We present an analytic solution of a Vaidya-charged black hole with a hyperscaling violating factor in an Einstein-Maxwell-dilaton model, where the scalar potential plays a key role in the existence of the solution. By making use of this result, we study the process of thermalization after a global quench in a theory which its gravitational description is provided by the resultant solution in the case of zero charge. In particular, we probe the system by entanglement entropy and show that it exhibits certain scaling behaviors during the process.
Using "complexity=action" proposal we study complexity growth of certain gravitational theories containing higher derivative terms. These include critical gravity in diverse dimensions. One observes that the complexity growth for neutral black holes saturates the proposed bound when the results are written in terms of physical quantities of the model. We will also study effects of shock wave to the complexity growth where we find that the presence of massive spin-2 mode slows down the rate of growth.
Using "complexity=action" proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.
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