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We study the metric corresponding to a three-dimensional coset space SO(4)/SO(3) in the lattice setting. With the use of three integers n 1 , n 2 , and n 3 , and a length scale, l μ , the continuous metric is transformed into a discrete space. The numerical outcomes are compared with the continuous ones. The singularity of the black hole is explored and different domains are studied. [ABSTRACT FROM AUTHOR]

We study numerically the curvature tensor in a three-dimensional discrete space. Starting from the continuous metric of a three-sphere, we transformed it into a discrete space using three integers n 1 , n 2 , and n 3 . The numerical results are compared with the expected values in the continuous limit. We show that as the number of cells in the lattice increases, the continuous limit is recovered. [ABSTRACT FROM AUTHOR]

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]