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We construct quartic quasitopological gravity, a theory of gravity containing terms quartic in the curvature that yields second order differential equations in the spherically symmetric case. Up to a term proportional to the quartic term in Lovelock gravity we find a unique solution for this quartic case, valid in any dimensionality larger than 4 except 8. This case is the highest degree of curvature coupling for which explicit black hole solutions can be constructed, and we obtain and analyze the various black hole solutions that emerge from the field equations in (n + 1) dimensions.We discuss the thermodynamics of these black holes and compute their entropy as a function of the horizon radius. We then make some general remarks about K-th order quasitopological gravity, and point out that the basic structure of the solutions will be the same in any dimensionality for general K apart from particular cases. *

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.

We consider the minimal area of the entanglement wedge cross section (EWCS) in Einstein gravity. In the context of holography, it is proposed that this quantity is dual to different information measures, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Motivated by these proposals, we examine in detail the low and high temperature corrections to this quantity and show that it obeys the area law even in the finite temperature. We also study EWCS in nonrelativistic field theories with nontrivial Lifshitz and hyperscaling violating exponents. The resultant EWCS is an increasing function of the dynamical exponent due to the enhancement of spatial correlations between subregions for larger values of z. We find that EWCS is monotonically decreasing as the hyperscaling violating exponent increases. We also obtain this quantity for an entangling region with singular boundary in a three dimensional field theory and find a universal contribution where the coefficient depends on the central charge. Finally, we verify that for higher dimensional singular regions the corresponding EWCS obeys the area law.where G N is the Newton constant and Γ A is a codimension-2, spacelike minimal hypersurface in the bulk spacetime, anchored to the asymptotic boundary such that ∂Γ A = ∂A (see figure 1). The RT proposal which passes a variety of consistency tests, generalizes to time dependent case [2] and higher derivative theories of gravity [3][4][5][6]. Using these prescriptions, the correlation of several disconnected components can also be considered. In particular when the entangling region is made by two disjoint spatial components, an important quantity to study is the holographic mutual