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Probing pure Lovelock gravity by Nariai and Bertotti-Robinson solutions · Around

2012

Probing pure Lovelock gravity by Nariai and Bertotti-Robinson solutions

Dadhich, Naresh, Pons, Josep M.

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The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $\Lambda$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$.

We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension.
We also consider these solutions for the conventional setting of Einstein-Gauss-Bonnet gravity.

Built on

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J. F. Plebanski and S. Hacyan, “Some excepcional electrovac type D metrics with cosmological constant”, J. Math. Phys. 20
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Then

N. Dadhich, “Characterization of the Lovelock gravity by Bianchi derivative,” Pramana 74
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N. Dadhich, “On Lovelock vacuum solution,” Math. Today 26
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2011
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H. Maeda, S. Willison and S. Ray, “Lovelock black holes with maximally symmetric horizons,” Class. Quant. Grav. 28
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N. Dadhich, S. G. Ghosh and S. Jhingan, “The Lovelock gravity in the critical spacetime dimension,” Phys. Lett. B 711
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N. Dadhich, J. M. Pons and K. Prabhu, “Thermodynamical universality of the Lovelock black holes,” Gen. Rel. Grav. 44
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