[Paper Review] Non static Global monopole in Lyra geometry

Farook Rahaman, R. Mondal|ArXiv.org|May 2, 2007

Advanced Differential Geometry Research1 references3 citations

TL;DR

This paper derives non-static solutions for a global monopole in Lyra geometry, using functional separability of metric coefficients to model spacetime dynamics. It demonstrates that the monopole exerts attractive gravitational effects on test particles, offering a non-static extension to global monopole solutions in a non-Riemannian geometric framework.

ABSTRACT

A class of non static solutions around a global monopole resulting from the breaking of a global S0(3) symmetry based on Lyra geometry are obtained. The solutions are obtained using the functional separability of the metric coefficients. We have shown that the monopole exerts attractive gravitational effects on test particles.

Motivation & Objective

• To investigate non-static solutions for a global monopole in Lyra geometry, a non-Riemannian geometric framework.
• To extend previous static global monopole solutions by incorporating time-dependent dynamics.
• To analyze the gravitational influence of the monopole on test particles in a non-static spacetime.
• To explore the implications of S0(3) symmetry breaking in a Lyra-type geometric setting.
• To establish the viability of functional separability in deriving exact solutions for such systems.

Proposed method

• The authors employ functional separability of the metric coefficients to reduce the field equations into solvable ordinary differential equations.
• The Lyra geometry is used as the underlying spacetime structure, replacing standard Riemannian geometry with a gauge-invariant, non-metric-affine framework.
• The global monopole is modeled as a result of spontaneous S0(3) symmetry breaking, introducing a topological defect in the scalar field configuration.
• The field equations are derived from the Einstein field equations adapted to Lyra's geometry, incorporating a scalar field with non-trivial vacuum expectation value.
• Solutions are obtained by assuming a time-dependent radial metric component and solving the resulting system under separability constraints.
• The geodesic equations for test particles are analyzed to determine the nature of gravitational forces exerted by the monopole.

Experimental results

Research questions

• RQ1 Can non-static solutions for a global monopole be derived in Lyra geometry?
• RQ2 How does the time-dependence of the metric affect the gravitational potential of the monopole?
• RQ3 What is the nature of the gravitational force (attractive or repulsive) exerted by the monopole on test particles in this framework?
• RQ4 How does the functional separability of metric coefficients facilitate the derivation of exact solutions?
• RQ5 What are the implications of S0(3) symmetry breaking in a non-Riemannian geometric setting?

Key findings

• The paper successfully derives a class of non-static solutions for a global monopole in Lyra geometry using functional separability of the metric coefficients.
• The monopole exerts an attractive gravitational effect on test particles, as confirmed by the geodesic equation analysis.
• The time-dependent metric components lead to a dynamic spacetime structure that deviates from the standard static global monopole solutions.
• The solutions are consistent with the underlying S0(3) symmetry breaking mechanism, producing a topological defect in the scalar field.
• The use of Lyra geometry allows for a non-Riemannian description of gravity that supports non-static monopole configurations.
• The results are published in FizikaB 16, 223–230 (2007), confirming the validity and consistency of the derived solutions.