Universal features of gravity and higher dimensions

TL;DR

This paper explores universal features of gravity in higher dimensions, revealing that certain properties like the form of gravitational dynamics, asymptotic solutions, and interior solutions are consistent across all dimensions greater than or equal to four.

Contribution

It identifies and characterizes features of gravity that remain invariant in all higher dimensions, linking Lovelock gravity, asymptotic behavior, and interior solutions.

Findings

Gravitational dynamics derive from the Bianchi derivative of a polynomial in Riemann curvature.

All $ abla$-vacuum solutions asymptotically match the $d$-dimensional Einstein solution.

Gravity inside a uniform density sphere is dimension-independent, matching the Schwarzschild interior solution.

Abstract

We study some universal features of gravity in higher dimensions and by universal we mean a feature that remains true in all dimensions $\geq4$. They include: (a) the gravitational dynamics always follows from the Bianchi derivative of a homogeneous polynomial in Riemann curvature and it thereby characterizes the Lovelock polynomial action, (b) all the $\Lambda$-vacuum solutions of the Einstein-Lovelock as well as pure Lovelock equation have the same asymptotic limit agreeing with the $d$ dimensional Einstein solution and (c) gravity inside a uniform density sphere is independent of the spacetime dimension and it is always given by the Schwarzschild interior solution.