https://doi.org/10.1140/epjc/s10052-018-5546-1
Regular Article - Theoretical Physics
1/r potential in higher dimensions
1
Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata, 700032, India
2
IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune, 411 007, India
3
Center for Theoretical Physics, Jamia Millia Islamia, New Delhi, 110025, India
* e-mail: sumantac.physics@gmail.com
Received:
17
July
2017
Accepted:
13
January
2018
Published online:
29
January
2018
In Einstein gravity, gravitational potential goes as 
in d non-compactified spacetime dimensions, which assumes the familiar 1 / r form in four dimensions. On the other hand, it goes as 
, with 
, 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 
. 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 
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.
© The Author(s), 2018
