A five-dimensional Schwarzschild-like solution

TL;DR

This paper presents a new five-dimensional Schwarzschild-like solution to Einstein's equations, highlighting differences from the four-dimensional case while maintaining similar geodesic behavior in observable regions.

Contribution

It introduces a novel five-dimensional static, spherically symmetric solution extending the Schwarzschild solution, with unique features and comparable geodesic properties in accessible regions.

Findings

The solution differs from the 4D Schwarzschild in certain aspects.

Geodesics in the new solution are similar to the 4D case in observable regions.

The solution advances understanding of higher-dimensional gravity models.

Abstract

In recent years, interest in extra dimensions has experienced a dramatic increase. A common practice has been to look for higher-dimensional generalizations of four-dimensional solutions to the Einstein equations. In this vein, we have found a static, spherically symmetric solution to the 5-d Einstein equations. Certain aspects of this solution are very different from the 4-d Schwarzschild solution. However, in observationally accessible regions, the geodesics of the two solutions are essentially the same.