[Paper Review] Nonsymmetric Gravitational Theory as a String Theory

J. W. Moffat|ArXiv.org|Dec 4, 1995

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes that nonsymmetric gravitational theory (NGT) can be interpreted as a string theory in which the antisymmetric field component corresponds to a massive spin-1+ vector boson mediating interactions between open strings. The theory predicts no black hole event horizons and exhibits a low-energy confinement regime described by a Yukawa potential at galactic scales, with a singular, non-perturbative transition in the weak field limit.

ABSTRACT

It is shown that the new version of nonsymmetric gravitational theory (NGT) corresponds in the linear approximation to linear Einstein gravity theory and antisymmetric field equations with a non-conserved string source current. The Hamiltonian for the antisymmetric field equations is bounded from below and describes the exchange of a spin $1^+$ massive vector boson between open strings. The non-Riemannian geometrical theory is formulated in terms of a nonsymmetric fundamental tensor $g_{μν}$. The weak field limit, $g_{[μν]} ightarrow 0$, associated with large distance scales, corresponds to the limit to a confinement region at low energies described by an effective Yukawa potential at galactic distance scales. The limit to this low-energy confinement region is expected to be singular and non-perturbative. The NGT string theory predicts that there are no black hole event horizons associated with infinite red shift null surfaces.

Motivation & Objective

• To establish a correspondence between nonsymmetric gravitational theory (NGT) and string theory in the linear approximation.
• To show that the antisymmetric field in NGT describes a massive spin-1+ vector boson with a bounded Hamiltonian, consistent with open string exchange.
• To explore the low-energy limit of NGT, particularly its behavior at large distances and galactic scales.
• To investigate the absence of black hole event horizons in NGT, implying no infinite redshift surfaces.
• To analyze the non-perturbative, singular nature of the weak field limit in NGT, interpreted as a confinement region.

Proposed method

• Formulate NGT using a nonsymmetric fundamental tensor $ g_{\mu\nu} $, with symmetric and antisymmetric parts.
• Linearize the field equations to show equivalence to Einstein gravity and antisymmetric field equations with a non-conserved string source current.
• Construct the Hamiltonian for the antisymmetric field, demonstrating it is bounded from below, indicating stability.
• Identify the antisymmetric field as a massive spin-1+ vector boson arising from open string interactions.
• Analyze the weak field limit $ g_{[\mu\nu]} \to 0 $, showing it corresponds to a confinement region at low energies.
• Derive an effective Yukawa potential at galactic scales, arising from the massive vector exchange in the low-energy limit.

Experimental results

Research questions

• RQ1 Can nonsymmetric gravitational theory be consistently interpreted as a string theory in the linear approximation?
• RQ2 Does the antisymmetric field in NGT describe a stable, massive vector boson with spin 1+ compatible with open string exchange?
• RQ3 What is the nature of the low-energy limit of NGT, and how does it relate to confinement and galactic-scale dynamics?
• RQ4 Why does NGT predict the absence of black hole event horizons and infinite redshift surfaces?
• RQ5 How is the weak field limit of NGT characterized, and what does its non-perturbative, singular behavior imply?

Key findings

• The linear approximation of NGT reproduces Einstein gravity and antisymmetric field equations with a non-conserved string source current.
• The Hamiltonian for the antisymmetric field is bounded from below, confirming the stability of the massive spin-1+ vector boson state.
• The antisymmetric field corresponds to the exchange of a massive spin-1+ vector boson between open strings, consistent with string theory.
• In the weak field limit, $ g_{[\mu\nu]} \to 0 $, NGT enters a confinement region at low energies, described by an effective Yukawa potential at galactic scales.
• The transition to this low-energy regime is singular and non-perturbative, indicating strong dynamics at large distances.
• NGT predicts no black hole event horizons, implying no infinite redshift null surfaces exist in this theory.