Configurational Entropy and Newton's Law in Double Sine‐Gordon Braneworlds.

The Shannon‐like entropic measure of spatially localized functions for a 5D braneworld generated by a double sine‐Gordon (DSG) potential is evaluated. The differential configurational entropy (DCE) has been shown in several recent works to be a configurational informational measure (CIM) that selects critical points and brings out phase transitions in confined energy models with arbitrary parameters. The DSG scenario is selected because it presents an energy‐degenerate spatially localized profile where the solutions to the scalar field demonstrate critical behavior that is only a result of geometrical effects. As is shown, the DCE evaluation provides a method for predicting the existence of a transition between the phases of the domain wall solutions. Moreover, the entropic measure reveals information about the model that is capable of describing the phase sector where resonance modes on the massive spectra of the graviton is obtained. The graviton resonance lifetimes are related to the existence of scales on which 4D gravity is recovered. Thus, the critical points defined by the CIMs with the existence of resonances and their lifetimes are correlated. To extend the research regarding this system, the corrections to Newton's law coming from the graviton modes are calculated. [ABSTRACT FROM AUTHOR]