Foundation Studies of the Curvature-Spacecraft Theory (I): Realization of Nonnegative-Energy Curvature Bubbles\\Explicit Construction of Ordinary-Matter Initial-Data Configurations and a Sharp Shaping Window}
Year: 2026
Type: preprint
Abstract: Traditional warp-driven configurations require negative energy to sustain a bubble-like spacetime; on time-symmetric initial data, this paper proves that ordinary matter satisfying the weak energy condition suffices to construct static curvature bubbles, and provides theoretical realization methods that construct the complete spacetime and the shell matter directly from the target triple (mass, texture, redshift), realizing a flat cabin in the interior. To this end, we establish the \textbf{Anyang Elliptic Constraint Mapping theory (AECM)}, a boundary encoding theory grown out of the constraint equations of general relativity (the elliptic sector of the 3+1 decomposition, which precedes evolution and must be satisfied before evolution can unfold): in the time-symmetric conformally flat sector, the constraint equations compress into a single Lichnerowicz equation, which under $u=\psi-1$ and $\sigma=\rho\psi^5/2$ becomes, verbatim, the Poisson equation of AECM (two names of the same equation). The exterior geometry is then uniquely determined from the boundary data of the diagnostic surface by elliptic development, and all global quantities are read out mode-by-mode along the Dirichlet-to-Neumann spectrum: \textbf{constraint is encoding; encoding precedes evolution}. This reveals two counterintuitive facts: first, Newton's structure survives exactly at the coding level (Einstein's nonlinearity compressed into a single algebraic factor $\sigma=\rho\psi^5/2$; the map from physical density to the external geometry remains a nonlinear fixed point); second, the shaping capacity depends only on the angular distribution of the source, independent of radial details (radial degeneracy theorem). The same spectral readout unifies a family of classical problems into corollaries: the explicit boundary versions of the positive mass and the charged positive mass ($M\ge|Q_e|$), the mode-by-mode pricing $4(\ell+2)$ of the Penrose texture deficit, the throat area correction $\kappa=-128/35$, the static-extension rigidity, and the CF--Bartnik mass. Along this framework, the static precursor receives a threefold verdict. \textbf{(i) Feasible}: the quadrupole moment ratio of WEC sources satisfies the universal window $[-\frac12,1]$ and the spectrally pure sharp window $[-\frac15,\frac25]$ (in the closure sense), saturated pointwise by the explicit extremal configuration $\sigma\propto3\cos^2\theta$ (thin-shell surface source; smooth volume sources approximate but never attain)\footnote{The moment ratio $\epsilon_\ell=a_\ell/(M_{\rm math}R^\ell)$ holds for the effective source $\sigma$; the window for the physical density $\rho$ follows in Corollary \ref{cor:rho-window} (normalized by $M_{\rm ADM}$, the same interval in the weak field).}; \textbf{(ii) Blocked}: the purely gravitational static extension of quadrupole texture inside the CF class is refuted by an explicit obstruction tensor (point value $1/3888$); \textbf{(iii) Existence and escape}: the spherically symmetric neutral bubble (full-spacetime WEC), the charged spherically symmetric family ($e/m\in[0,1]$), and the arbitrarily-shaped charged MP bubble (strictly Minkowski cabin, full-spacetime WEC/DEC) are all exact solutions. The endpoint of this paper is not abstract existence theorems, but \textbf{physical realizability}: constructive existence and realization methods. For each class of targets, this paper provides \textbf{constructive existence and realization methods}: the negative-frame locking theorem unifies all static flat-cabin bubbles into two branches of a conductor-potential structure (the mass function law $M_{\rm ADM}=f(N)C(\Sigma)$, $\ln(1/N)$ neutral, $1/N-1$ charged); the five-step construction algorithm builds, from the target triple (mass, texture, redshift), the complete spacetime and shell matter; unique when the shape is given, a family of equivalent realizations when only finitely many moments are given; the geometrically induced equation of state identifies the material of the shell; the realization-domain criterion delimits which targets are feasible. The constructive existence of the arbitrarily-shaped neutral cell is given directly by the negative-frame locking and the construction algorithm, \textbf{independent of any hypothetical existence theorem} (axisymmetric shapes are strict theorems; general shapes are numerically verified, \S19). The ship of the curvature bubble floats first at the static level; navigation is left to the follow-up series.
Author: Li, Peng
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204044764