Računalna simulacija perspektive promatrača u zakrivljenom prostorvremenu

undergraduate thesis

• Title (english): Computer simulation of the observer's perspective in curved spacetime
• Author: Matko Parlov
• Mentor: Vladimir Milić (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2024-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics; Astronomy and Astrophysics

Abstract

U ovom radu će se kroz uvodnih par poglavlja dati pregled i sažeti opis opće teorije
relativnosti i kako se ona nadovezuje na specijalnu teoriju relativnosti te prijašnja
shvaćanja o gravitaciji i vremenu. Kako mnogi izrazi nisu učestali u strojarstvu, ali i u
većini ostalih grana znanosti, uvidjela se potreba da se svi termini ne uvode bez
nadovezujućih objašnjenja kako bi se laik u ovom području i dalje mogao dobro
orijentirati čitajući ovaj rad. Krajnji ishod rada je simulacija i vizualizacija, kako i sam
naslov kaže, promatračeve perspektive u jako zakrivljenom prostor-vremenu. Nakon što
opišemo termine i korišteni žargon, kako smo napomenuli, predstavit ćemo
upotrebljavani sustav sa koncentriranom masom u točci, tzv. Schwarzschildovo rješenje
Einsteinovih jednadžbi polja. Na temelju toga ćemo numeričkim putem riješiti putanju
fotona natrag kroz vrijeme, koji su došli u promatračevo vidno polje, tako ćemo dobiti
njegovu sliku odnosno vidno polje. Pri numeričkom rješavanju ćemo usporediti metode
rješavanja običnih diferencijalnih jednadžbi za ovaj sustav i usporediti njihove učinke.
Na koncu ćemo dobivene rezultate simulacija predstaviti u kontekstu dosadašnjih
promatranja i spoznaja o crnim rupama u astronomiji i astrofizici.

Abstract (english)

In this work we will go through a few introductory chapters where we will hand out a
brief description of the general theory of relativity and how it is tied to the special theory
of relativity and earlier studies about gravitation and time. While many terms aren’t
common in engineering, and for that matter other branches of science, it was up most
important to not introduce them without proper explanation where a rookie in the field
could still find a footing while going through this paper. Final outcome of this work is
simulation and visualization, as the title indicates, of observer’s perspective in a strongly
curved space-time. After we go over the terminology and jargon, as we have mentioned,
we will present a specific solution used, the so called Schwarzchild’s solution of Einstein’s
field equations. From there we will numerically solve photon trajectories back through
time which entered the observer’s field of view, thus we will get an image of what he
sees. For numeric approach we will compare methods of integrating differential equations
that describe the motion of a photon particle. Lastly, all results will be put into context
of current astronomical and astrophysical observations and knowledge we have on the
subject of black holes.

• Keywords: opća teorija relativnosti; zakrivljeni prostor-vrijeme; Schwarzschildovo rješenje; Einsteinova jednadžba polja; crna rupa
• Keywords (english): general theory of relativity; curved space-time; Schwarzschild’s solution; Einstein’s field equation; black hole
• Language: croatian
• URN:NBN: urn:nbn:hr:235:389115
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-22 11:45:40