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We consider mimetic Horava gravity, where the scalar field of mimetic gravity was used in the construction of diffeomorphism invariant models reducing to Horava gravity in the synchronous gauge. It will be shown that the gravitational action with the addition of the Gibbons–Hawking–York term and the mimetic Horava action are equivalent for manifolds whose topology is R × Σ , where Σ is a three-dimensional hypersurface; otherwise, the mimetic Horava action does not contain any surface terms. [ABSTRACT FROM AUTHOR]

We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers, while in the second we consider the case where one of the coordinates is ignorable. The numerical results of both cases are then compared with the expected values in the continuous limit as the number of cells of the lattice becomes very large. [ABSTRACT FROM AUTHOR]