arXiv subjects

Gary Nash

Publications and source records attributed to Gary Nash.

5 recordsLinked to original sources

arXiv2026

On the physical origin of the radial acceleration relation

The radial acceleration relation (RAR) is a tight correlation between the distribution of baryonic matter in galaxies and their observed dynamics, even in systems where dark matter dominates. This suggests a universal acceleration scale exists in galaxies, which appears to challenge the $\Lambda$CDM standard cosmological model and favor Modified Newtonian dynamics (MOND). However, MOND also deviates from the RAR, so these deviations are not fully explained by the $\Lambda$CDM model or MOND. A theory that explains gravity and the dark sector geometrically, and treats dark matter as a spin-1 particle, is required, such as Modified General Relativity (MGR). It is the only metric-compatible theory of gravity that describes local gravitational energy-momentum by the connection-independent symmetric tensor $\varPhi_{\alpha\beta}$, which completes the total energy-momentum tensor of the Einstein equation. Dark energy is explained by the energy-related component $\varPhi_{00}$, and dark matter by the stress components $\varPhi_{ij}$. Dark matter is extremely difficult to observe because it is fundamentally related to the Lorentzian metric of spacetime itself. The physical origin of the RAR follows directly from the equilibrium between the dark energy and Newtonian forces in the outer part of the rotation curve of galaxies or galaxy clusters, and that between the dark sector forces in the inner part of the rotation curve. It is shown that MGR subsumes MOND, accounts for the gravitational anomaly observed in wide binaries, and exhibits the observed Newtonian behavior of gravity at large scales.

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arXiv2025

The unification of gravity and the spin-1 field

Unifying the massive spin-1 field with gravity requires the implementation of a regular vector field that satisfies the spin-1 Proca equation and is a fundamental part of the spacetime metric. That vector field is one of the pair of vectors in the line element field (\textbf{X},-\textbf{X}), which is paramount to the existence of all Lorentzian metrics and Modified General Relativity (MGR). Symmetrization of the spin-1 Klein-Gordon equation in a curved Lorentzian spacetime introduces the Lie derivative of the metric along the flow of one of the regular vectors in the line element field. The Proca equation in curved spacetime can then be described geometrically in terms of the line element vector, the Lie derivative of the Lorentzian metric, and the Ricci tensor, which unifies gravity and the spin-1 field. Related issues concerning charge conservation and the Lorenz constraint, singularities in a spherically symmetric curved spacetime, and geometrical implications of MGR to quantum theory are discussed. A geometrical unification of gravity with quantum field theory is presented.

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arXiv2023

Modified General Relativity and dark matter

Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy-momentum of the gravitational field. It solves the problem of the non-localization of gravitational energy-momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully-Fisher relation is derived, and the gravitational energy density is calculated. The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein-Gordon wave equation. The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies.

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arXiv2019

Modified General Relativity and quantum theory in curved spacetime

With appropriate modifications, the multi-spin Klein-Gordon (KG) equation of quantum field theory can be adapted to curved spacetime for spins 0,1,1/2. The associated particles in the microworld then move as a wave at all spacetime coordinates. From the existence in a Lorentzian spacetime of a line element field $(X^{\beta},-X^{\beta}) $, the spin-1 KG equation $\nabla_{\mu}\nabla^{\mu}X^{\beta}=k^{2}X^{\beta} $ is derived from an action functional involving $X^{\beta} $ and its covariant derivative. The spin-0 KG equation and the KG equation of the outer product of a spin-1/2 Dirac spinor and its Hermitian conjugate are then constructed. Thus, $ X^{\beta} $ acts as a fundamental quantum vector field. The symmetric part of the spin-1 KG equation, $ \tilde{\varPsi}_{\alpha\beta}$, is the Lie derivative of the metric. That links the multi-spin Klein-Gordon equation to Modified General Relativity (MGR) through its energy-momentum tensor of the gravitational field. From the invariance of the action functionals under the diffeomorphism group Diff(M), which is not restricted to the Lorentz group, $ \tilde{\varPsi}_{\alpha\beta}$ can instantaneously transmit information along $ X^{\beta} $. That establishes the concept of entanglement within a Lorentzian formalism. The respective local/nonlocal characteristics of MGR and quantum theory no longer present an insurmountable problem to unify the theories.

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arXiv2019

Modified general relativity

In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric tensors can be constructed in terms of the Lie derivative along $ \bm{X} $ of the metric and a product of the unit vectors; and a linear sum of divergenceless symmetric tensors. A modified Einstein equation of general relativity is then obtained by using the principle of least action, the decomposition and a fundamental postulate of general relativity. The decomposition introduces a new symmetric tensor $ \varPhi_{\alpha\beta} $ which describes the energy-momentum of the gravitational field. It completes Einstein's equation and addresses the energy localization problem. Variation of the action with respect to $ X^{\mu} $ restricts $u_{\mu}$ to a particular value, which defines the possible Lorentzian metrics. $ \Phi $, the trace of $ \varPhi_{\alpha\beta} $, describes dark energy. The cosmological constant is dynamically replaced by $ \Phi $. A cyclic universe that developed after the Big Bang is described. The dark energy density provides a natural explanation of why the vacuum energy density is so small, and why it dominates the present epoch. Assuming dark matter does not exist, a solution to the modified Einstein equation introduces two additional terms into the Newtonian radial force equation, from which the baryonic Tully-Fisher relation is obtained.

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