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
- 折叠
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
Within the unified framework of a vacuum scalar field, this work systematically investigates the field-theoretic derivation of gravitational geometry, the observable effects in the strong-field environment of neutron stars, and their multi-scale physical self-consistency, all from first principles. The basic assumption of the model is the existence of a classical scalar field $\phi$, to which particles couple via $S = -m\int \phi\,d\tau$; the equivalence principle thereby acquires a rigorous field-theoretic formulation: the acceleration $\mathbf{a} = -\nabla\phi$ describes gravitational and inertial accelerations in a unified manner. The physical requirement that photon frequencies fix time scales and photon wavelengths fix spatial scales rigidly yields the Schwarzschild metric in the static spherically symmetric case; for rotating sources, the non-integrability of the Lorentz group activates the fiber-bundle connection construction theorem, forcing the introduction of compensator fields whose low-energy dynamics is locked by symmetry to the Einstein--Hilbert action, with the stationary axisymmetric solution being the Kerr metric. On this foundation, through analytical derivation and numerical computation, we establish and rigorously justify an ``astrophysical mass window'' for the scalar field---a mass of approximately $10^{-10}$~eV and a Compton wavelength of approximately $2.2$~km---which endows the theory with a highly self-consistent structure across multi-scale astrophysical tests. On Solar-System and binary-system scales, the scalar fifth force is exponentially suppressed by Yukawa screening, and the scalar radiation channel is closed by strong kinematic suppression due to the threshold frequency of about $21.7$~kHz; all weak-field and post-Newtonian constraints---including Cassini PPN measurements and the orbital decay observations of PSR~B1913+16 and PSR~J0737$-$3039A/B---are precisely satisfied. Inside neutron stars, the condition that the Compton wavelength is slightly smaller than the stellar radius allows the scalar field to respond to the non-minimal coupling source term, triggering forced scalarization that reshapes the macroscopic structure and oscillation eigenfrequencies. Numerical calculations based on the one-dimensional static TOV equations indicate that the $f_2$-mode oscillation frequency of the post-merger hypermassive neutron star remnant may undergo a macroscopic shift of about twelve percent---with the caution that this value is an order-of-magnitude estimation; its precise spectral features and phase-shift magnitude require final confirmation by future three-dimensional, fully nonlinear numerical relativity simulations. At the gravitational-wave detector, the received signal is always a pure general-relativistic tensor wave, but the waveform spectrum exhibits a pronounced shift due to the internal modification of the source by the scalar skeleton. Furthermore, a rigorous derivation of the black-hole Wald entropy including the non-minimal coupling term confirms the cross-domain self-consistency between the entropy correction coefficient and the effective gravitational constant obtained from neutron-star calculations. The triple characteristics---external kinematic suppression, internal mesoscopic dynamical polarization, and pure-tensor waveform spectral shift---which start from a single scalar-field foundation, recover general relativity as the low-energy limit, and retain a testable strong-field prediction, provide the model with a unique and observationally accessible target for third-generation gravitational-wave detectors, while respecting all known constraints.关键词
vacuum scalar field/equivalence principle/Schwarzschild metric/Kerr metric/scalar gravitational waves/breathing mode/geometric emergence/cosmological constant problemKey words
modified gravity theory/ neutron star equation of state/ dynamic vacuum unlocking/ multi-messenger astronomy/ gravitational waves/ cosmological constant引用本文复制引用
Li Xiaoyun.Geometric Emergence and Scalar Modes in Vacuum Scalar-Field Gravity[EB/OL].(2026-05-28)[2026-06-04].https://chinaxiv.org/abs/202604.00081.学科分类
天文学/物理学
