[Paper Review] Plane symmetric inhomogeneous bulk viscous domain wall in Lyra geometry

Anirudh Pradhan, Vandana Rai+1 more|University of Zagreb University Computing Centre (SRCE)|Aug 20, 2005

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper investigates plane-symmetric, inhomogeneous domain walls in Lyra geometry with bulk viscous fluid, deriving exact solutions for energy density and pressure under both constant and time-varying displacement fields ($\beta$). The key contribution is demonstrating that bulk viscosity and $\beta$ significantly influence the solution structure, with the gravitational field showing repulsive or attractive behavior depending on parameters, and revealing that the big bang singularity may still occur in finite past despite viscous effects.

ABSTRACT

Some bulk viscous general solutions are found for domain walls in Lyra geometry in the plane symmetric inhomogeneous spacetime. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field $β$. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.

Motivation & Objective

• To explore the dynamics of inhomogeneous, plane-symmetric domain walls in Lyra geometry with bulk viscous fluid.
• To derive exact solutions for energy density and pressure of domain walls under both constant and time-varying displacement fields ($\beta$).
• To examine the influence of bulk viscosity—assumed as a power function of mass density—on the spacetime structure and cosmological evolution.
• To analyze geodesic equations and particle acceleration to assess the nature of the gravitational field (attractive, repulsive, or neutral).
• To investigate whether bulk viscous models avoid the big bang singularity, challenging Murphy’s earlier conclusion.

Proposed method

• Adopting Lyra’s geometry with a displacement vector field $\beta$, the study modifies Einstein’s field equations to include bulk viscosity and inhomogeneous plane symmetry.
• Assuming the bulk viscosity coefficient $\eta \propto \rho^{m}$, the field equations are solved under two cases: constant $\beta$ and time-varying $\beta$.
• The energy density $\rho$ and pressure $p$ are derived from the modified field equations, showing exponential decay away from the symmetry plane.
• Geodesic equations are solved to determine particle acceleration, with the z-direction component depending on metric gradients and velocity components.
• Solutions are analyzed for reflection symmetry and asymptotic behavior, confirming that $\rho$ and $p$ vanish as $z \to \pm\infty$.
• The model incorporates the displacement field $\beta$ as a gauge function, replacing the cosmological constant in standard relativity.

Experimental results

Research questions

• RQ1 How do constant and time-varying displacement fields ($\beta$) affect the structure and evolution of inhomogeneous domain walls in Lyra geometry?
• RQ2 What are the exact expressions for energy density and pressure in bulk viscous domain walls under plane symmetry in Lyra spacetime?
• RQ3 How does bulk viscosity—modeled as a power function of mass density—affect the formation and nature of the big bang singularity?
• RQ4 What is the nature of the gravitational field (attractive, repulsive, or neutral) as determined by particle acceleration in the domain wall spacetime?
• RQ5 Does the inclusion of bulk viscosity in Lyra geometry prevent the big bang singularity, as claimed by Murphy?

Key findings

• The energy density $\rho$ and pressure $p$ in the direction perpendicular to the domain wall decrease exponentially away from the symmetry plane and vanish as $z \to \pm\infty$, confirming domain wall structure.
• The solutions exhibit reflection symmetry about the wall, consistent with expected physical behavior of domain walls.
• The displacement field $\beta$ and bulk viscosity both significantly influence the solution character, altering the spacetime geometry and dynamics.
• Particle acceleration in the z-direction can be positive, negative, or zero depending on parameter choices, indicating that the gravitational field may be repulsive, attractive, or neutral.
• The big bang singularity may still occur in finite past even in bulk viscous models, contradicting Murphy’s conclusion that it appears only in infinite past.
• The pressure perpendicular to the wall is non-zero, a key result indicating non-trivial dynamics in the transverse direction.