Butterfly Velocity in Quadratic Gravity · arXivDesk
1804.05527Apr 16, 201828 pages. Add the investigation of the butterfly velocity in the Gauss-Bonnet massive gravity. Add more discussions about AdS/CFT. Rewrite in compact form. Typos corrected
We present a systematic procedure of finding the shock wave equation in anisotropic spacetime of quadratic gravity with Lagrangian L=R+Λ+αRμνσρRμνσρ+βRμνRμν+γR2+Lmatter
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. 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 Einstein-Gauss-Bonnet gravity is the same as that in Einstein gravity if 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 a 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, depends on the values of
α
,
β
,
γ
and temperature. We also investigate the butterfly velocity in the Gauss-Bonnet massive gravity.