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^{alpha }, with alpha =(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 non-compactified 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.
Highlights
Lanczos-Lovelock gravity is important for various reasons
Pure Lovelock theories, i.e., a single term in the Lovelock polynomial, exhibit very interesting features. These include – (a) there is a close connection between pure Lovelock and dimensionally continued black holes [15,16], (b) gravity is kinematic in all critical d = 2m +1 dimensions, i.e., vacuum is pure Lovelock flat [17], (c) bound orbits exist for a given m in all 2m +1 < d < 4m +1 dimensions, in contrast, for Einstein gravity they do so only in four dimensions [18] and (d) equipartition of gravitational and non
At least, whether from a gravitational viewpoint we may as well be living in a higher dimensional spacetime rather than the usual four with gravity being described by pure Lovelock instead of Einstein gravity, is the question we wish to pose and wonder about in this note
Summary
Lanczos-Lovelock gravity is important for various reasons. It is generally believed that Einstein-Hilbert action is an effective action, valid at small enough energy (or large length) scales. Further thermodynamic interpretation of Einstein’s equations generalize in a straightforward and natural but non-trivial manner to Lanczos-Lovelock gravity. Pure Lovelock theories, i.e., a single term in the Lovelock polynomial, exhibit very interesting features These include – (a) there is a close connection between pure Lovelock and dimensionally continued black holes [15,16], (b) gravity is kinematic in all critical d = 2m +1 dimensions, i.e., vacuum is pure Lovelock flat [17], (c) bound orbits exist for a given m in all 2m +1 < d < 4m +1 dimensions, in contrast, for Einstein gravity they do so only in four dimensions [18] and (d) equipartition of gravitational and non-
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
