Under the assumption that a UV theory does not display superluminal behavior, we ask what constraints on superluminality are satisfied in the effective field theory (EFT). We study two examples of effective theories: quantum electrodynamics (QED) coupled to gravity after the electron is integrated out, and the flat-space galileon. The first is realized in nature, the second is more speculative, but they both exhibit apparent superluminality around non-trivial backgrounds. In the QED case, we attempt, and fail, to find backgrounds for which the superluminal signal advance can be made larger than the putative resolving power of the EFT. In contrast, in the galileon case it is easy to find such backgrounds, indicating that if the UV completion of the galileon is (sub)luminal, quantum corrections must become important at distance scales of order the Vainshtein radius of the background configuration, much larger than the naive EFT strong coupling distance scale. Such corrections would be reminiscent of the non-perturbative Schwarzschild scale quantum effects that are expected to resolve the black hole information problem. Finally, a byproduct of our analysis is a calculation of how perturbative quantum effects alter charged Reissner-Nordstrom black holes.
J. Friedman et al., Cauchy problem in space-times with closed timelike curves, Phys. Rev. D 42 (1990) 1915 [INSPIRE].
I.T. Drummond and S.J. Hathrell, QED Vacuum Polarization in a Background Gravitational Field and Its Effect on the Velocity of Photons, Phys. Rev. D 22 (1980) 343 [INSPIRE].
G. Preti, A note on the geometrical-optics solution to the Maxwell tensor wave equation in curved spacetime, Nucl. Phys. B 834 (2010) 390 [INSPIRE].
J.Z. Simon, Higher Derivative Lagrangians, Nonlocality, Problems and Solutions, Phys. Rev. D 41 (1990) 3720 [INSPIRE].
X. Jaen, J. Llosa and A. Molina, A reduction of order two for infinite order lagrangians, Phys. Rev. D 34 (1986) 2302 [INSPIRE].
L. Brillouin, Wave Propagation and Group Velocity, Series in Pure & Applied Physics), Elsevier (1960).
P. Milonni, Fast Light, Slow Light and Left-Handed Light, Series in Optics and Optoelectronics, CRC Press (2004).
A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [INSPIRE].
S.M. Carroll, Spacetime and geometry: An introduction to general relativity, Addison Wesley (2004).
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, San Francisco, U.S.A. (1973).
R. Penrose, On Schwarzschild Causality — A Problem for “Lorentz Covariant” General Relativity, in Essays in General Relativity: A Festschrift for Abraham Taub, Academic Press (1980).
S.D. Majumdar, A class of exact solutions of Einstein's field equations, Phys. Rev. 72 (1947) 390 [INSPIRE].
A. Papaetrou, A static solution of the equations of the gravitational field for an arbitrary charge distribution, Proc. Roy. Irish Acad. A 51 (1947) 191 [INSPIRE].
J.B. Hartle and S.W. Hawking, Solutions of the Einstein-Maxwell equations with many black holes, Commun. Math. Phys. 26 (1972) 87 [INSPIRE].
M.D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, (2014).
A. Kamenev, Field Theory of Non-Equilibrium Systems, Cambridge University Press, (2011).
M.J. Duff, Quantum Tree Graphs and the Schwarzschild Solution, Phys. Rev. D 7 (1973) 2317 [INSPIRE].
M.J. Duff, Quantum corrections to the Schwarzschild solution, Phys. Rev. D 9 (1974) 1837 [INSPIRE].
G.W. Gibbons, Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes, Commun. Math. Phys. 44 (1975) 245 [INSPIRE].
G. Goon and K. Hinterbichler, in preparation.
G. ’t Hooft and M.J.G. Veltman, One loop divergencies in the theory of gravitation, Annales Poincare Phys. Theor. A 20 (1974) 69.
M.H. Goro and A. Sagnotti, The Ultraviolet Behavior of Einstein Gravity, Nucl. Phys. B 266 (1986) 709 [INSPIRE].
D.M. Capper, M.J. Duff and L. Halpern, Photon corrections to the graviton propagator, Phys. Rev. D 10 (1974) 461 [INSPIRE].
J.F. Donoghue, B.R. Holstein, B. Garbrecht and T. Konstandin, Quantum corrections to the Reissner-Nordstrom and Kerr-Newman metrics, Phys. Lett. B 529 (2002) 132 [Erratum ibid. B 612 (2005) 311] [hep-th/0112237] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum corrections to the Schwarzschild and Kerr metrics, Phys. Rev. D 68 (2003) 084005 [Erratum ibid. D 71 (2005) 069904] [hep-th/0211071] [INSPIRE].
L.F. Abbott, Introduction to the Background Field Method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].
A.O. Barvinsky and G.A. Vilkovisky, The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
N.K. Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl. Phys. B 101 (1975) 173 [INSPIRE].
R. Fukuda and T. Kugo, Gauge Invariance in the Effective Action and Potential, Phys. Rev. D 13 (1976) 3469 [INSPIRE].
I.J.R. Aitchison and C.M. Fraser, Gauge Invariance and the Effective Potential, Annals Phys. 156 (1984) 1 [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum gravitational corrections to the nonrelativistic scattering potential of two masses, Phys. Rev. D 67 (2003) 084033 [Erratum ibid. D 71 (2005) 069903] [hep-th/0211072] [INSPIRE].
S.L. Adler, Photon splitting and photon dispersion in a strong magnetic field, Annals Phys. 67 (1971) 599 [INSPIRE].
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.
ArXiv ePrint: 1609.00723
About this article
Cite this article
Goon, G., Hinterbichler, K. Superluminality, black holes and EFT. J. High Energ. Phys. 2017, 134 (2017). https://doi.org/10.1007/JHEP02(2017)134