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PWS: Understanding black holes

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In this document of 50 pages, black holes will be explained thoroughly. The subjects we wrote about are: - Origin of black holes - Debunking misconceptions - Spacetime explained - Complete derivation of Einsteins time dilation equation - What is a black hole - Different parts of a black hole - Complete derivation of the equations for the radii of the ISCO and photon sphere - Understanding and partially deriving the Schwarzschild metric - Explaining different kinds of black holes and relating them to the black hole that was photographed in 2019 by the EHT collaboration. - Understanding how the picture was made with radio telescopes and interferometry. - Phenomena around black holes (gravitational lensing and time dilation)

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Capturing the invisible
The research behind the first image of a black hole
PWS




24-01-2022
E. Moonen & C. Zaky
Het Vechtstede College
VWO 6 - NT/NG - Natuurkunde
Docent Natuurkunde/NLT/O&W- Mentor VWO 4- Coördinator PWS VWO - Dhr F. Kegel

,Index of content

1 Introduction 3

2 Research - Misconceptions 5
2.1 Method 5
2.2 Results and conclusion 6

3 Theoretical framework 8
3.1 What is a black hole? 8
3.2 Origin of black holes 11
3.2.1 Doppler effect 12
3.3 Parts of a black hole 13
3.3.1 How to derive the radii of the ISCO and the photon sphere 16
3.4 The effects and phenomena surrounding black holes 19
3.4.1 Gravitational lensing 19
3.4.2 Spacetime 20
3.4.3 Time 25
3.5 The Schwarzschild metric 28
3.5.1 How to interpret the Schwarzschild metric 28
3.5.2 How to apply 30

4 Model of a black hole 33
4.1 Materials and method 33
4.2 Results and conclusion 34

5 Explanation of the first black hole image 35
5.1 Explanation of the used technology 35
5.2.1 Radiation from black holes 36
5.2.2 Radio telescopes 37
5.2.3 Interferometry 38
5.2 Complications during the research 39

6 Picture analysis 40

7 What is next? 42
7.1 The importance of the image 42
7.2 Next mission 43

Conclusion 44

Discussion 45
Follow-up study 45

Sources 46


PWS | Vechtstede College | Term 3 | 2022
1

,Appendix 49
I Raw data of the inquiry 49
II Photos of the experiment 51
III Scan of full calculation of derivative 52




PWS | Vechtstede College | Term 3 | 2022
2

, 1 Introduction
When we look at the sky, all that is visible to us are stars, very distant supernovae or little
smudges that are remote galaxies. However, there are many objects that are invisible to us,
and can only be seen with highly advanced telescopes. One of those objects is the black
hole. This vaguely understood object was undetected for a long time, and only recently were
we able to generate the first photograph of a supermassive black hole. Since the publication
in 2019, which was a major breakthrough, many misconceptions have arisen. The term
‘’black hole’’ is actually extremely misleading. Contrary to common belief, black holes are not
actually holes nor are they black. One thing that is not misunderstood, is the complexity of
these objects. This made the creation of the picture an even bigger victory of modern
science. To understand how and why the work and research behind the picture were so
extensive, the research question goes as follows,

´How was the first image of a black hole constructed?´

Aside from the analysis of the picture, this paper is going to analyse common
misconceptions. When thinking about black holes, and the topics we were going to discuss
prior to writing, we noticed that many students, teachers and our own parents sometimes did
not know what a black hole was. They described a black hole as a “very deep hole”, or a “very
empty space”, and these assumptions are not even that far-fetched when you think about it.
Thereby explaining the motivation behind this research paper. This paper is going to discuss
these misconceptions and how they came to be.
Before all else, to understand the misconceptions and the picture, it is of importance to know
what black holes are. This paper is going to explain the different types of black holes, the
origin and black hole its effects. We will close this paper with a chapter about the future of
astronomy. The only way to fully appreciate the picture made in 2019, is to comprehend the
intricacy of black holes.
Our subquestions goes as follows,
- What is a black hole?
- Origin of black holes
- Kinds of black holes
- Parts of a black hole
- The effects and phenomena surrounding black holes
- What are a few of the most common misconceptions surrounding black holes
- What would an accurate model of a black hole look like?
- Where and by whom was the image made?
- What technology was needed to make the image?
- What complications arose during the research?

However, black holes cannot be fully explained through words only. To completely
understand the phenomena around black holes and how they interact with spacetime, we
will dive into the mathematics and physics around them. Throughout this paper, equations
will be shown in order to explain exactly where certain values or conclusions are based on.
All the equations will be numbered, except if an equation arises from the substitution of two
or more equations that have been numbered already or the equation has been mentioned
before/ is a single term of a bigger equation.




PWS | Vechtstede College | Term 3 | 2022
3

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