The Curved Space is The Electrified Flat Space

TL;DR

This paper demonstrates how electric fields can induce curvature in space by affecting string and brane perturbations, showing a transition from flat to curved space as the electric field approaches a critical value.

Contribution

It reveals the direct role of electric fields in transforming flat space into curved space through perturbation analysis of strings and D-branes in supergravity backgrounds.

Findings

Perturbations diminish as electric field approaches critical value

Perturbations vanish in curved space regardless of electric field strength

Electric field influences the potential and stability of string configurations

Abstract

The responsibility of the electric field $E$ in the modification of the nature of the space is proved. We investigate the way the fundamental strings are related to supergravity background of D5-branes; i.e. once the endpoints of the D-strings are electrified the flat space becomes curved. We study the electrified relative and overall transverse perturbations of fuzzy funnel solutions of intersecting $(N,N_f)$-strings and D5-branes in flat and supergravity backgrounds respectively. As result the perturbations have a discontinuity which corresponds to a zero phase shift realizing Polchinski's open string Neumann boundary condition. And once the electric field $E$ is turned on in flat space these perturbations decrease and when $E$ is close to the critical value $\frac{1}{\lambda}$ the perturbations disappear forever and the string coupling becomes strong. At this stage the space is considered curved and the electric field is responsible for this effect. This phenomena is also enhanced by the behavior of the potential $V$ associated to the perturbations $\Phi$ on the funnel solutions under the influence of the electric field. The potential goes too fast to $-\infty$ when $E$ goes to the critical value $\frac{1}{\lambda}$ in flat space which looks like a kink to increase the velocity for $\Phi$ to disappear. But in curved space and close to the intersecting point we do not find any perturbation for all $E$ and there is no effect of $E$ on $V$ and this is a sign to the absence of the perturbation effects in supergravity background. This clarifies the existence of a relation between the electric field and the supergravity background.