Geometric Emergence and Tensor Modes in Vacuum Tensor-Field Gravity
Geometric Emergence and Tensor Modes in Vacuum Tensor-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
Inspired by analogue gravity and induced gravity, we propose a vacuum tensor-polarization (VTP) field theory in Minkowski spacetime, in which the vacuum is modeled as a single massless spin-2 tensor field $h_{\mu\nu}$. Its local coupling to matter follows from global Poincar symmetry and the principle of least action. A Lie group exponential map, $M=\exp(h)$, yields an effective dielectric constitutive tensor. In the weak-field regime, this mapping analytically breaks Maxwell conformal invariance, reproducing the PPN parameters $\gamma \equiv 1$ and $\beta \equiv 1$, preserving the strong equivalence principle and precluding gravitational dipole radiation, consistent with binary pulsar orbital decay. For strong-field astrophysics, the theory predicts: (1) exponential softening in the hydrodynamic equilibrium equation alleviates core gravitational runaway, allowing superheavy neutron stars beyond traditional limits, such as a $2.6\,M_{\odot}$ mass-gap object; (2) positive definiteness of the exponential constitutive relation eliminates dynamical singularities and classical event horizons, making the endpoint of extreme collapse a Magnetospheric Eternally Collapsing Object (MECO); (3) the photon-sphere shadow radius of compact objects (M87* and Sgr~A*) is predicted to be $+4.63\%$ larger than in general relativity, providing a sensitive target for the next-generation Event Horizon Telescope (ngEHT).关键词
vacuum scalar field/equivalence principle/Schwarzschild metric/Kerr metric/scalar gravitational waves/breathing mode/geometric emergence/cosmological constant problemKey words
Emergent Gravity/Effective Field Theory/Neutron Star Mass Gap/Magnetospheric Eternally Collapsing Object (MECO)/Black Hole Shadow/Event Horizon Telescope (EHT)/multi-messenger astronomy/gravitational waves引用本文复制引用
Li Xiaoyun.Geometric Emergence and Tensor Modes in Vacuum Tensor-Field Gravity[EB/OL].(2026-09-28)[2026-10-01].https://chinaxiv.org/abs/202604.00081.学科分类
天文学
