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Discrete gravity

https://doi.org/10.1007/JHEP11(2021)013

Chamseddine, Ali H.; Mukhanov, Viatcheslav (November 2021, Journal of High Energy Physics)

A bstract We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of freedom per elementary volume. In such discrete spaces, each elementary cell is completely characterized by displacement operators connecting a cell to the neighboring cells and by the spin connection. We define the torsion and curvature of the discrete spaces and show that in the limiting case of vanishing elementary volume the standard results for the continuous curved differentiable manifolds are completely reproduced.
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Mimetic Hořava gravity

https://doi.org/10.1016/j.physletb.2019.134939

Chamseddine, Ali H.; Mukhanov, Viatcheslav; Russ, Tobias B. (November 2019, Physics Letters B)

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Black hole remnants

https://doi.org/10.1007/JHEP10(2019)104

Chamseddine, Ali H.; Mukhanov, Viatcheslav; Russ, Tobias B. (October 2019, Journal of High Energy Physics)

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Asymptotically free mimetic gravity

https://doi.org/10.1140/epjc/s10052-019-7075-y

Chamseddine, Ali H.; Mukhanov, Viatcheslav; Russ, Tobias B. (July 2019, The European Physical Journal C)

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Non‐Flat Universes and Black Holes in Asymptotically Free Mimetic Gravity

https://doi.org/10.1002/prop.201900103

Chamseddine, Ali H.; Mukhanov, Viatcheslav; Russ, Tobias B. (December 2019, Fortschritte der Physik)

Abstract The recently proposed theory of “Asymptotically Free Mimetic Gravity” is extended to the general non‐homogeneous, spatially non‐flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non‐singular, bouncing modifications of spatially non‐flat Friedmann and Bianchi universes.
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