Gravitational measurements in higher dimensions

TL;DR

This paper investigates gravitational phenomena in higher-dimensional spaces, considering non-commutative geometry effects, and explores how extra dimensions influence black hole properties, gravitational lensing, redshift, and time delay.

Contribution

It introduces a model of higher-dimensional black holes with non-commutative geometry, analyzing their observable effects and deriving bounds on extra dimension sizes.

Findings

Significant modifications in gravitational effects due to extra dimensions.

Black hole solutions interpolating between Schwarzschild and de-Sitter geometries.

Lower bounds on the size of extra dimensions and black hole formation mass.

Abstract

We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in higher dimensions with a source given by a static, spherically symmetric Gaussian distribution of mass. The resulting metric would describe a regular or curvature singularity free black hole in higher dimensions. The metric should smoothly interpolate between Schwarzschild geometry at large distance and de-Sitter spacetime at short distance. We will consider gravitational redshift, lensing, and time delay in each sector. It will be shown that, compared to the four-dimensional spacetime, there can be significant modifications due to the presence of extra dimensions and the non-commutative corrected black holes. Finally, we shall attempt to obtain a lower bound on the size of the extra dimensions and on the mass needed to form a black hole in different dimensions.