tensors. I, Proc. Roy. Soc. Lond. A 375 (1981) 361.
Acknowledgments
CH is supported in part by the STFC Consolidated Grants ST/T000791/1 and ST/X000575/1. MLH was supported by a President’s Scholarship from Imperial College London. UL gratefully acknowledges a Leverhulme visiting professorship to Imperial College as well as the hospitality of the theory group at Imperial.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2401.17361
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Hull, C., Hutt, M.L. & Lindström, U. Charges and topology in linearised gravity. J. High Energ. Phys. 2024, 97 (2024). https://doi.org/10.1007/JHEP07(2024)097
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)097