Geometric Emergence and Scalar Modes in Vacuum Scalar-Field Gravity
Geometric Emergence and Scalar Modes in Vacuum Scalar-Field Gravity
Li Xiaoyun1
作者信息
- 1. The Chinese University of Hong Kong, Shenzhen
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摘要
We present a gravitational framework rooted in a cosmic vacuum scalar field \(\phi\), where the energy relation \(E = m\phi\) and the field equation \(\square(\phi^{2}) = 0\) define the dynamics. In static spherically symmetric configurations, the Schwarzschild metric emerges geometrically, recovering the classical tests of general relativity. For rotating sources, the non-commutativity of Lorentz transformations along different directions naturally incorporates angular momentum, yielding the Kerr metric in the weak-field limit and reproducing frame-dragging effects relevant to astrophysical black holes such as Sgr A* and M87*. Linear perturbations \(\delta\phi\) propagate as massless waves and source purely transverse breathing modes in gravitational waves without longitudinal components, offering a polarization signature distinct from general relativity and general scalar-tensor theories. In unequal-mass binary systems, these modes may give rise to scalar dipole radiation, providing observational targets for future space-borne detectors (LISA, TianQin, Taiji) and pulsar timing arrays. On cosmological scales, the background field \(\phi_{0}(t)\) evolves consistently with dark energy dynamics, while the coupling of gravity exclusively to spatial gradients of \(\phi\) decouples vacuum energy from gravitational sources, offering a new perspective on the cosmological constant problem. This framework unifies the description of local gravity, rotating compact objects, gravitational-wave polarization, and cosmic expansion, with testable predictions across multiple astrophysical and cosmological windows.
Abstract
We present a unified framework for gravitational and gauge interactions based on a cosmic vacuum scalar field $\phi$. The theory begins from a single constructive hypothesis---the simplest action coupling a particle to the vacuum field---and connects the origin of gravitational and gauge interactions through the core mechanism of ``non-integrability mandating the introduction of compensation fields.''In a static spherically symmetric configuration, the vacuum field distribution is obtained by solving the field equation. The local clock rate and spatial scale are anchored via energy scaling relations, which rigorously yields the Schwarzschild metric without presupposing the Einstein field equations. For rotating sources, the non-integrability of the Lorentz group activates the fiber bundle connection construction theorem, enforcing the introduction of a frame and spin connection as compensation fields. Their low-energy dynamics are locked by symmetry constraints to the Einstein-Hilbert action, and the Kerr metric is derived as the stationary axisymmetric vacuum solution. Furthermore, a U-field action describing rotational gravitomagnetic dynamics is constructed, leading to the following unique, parameter-free, testable predictions.Scalar gravitational waves exist exclusively as quadrupolar longitudinal modes. The polarization tensor is rigidly locked to a pure longitudinal mode, massless, coexisting with the general relativistic tensor modes with strictly synchronous timing. The amplitude ratio depends solely on the spatial orientation of the source. In extreme-mass-ratio inspiral systems, the combined effect of the rotating source's quadrupole moment deviation and scalar longitudinal mode radiation induces a gravitational wave phase offset of tens of thousands of radians, far exceeding the distinguishability threshold, which can be directly tested by space-based gravitational wave detectors. Black hole thermodynamic entropy acquires a constant correction independent of the black hole mass, providing a cutoff condition for the endpoint of primordial black hole evaporation; the remnant constitutes a natural dark matter candidate. On cosmological scales, gravity originates exclusively from the spatial gradient of the vacuum field; a uniform background produces no gravitational acceleration, offering a new perspective on the cosmological constant problem.关键词
vacuum scalar field/equivalence principle/Schwarzschild metric/Kerr metric/scalar gravitational waves/breathing mode/geometric emergence/cosmological constant problemKey words
vacuum scalar field/equivalence principle/emergent spacetime geometry/Schwarzschild metric/longitudinal gravitational wave/cosmological constant problem/black hole thermodynamics/dark matter引用本文复制引用
Li Xiaoyun.Geometric Emergence and Scalar Modes in Vacuum Scalar-Field Gravity[EB/OL].(2026-05-13)[2026-05-14].https://chinaxiv.org/abs/202604.00081.学科分类
物理学/天文学
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