TY - JOUR

T1 - Butterfly velocity in quadratic gravity

AU - Huang, Wung Hong

N1 - Publisher Copyright:
© 2018 IOP Publishing Ltd.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/9/7

Y1 - 2018/9/7

N2 - We present a systematic procedure of finding the shock wave equation in anisotropic spacetime of quadratic gravity with Lagrangian Λ = R + λ + αRμ vδ p Rμ vδ p+ βRμ vγRμ v + ΛR2 + λmatter. The general formula of the butterfly velocity is derived. We show that the shock wave equation in the planar, spherical or hyperbolic black hole spacetime of EinsteinGaussBonnet gravity is the same as that in Einstein gravity if the space is isotropic. We consider the modified AdS spacetime deformed by the leading correction of the quadratic curvatures and find that the fourth order derivative shock wave equation leads to two butterfly velocities if 4α+β < 0. We also show that the butterfly velocity in the D = 4 planar black hole is not corrected by the quadratic gravity if 4α+β = 0, which includes the R2 gravity. In general, the correction of butterfly velocity by the quadratic gravity may be positive or negative, depending on the values of α, β, γand temperature. We also investigate the butterfly velocity in the Gauss-Bonnet massive gravity.

AB - We present a systematic procedure of finding the shock wave equation in anisotropic spacetime of quadratic gravity with Lagrangian Λ = R + λ + αRμ vδ p Rμ vδ p+ βRμ vγRμ v + ΛR2 + λmatter. The general formula of the butterfly velocity is derived. We show that the shock wave equation in the planar, spherical or hyperbolic black hole spacetime of EinsteinGaussBonnet gravity is the same as that in Einstein gravity if the space is isotropic. We consider the modified AdS spacetime deformed by the leading correction of the quadratic curvatures and find that the fourth order derivative shock wave equation leads to two butterfly velocities if 4α+β < 0. We also show that the butterfly velocity in the D = 4 planar black hole is not corrected by the quadratic gravity if 4α+β = 0, which includes the R2 gravity. In general, the correction of butterfly velocity by the quadratic gravity may be positive or negative, depending on the values of α, β, γand temperature. We also investigate the butterfly velocity in the Gauss-Bonnet massive gravity.

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U2 - 10.1088/1361-6382/aadb32

DO - 10.1088/1361-6382/aadb32

M3 - Article

AN - SCOPUS:85053924913

VL - 35

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 19

M1 - 195004

ER -