1/r potential in higher dimensions

Abstract

In Einstein gravity, gravitational potential goes as 1/r d−3 in d non-compactified spacetime dimensions, which assumes the familiar 1/r form in four dimensions. On the other hand, it goes as 1/r α , with α = (d −2m −1)/m, in pure Lovelock gravity involving only one mth order term of the Lovelock polynomial in the gravitational action. The latter offers a novel possibility of having 1/r potential for the noncompactified dimension spectrum given by d = 3m+1. Thus it turns out that in the two prototype gravitational settings of isolated objects, like black holes and the universe as a whole -cosmological models, the Einstein gravity in four and mth order pure Lovelock gravity in 3m + 1 dimensions behave in a similar fashion as far as gravitational interactions are considered. However propagation of gravitational waves (or the number of degrees of freedom) does indeed serve as a discriminator because it has two polarizations only in four dimensions.

How do rotating black holes form in higher dimensions?

“…Since for bound orbits for pure GB, the allowed range is 6 ≤ D ≤ 8, the behavior of V eff would be so for D = 7, 8, as well. In particular, for D = 7 (in general for D = 3N + 1 [7]), potential has the same fall off, 1/r as for the Kerr black hole, and hence, the effective potential would be the same as for the Kerr metric in four dimension. However, for D ≥ 9, there would occur only a maximum indicating absence of bound orbits and consequently also of stable circular orbits (see Fig.…”

Circular orbits around higher dimensional Einstein and pure Gauss-Bonnet rotating black holes

“…In particular for D = 7 (in general for D = 3N + 1 [14]), potential has the same fall off, 1/r as for the Kerr black hole, and hence the effective potential would be the same as for the Kerr metric in four dimension. However for D ≥ 9, there would occur only a maximum indicating absence of bound orbits and consequently also of stable circular orbits (see Fig.…”

Strong cosmic censorship conjecture in higher curvature gravity

“…Thus one can ask whether the solution can be extended beyond the Cauchy horizon. Our second example involves the study of pure lovelock black hole solutions [41][42][43][44][45][46] in dimensions d ≥ (3k + 1), with 'k' being the lovelock order, i.e., k = 1 is the pure Einstein Gravity, while k = 2 is pure Gauss-Bonnet Gravity and so on. We would like to emphasize that, although the pure lovelock solutions may not represent a physical black hole, it does provide a natural platform to study the effect of higher curvature terms to the strong cosmic censorship conjecture, which is the ultimate aim of our work.…”