Gravitational Lensing

Visualizing Gravitational Lensing

Gravitational Lensing is a phenomena in astrophysics that intressted me and which I then chose as my technical science project. The goal of this project is to visualize gravitaional lensing using either code or an editing software. Intuitively I wanted to make it interactive and if possible, in a VR enviornment. Since the theory behind gravitaional lensing is quite difficult and heavy, it's extremely time consuming. Being very ambitious I wanted to make it as good as possible from the beginning but being realistic I see that I will have to simplify it a bit but then continue the work next year. The plan is now to use the programming classes to work on this project and then do it entirely in code.

Symbols

Psi /ˈsaɪ/ (uppercase Ψ, lowercase ψ)
Kappa (uppercase Κ, lowercase κ or cursive ϰ)
Chi (uppercase Χ, lowercase χ)
Lambda / λ
Theta / 𝜃
Beta / 𝛽
Alpha / α
Gamma / 𝛾
Del / Nabla / ∇

Termology

Arclets
Caustics
Lensing Potential
Partial Derivative
Gradient
Hubble Constant
Velocity Field
Thin Screen Approximation
Quasi-Optical Approximation
Scintillations
Escape Velocity
Einstein Ring, Einstein Cross
Schwartzchild Radius
Schwartz Function
Lens Equation
Lensing Deflection Angle
Galaxy Clusters
Einstein Radius
Shearing
Event Horizon
Photon Sphere
Convergence
Poisson Equation
Redshift
Newton Potential
Laplaceoperator
Critical Surface
Jacobian
Orthogonal Component
Euclidean Vector
Differential Operator

Gravitational Lensing is a phenomena in astrophysics based off of Albert Einsten's prediction and theory of relativity. It's highly useful to determine distance of stars located very far away as well as just being able to see them. How it works is that massive objects curve the light rays coming from very distant light sources such as quasars. The fabric of spacetime is also bent due to the enormous force of gravity that a massive object has. Then gives the observer, us, recieves distorted images of the distant object behind the massive object. Usually these massive objects are galaxy clusters, black holes, the sun and such. The difference between Einstein's theory of relativity and gravitational lensing is that, while both bend light rays, gravitational lensing bends the spacetime itself, rather than bending light with curved material.

There are different variations of gravitaional lensing. These are microlensing, strong lensing and weak lensing. Weak lensing shows arclets and some shearing. Weak lensing can only be revealed and observed through vast amounts of statistical analytics of star- and galaxy fields. Strong lensing produces multiple images or large arcs, eg. Einstein Rings. These are the more rare types of gravitational lensing. Microlensing manifests as small changes brightness of objects nearby. In microlensing the brightness also changes over time due to relative movement of multiple bodies. Microlensing is also difficult to not get confused and mixed up with changes in the brightness and the radiating light of stars since it manifests as just that. The difference between them is the cause of the change in brightness. If its microlensing then the cause of the change is star lenses whereas otherwise it could be because of variable stars (stars that change in brightness) or novae.

Before the images that are produced by the gravitaional lens reaches our eye and can be observed, the radiated radioativity of the background source gets distorted by a lensing galaxy. This is calculated using the equation

𝛽=𝜃-α(𝜃)

The vast amount of matter and the size of a lensing galaxy is much smaller than the relative distances between the original source, the lens and the observer, us. This means that the distribution of the mass of the lens itself becomes approximated to a bi-dimensional distribution, also known as the thin screen approximation.