[Paper Review] Deflection of light by the screw dislocation in space-time

Miroslav Pardy|ArXiv.org|Jun 6, 2001

Geophysics and Sensor Technology1 references3 citations

TL;DR

This paper proposes that gravity arises from deformations in a space-time medium, modeling a screw dislocation as a topological defect in space-time geometry. Using a deformation tensor formalism to derive the metric, it calculates the deflection angle of light passing near such a dislocation, finding a deflection proportional to the Burgers vector and inversely proportional to the cube of the impact parameter.

ABSTRACT

We derive the light deflection caused by the screw dislocation in space-time. The derivation is based on the idea that space-time is a medium which can be deformed by gravity and that the deformation of space-time is equivalent to the existence of gravity.

Motivation & Objective

• To explore the microphysical origin of the space-time metric by modeling it as a deformation of a continuous medium.
• To investigate whether topological defects like screw dislocations in space-time can produce measurable gravitational effects, such as light deflection.
• To extend the analogy between elasticity theory and general relativity by introducing a deformation tensor formalism for gravity.
• To derive the deflection angle of light in the presence of a screw dislocation in space-time, a scenario not previously analyzed in standard relativity literature.
• To provide a phenomenological framework for gravity based on space-time deformation, avoiding direct reliance on Einstein's field equations.

Proposed method

• Postulates that the metric tensor $ g_{\mu\nu} $ arises from a deformation tensor $ u_{\mu\nu} $, with $ g_{\mu\nu} = \eta_{\mu\nu} + u_{\mu\nu} $, where $ \eta_{\mu\nu} $ is the Minkowski metric.
• Applies the deformation tensor formalism to the nonrelativistic limit, recovering the gravitational redshift and time dilation via $ u_0 \approx \varphi t / c $, consistent with Einstein's results.
• Models the screw dislocation using a specific deformation component $ u_{z\varphi} = b/(4\pi r) $, where $ b $ is the Burgers vector component.
• Derives the modified space-time metric $ ds^2 = c^2 dt^2 - dr^2 - r^2 d\varphi^2 - \frac{2b}{4\pi r} dz d\varphi - dz^2 $, incorporating the dislocation.
• Imposes the null condition $ ds = 0 $ for light rays to derive the geodesic equation in the deformed space-time.
• Assumes a straight-line trajectory along the z-axis at radius $ r = a $, with constant $ \dot{z} = v \approx c $, and solves for the angular deflection $ \Delta\varphi $.

Experimental results

Research questions

• RQ1 Can the metric of space-time be derived from a fundamental deformation tensor, analogous to elasticity theory?
• RQ2 What is the gravitational effect of a screw dislocation in space-time on the propagation of light?
• RQ3 Does the deformation-based approach reproduce known relativistic effects like gravitational redshift in the weak-field limit?
• RQ4 What is the deflection angle of a light ray passing near a screw dislocation in space-time?
• RQ5 How does the presence of topological defects like dislocations modify the geometry of space-time and affect light trajectories?

Key findings

• The deformation tensor formalism successfully reproduces the gravitational redshift and time dilation in the nonrelativistic limit, validating the approach.
• The metric of space-time with a screw dislocation is given by $ ds^2 = c^2 dt^2 - dr^2 - r^2 d\varphi^2 - \frac{2b}{4\pi r} dz d\varphi - dz^2 $, incorporating the dislocation via the $ u_{z\varphi} $ component.
• For a light ray traveling parallel to the dislocation axis at distance $ a $, the angular deflection is $ \Delta\varphi \approx -\frac{bl}{2\pi a^3} $, where $ l $ is the path length.
• The deflection is proportional to the Burgers vector $ b $ and inversely proportional to the cube of the impact parameter $ a $, indicating a strong dependence on proximity.
• The result is derived under the approximation $ v \approx c $, and the deflection is non-zero even in the absence of mass, due to the topological nature of the dislocation.
• The model suggests that space-time dislocations could produce measurable gravitational effects, offering a new perspective on the origin of gravity beyond Einstein's field equations.