RLMT: Do Shortcuts Through the R-Direction Exist? Constraints from GW170817 and the Layered Expansion of Vol. XLI-L

Abstract

If four-dimensional spacetime is a projection from a higher-dimensional manifold, signals that travel through the extra direction could arrive before light confined to four dimensions. R-layer Mode Theory (RLMT) contains such a direction, the layer coordinate R with five-dimensional gravity. We ask whether it provides shortcuts. (1) If the four-dimensional metric of every layer is Lorentz invariant, no bulk path can beat light on the brane; a shortcut requires asymmetric warping, n(R)/a(R) > 1, i.e. gravitational Lorentz violation as seen from the brane.(2) In the geometric-optics regime, GW170817 bounds the asymmetry of a layer at depth R0 by ε ≲ (2R0 + c·1.74 s)/D, from 4×10⁻¹⁶ at 1000 km to 5×10⁻⁵ at 1 kpc. In the zero-mode regime relevant for curvature radii allowed by short-range gravity tests, the bound is |c_T − 1| ≲ 10⁻¹⁵ on the profile-weighted asymmetry.(3) Either way, the largest Earth–Mars time saving compatible with GW170817 is about 10⁻¹² s.(4) Read as asymmetric warping, the layer-dependent expansion rates of RLMT Vol. XLI-L would let the gravitational waves of GW170817 arrive 3×10⁴–7×10⁴ years early unless the faster layers lie kiloparsecs deep in R, which is incompatible with warped localization of gravity at the micrometre scale. The Vol. XLI-L picture survives only if gravity does not propagate through its outer layers; this is recorded as a correction. Together with the companion paper on preferred foliations (doi:10.5281/zenodo.23274007), this closes both routes considered for faster-than-light information transfer in RLMT. Numerical scripts are included.