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[2] viXra:2610.0076 [pdf] submitted on 2026-10-19 12:43:31
Authors: Holger Döring
Comments: 11 Pages.
Developed is a theoretical framework for localized, dynamic spacetime configurations, the definingcharacteristic of which is not primarily a spatial concentration of energy, but rather a locally alteredproper-time structure. The starting point is a self-coupled real scalar field whose energy-momentumtensor generates a spherically symmetric spacetime curvature via the Einstein equations. The localproper time is determined by the time-dependent metric component (g tt ) .Examined then is bothstatic and oscillating configurations, demonstrating that a harmonic evolution of the scalar field—comprising odd harmonic s=s( ω ;3 ω ;5 ω ;...) —is naturally coupled to even harmonics ofh=h(0 ;2 ω ; 4 ω ;...) of the metric. This provides a mathematically precise foundation for anoscillating "time bubble." The frequently encountered ( N=2n+1) structure is identified here as aharmonic structure, rather than being interpreted as an established quantization of proper time.The resulting problem is a nonlinear, self-consistent eigenvalue problem for the scalar field and thespacetime metric. The existence, stability, lifespan, and potential discrete spectrum of such solutionsmust be investigated numerically. In particular, a possible Planck-scale quantization of proper timeis formulated as a testable spectral hypothesis.
Category: Quantum Gravity and String Theory
[1] viXra:2610.0022 [pdf] submitted on 2026-10-06 20:16:24
Authors: Charles Ba Oumar
Comments: 8 Pages.
This paper presents a Vector Gravitational Field Theory asymptotically equivalent to standard Minkowski spacetime in the limit of a classical vacuum. From such a theory we then derive a new definition of rest mass energy as well as an approximation of the quantum of gravitational action via a graviton particle of energy ℎ��proportional to the gravitational charge quantified by matter-energy density and compute solar system graviton energy ranges.
Category: Quantum Gravity and String Theory
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