Geometric Bounds on Metric Communication Channels in Static Spherically Symmetric Spacetimes

Abstract

We examine a restricted family of static, spherically symmetric zero-redshift geometries that act as localized radial deformations of the flat radial metric. The motivation is simple: for radial null curves between two fixed areal-radius spheres, the same coefficient that changes the radial line element also changes the coordinate travel time. In this setting the metric coefficient a(r) determines the null latency, while Einstein's equations determine the effective anisotropic source needed to support the profile. We derive the corresponding density and pressure components and show that the radial null energy condition reduces to a derivative condition on a(r). It follows that any nontrivial localized profile which returns to the flat radial value at both endpoints and satisfies a(r) < 1 somewhere inside the interval must violate the radial null energy condition. We also derive a quantitative bound showing that the latency gain is controlled by the integrated radial null-energy-condition violation. The geometric analysis is supplemented by a deliberately model-dependent communication diagnostic: Shannon-type quantities are used only to compare profiles after their effective source structure has been fixed. Numerical examples and inverse-designed profiles illustrate how latency gain, source magnitude, and exoticity trade off against each other, without removing the null-energy obstruction.