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We studied the upper bounds of the holographic entanglement entropy growthrate for thermofield double (TFD) states. By comparing the cases of vacuum AdSand charged AdS black holes, we conjecture: for all static planar orspherically symmetric asymptotically Schwarzschild-AdS black holes of same massdensity or entropy density, the vacuum AdS black hole gives the maximumentanglement entropy growth rate. We gave proofs by assuming dominant energycondition. We also considered the AdS black hole spacetime with real scalarfields case, where the scalar fields violate the dominant energy condition andthe bulk geometry is not asymptotically Schwarzschild-AdS. Numerical resultsshow that this case vacuum black hole still has maximal growth rate if we fixedentropy. However, in the case of fixed energy, vacuum case has maximal growthrate of entanglement entropy only under standard quantization scheme.

Upper bounds of holographic entanglement entropy growth rate for thermofield double states