MG15 - Talk detail

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We explore a specific class of $F(Riem,\nabla)$ gravitational theories, called Non-Polynomial Gravities, which are able to give second order field equations (at least) for spherically symmetric and cosmological spacetimes, in four dimensions, thanks to the existence of algebraic identities among curvature tensors in these spacetimes. Non-singular black hole and cosmological solutions are found from specific models, in particular, we find the loop quantum cosmology bounce solution, the Poisson-Israel and the Balakin-Lemos-Zayats regular black holes. Therefore, these models violate both the singularity and Lovelock theorems, in the considered class of spacetimes. First,we will briefly introduce the conceptual issues arising from the existence of singularities, then review the different paths that have been explored to modify General Relativity in order to cure singularities, and the types of non-singular spacetimes emerging from these. Finally, in the main part of the talk, we will present some Non-Polynomial Gravity models, together with their non-singular solutions. See Int.J.Mod.Phys.D 27(3), 1830002 (2018), [arXiv:1712.03730] ; Galaxies, 5, 51 (2017) [arXiv:1708.08667].

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From a specific F(Riem,D) non-polynomial theory of gravity in a power series form, F(Riem,D)= \sum_{i=0}^{m} L^{2i} F_i(Riem,D), where F_0 = R, we show that for each order of the series, m>1, the unique spherically symmetric solution is a rational regular black hole with Schwarzschild asymptotic behaviour. For a suitable choice of coupling constants, and for all m>1, it is possible to impose a common vacuum state (M=0) describing an extremal regular black hole of radius L (and Minkowski spacetime in the limit of vanishing parameter L), which can be seen as a realization of the semi-classical Bronstein argument. These requirements (regularity, Schwarzschild asymptotics, extremal vacuum) result in an interesting behaviour for the inner horizon surface gravity and for the phenomenology of the regular solutions. As the number m of high energy corrections grows, the inner horizon surface gravity decreases, meaning that within this setup, the effect of mass inflation can be cancelled by considering a very large number of radiative corrections.

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