Abstract
Gravitational shockwaves are simple exact solutions of Einstein equations representing the fields of ultrarelativistic sources and idealized gravitational waves (shocks). Historically, much work has focused on shockwaves in the context of possible black hole formation in high energy particle collisions, yet they remain at the forefront of research even today. Representing hard modes in the bulk, shocks give rise to the gravitational memory effect at the classical level and implant supertranslation (BMS) hair onto a classical spacetime at the quantum level. The aim of this paper is to further our understanding of the ‘information content’ of such supertranslations. Namely, we show that, contrary to the several claims in the literature, a gravitational shockwave does leave a quantum imprint on the vacuum state of a test quantum field and that this imprint is accessible to local observers carrying Unruh-DeWitt (UDW) detectors in this spacetime.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y.B. Zel’dovich and A.G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17 [INSPIRE].
M. Favata, The gravitational-wave memory effect, Class. Quant. Grav. 27 (2010) 084036 [arXiv:1003.3486] [INSPIRE].
A. Tolish, L. Bieri, D. Garfinkle and R.M. Wald, Examination of a simple example of gravitational wave memory, Phys. Rev. D 90 (2014) 044060 [arXiv:1405.6396] [INSPIRE].
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
J. Winicour, Global aspects of radiation memory, Class. Quant. Grav. 31 (2014) 205003 [arXiv:1407.0259] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
A.P. Saha, B. Sahoo and A. Sen, Proof of the classical soft graviton theorem in D = 4, JHEP 06 (2020) 153 [arXiv:1912.06413] [INSPIRE].
A. Laddha and A. Sen, Classical proof of the classical soft graviton theorem in D>4, Phys. Rev. D 101 (2020) 084011 [arXiv:1906.08288] [INSPIRE].
R.K. Sachs and H. Bondi, Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time, Proc. Roy. Soc. Lond. A 270 (1962) 103.
H. Bondi, M.G.J. Van der Burg and A.W.K. Metzner, Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system, Proc. Roy. Soc. Lond. A 269 (1962) 21.
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
A. Ashtekar, Asymptotic Quantization of the Gravitational Field, Phys. Rev. Lett. 46 (1981) 573 [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07 (2015) 115 [arXiv:1505.05346] [INSPIRE].
A. Strominger, Asymptotic Symmetries of Yang-Mills Theory, JHEP 07 (2014) 151 [arXiv:1308.0589] [INSPIRE].
G. Compère, Infinite towers of supertranslation and superrotation memories, Phys. Rev. Lett. 123 (2019) 021101 [arXiv:1904.00280] [INSPIRE].
P.M. Zhang, C. Duval, G.W. Gibbons and P.A. Horvathy, Soft gravitons and the memory effect for plane gravitational waves, Phys. Rev. D 96 (2017) 064013 [arXiv:1705.01378] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Superrotation Charge and Supertranslation Hair on Black Holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].
P.C. Aichelburg and R.U. Sexl, On the Gravitational field of a massless particle, Gen. Rel. Grav. 2 (1971) 303 [INSPIRE].
T. Dray and G. ’t Hooft, The Gravitational Shock Wave of a Massless Particle, Nucl. Phys. B 253 (1985) 173 [INSPIRE].
G. ’t Hooft, Graviton Dominance in Ultrahigh-Energy Scattering, Phys. Lett. B 198 (1987) 61 [INSPIRE].
H.J. de Vega and N.G. Sanchez, Particle Scattering at the Planck Scale and the Aichelburg-sexl Geometry, Nucl. Phys. B 317 (1989) 731 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Planckian scattering beyond the semiclassical approximation, Phys. Lett. B 289 (1992) 87 [INSPIRE].
D.N. Kabat and M. Ortiz, Eikonal quantum gravity and Planckian scattering, Nucl. Phys. B 388 (1992) 570 [hep-th/9203082] [INSPIRE].
D.M. Eardley and S.B. Giddings, Classical black hole production in high-energy collisions, Phys. Rev. D 66 (2002) 044011 [gr-qc/0201034] [INSPIRE].
S. Kolekar and J. Louko, Gravitational memory for uniformly accelerated observers, Phys. Rev. D 96 (2017) 024054 [arXiv:1703.10619] [INSPIRE].
G.M. Shore, Memory, Penrose Limits and the Geometry of Gravitational Shockwaves and Gyratons, JHEP 12 (2018) 133 [arXiv:1811.08827] [INSPIRE].
L. Donnay, G. Giribet, H.A. González and A. Puhm, Black hole memory effect, Phys. Rev. D 98 (2018) 124016 [arXiv:1809.07266] [INSPIRE].
S. Liu and B. Yoshida, Soft thermodynamics of gravitational shock wave, arXiv:2104.13377 [INSPIRE].
A. Strominger, Black Hole Information Revisited, (2020), DOI [arXiv:1706.07143] [INSPIRE].
N. Gaddam and N. Groenenboom, Soft graviton exchange and the information paradox, arXiv:2012.02355 [INSPIRE].
S. Kolekar and J. Louko, Quantum memory for Rindler supertranslations, Phys. Rev. D 97 (2018) 085012 [arXiv:1709.07355] [INSPIRE].
G. Compère, J. Long and M. Riegler, Invariance of Unruh and Hawking radiation under matter-induced supertranslations, JHEP 05 (2019) 053 [arXiv:1903.01812] [INSPIRE].
B.R. Majhi, Are non-vacuum states much relevant for retrieving shock wave memory of spacetime?, Phys. Lett. B 808 (2020) 135640.
R.Z. Ferreira and C. Heissenberg, Super-Hawking Radiation, JHEP 02 (2021) 038 [arXiv:2011.04688] [INSPIRE].
F. Dowker, Useless Qubits in ‘Relativistic Quantum Information’, arXiv:1111.2308 [INSPIRE].
A.M. Kubicki, H. Westman and J. Leon, Localization for Dirac fermions, arXiv:1606.03286 [INSPIRE].
D. Colosi and C. Rovelli, What is a particle?, Class. Quant. Grav. 26 (2009) 025002 [gr-qc/0409054] [INSPIRE].
A.L. Licht, Strict localization, J. Math. Phys. 4 (1963) 1443.
E. Witten, APS medal for exceptional achievement in research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys. 90 (2018) 045003.
A. Strohmaier, R. Verch and M. Wollenberg, Microlocal analysis of quantum fields on curved space-times: Analytic wavefront sets and Reeh-Schlieder theorems, J. Math. Phys. 43 (2002) 5514 [math-ph/0202003] [INSPIRE].
J. De Ramón, L.J. Garay and E. Martín-Martínez, Direct measurement of the two-point function in quantum fields, Phys. Rev. D 98 (2018) 105011 [arXiv:1807.00013] [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
B.S. DeWitt, Quantum gravity: the new synthesis, in General Relativity: An Einstein centenary survey, S.W. Hawking and W. Israel, eds., Cambridge University Press (1979), pp. 680–745.
A. Pozas-Kerstjens and E. Martín-Martínez, Entanglement harvesting from the electromagnetic vacuum with hydrogenlike atoms, Phys. Rev. D 94 (2016) 064074 [arXiv:1605.07180] [INSPIRE].
R. Lopp and E. Martín-Martínez, Quantum delocalization, gauge, and quantum optics: Light-matter interaction in relativistic quantum information, Phys. Rev. A 103 (2021) 013703 [arXiv:2008.12785] [INSPIRE].
E. Martín-Martínez, A.R.H. Smith and D.R. Terno, Spacetime structure and vacuum entanglement, Phys. Rev. D 93 (2016) 044001 [arXiv:1507.02688] [INSPIRE].
Q. Xu, S.A. Ahmad and A.R.H. Smith, Gravitational waves affect vacuum entanglement, Phys. Rev. D 102 (2020) 065019 [arXiv:2006.11301] [INSPIRE].
G.L. Ver Steeg and N.C. Menicucci, Entangling power of an expanding universe, Phys. Rev. D 79 (2009) 044027 [arXiv:0711.3066] [INSPIRE].
E. Tjoa and R.B. Mann, Harvesting correlations in Schwarzschild and collapsing shell spacetimes, JHEP 08 (2020) 155 [arXiv:2007.02955] [INSPIRE].
R. de León Ardón, Semiclassical p-branes in hyperbolic space, Class. Quant. Grav. 37 (2020) 237001 [arXiv:2007.03591] [INSPIRE].
L.J. Henderson, R.A. Hennigar, R.B. Mann, A.R.H. Smith and J. Zhang, Entangling detectors in anti-de Sitter space, JHEP 05 (2019) 178 [arXiv:1809.06862] [INSPIRE].
W. Cong, E. Tjoa and R.B. Mann, Entanglement Harvesting with Moving Mirrors, JHEP 06 (2019) 021 [Erratum ibid. 07 (2019) 051] [arXiv:1810.07359] [INSPIRE].
W. Cong, J. Bičák, D. Kubizňák and R.B. Mann, Quantum Detection of Inertial Frame Dragging, Phys. Rev. D 103 (2021) 024027 [arXiv:2009.10584] [INSPIRE].
L.J. Garay, E. Martín-Martínez and J. de Ramón, Thermalization of particle detectors: The Unruh effect and its reverse, Phys. Rev. D 94 (2016) 104048 [arXiv:1607.05287] [INSPIRE].
W.G. Brenna, R.B. Mann and E. Martín-Martínez, Anti-Unruh Phenomena, Phys. Lett. B 757 (2016) 307 [arXiv:1504.02468] [INSPIRE].
L.J. Henderson, R.A. Hennigar, R.B. Mann, A.R. Smith and J. Zhang, Anti-Hawking phenomena, Phys. Lett. B 809 (2020) 135732.
L. de Souza Campos and C. Dappiaggi, The anti-Hawking effect on a BTZ black hole with robin boundary conditions, Phys. Lett. B 816 (2021) 136198.
A. Pozas-Kerstjens and E. Martín-Martínez, Harvesting correlations from the quantum vacuum, Phys. Rev. D 92 (2015) 064042 [arXiv:1506.03081] [INSPIRE].
A. Valentini, Non-local correlations in quantum electrodynamics, Phys. Lett. A 153 (1991) 321.
B. Reznik, Entanglement from the vacuum, Found. Phys. 33 (2003) 167 [quant-ph/0212044] [INSPIRE].
E.-A. Kontou and K. Sanders, Energy conditions in general relativity and quantum field theory, Class. Quant. Grav. 37 (2020) 193001 [arXiv:2003.01815] [INSPIRE].
E. Curiel, A primer on energy conditions, Einstein Stud. 13 (2017) 43.
A. Vilenkin, Gravitational Field of Vacuum Domain Walls, Phys. Lett. B 133 (1983) 177 [INSPIRE].
C.O. Lousto and N.G. Sanchez, Gravitational shock waves generated by extended sources: Ultrarelativistic cosmic strings, monopoles and domain walls, Nucl. Phys. B 355 (1991) 231 [INSPIRE].
C. Barrabes, P.A. Hogan and W. Israel, The Aichelburg-Sexl boost of domain walls and cosmic strings, Phys. Rev. D 66 (2002) 025032 [gr-qc/0206021] [INSPIRE].
R. Penrose, The geometry of impulsive gravitational waves, in General relativity: Papers in honour of J.L. Synge, L. O’Raifeartaigh ed., Clarendon Press, Oxford, U.K. (1972).
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
V. Ferrari, P. Pendenza and G. Veneziano, Beamlike Gravitational Waves and Their Geodesics, Gen. Rel. Grav. 20 (1988) 1185 [INSPIRE].
H. Balasin, Geodesics for impulsive gravitational waves and the multiplication of distributions, Class. Quant. Grav. 14 (1997) 455 [gr-qc/9607076] [INSPIRE].
M. Kunzinger and R. Steinbauer, A Rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves, J. Math. Phys. 40 (1999) 1479 [gr-qc/9806009] [INSPIRE].
G.W. Gibbons, Quantized Fields Propagating in Plane Wave Space-Times, Commun. Math. Phys. 45 (1975) 191 [INSPIRE].
J. Garriga and E. Verdaguer, Scattering of quantum particles by gravitational plane waves, Phys. Rev. D 43 (1991) 391 [INSPIRE].
C. Klimčík, Quantum Field Theory in Gravitational Shock Wave Background, Phys. Lett. B 208 (1988) 373 [INSPIRE].
I. Agullo and A. Ashtekar, Unitarity and ultraviolet regularity in cosmology, Phys. Rev. D 91 (2015) 124010 [arXiv:1503.03407] [INSPIRE].
S.J. Summers and R. Werner, The vacuum violates Bell’s inequalities, Phys. Lett. A 110 (1985) 257.
S.J. Summers and R. Werner, Bell’s Inequalities and Quantum Field Theory. 1. General Setting, J. Math. Phys. 28 (1987) 2440 [INSPIRE].
E. Martín-Martínez, T.R. Perche and B. de S.L. Torres, General Relativistic Quantum Optics: Finite-size particle detector models in curved spacetimes, Phys. Rev. D 101 (2020) 045017 [arXiv:2001.10010] [INSPIRE].
E. Martín-Martínez, T.R. Perche and B.d.S.L. Torres, Broken covariance of particle detector models in relativistic quantum information, Phys. Rev. D 103 (2021) 025007 [arXiv:2006.12514] [INSPIRE].
W.K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80 (1998) 2245 [quant-ph/9709029] [INSPIRE].
M. Horodecki, P. Horodecki and R. Horodecki, On the necessary and sufficient conditions for separability of mixed quantum states, Phys. Lett. A 223 (1996) 1 [quant-ph/9605038] [INSPIRE].
G. Vidal and R.F. Werner, Computable measure of entanglement, Phys. Rev. A 65 (2002) 032314 [quant-ph/0102117] [INSPIRE].
M.D. Schwartz, Quantum field theory and the standard model, Cambridge University Press (2014).
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: 2105.09337
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
Gray, F., Kubizňák, D., May, T. et al. Quantum imprints of gravitational shockwaves. J. High Energ. Phys. 2021, 54 (2021). https://doi.org/10.1007/JHEP11(2021)054
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2021)054