Outline

Overview

Einstein's General Theory of Relativity represents a pinnacle of modern physics, providing the most accurate description of the action of gravity across the cosmos. To Newton, gravity was simply a force between masses, but Einstein's mathematical language describes gravity in terms of the bending and stretching of space-time. In this course, students will review Einstein's principle of relativity, and the mathematical form of special relativity, and the flat space-time this implies. This will be expanded and generalised to consider Einstein's principle of equivalence and the implications for particle and photon motion with curved space-time. Students will explore the observational consequences of general relativity in several space-time metrics, in particular the Schwarzschild black hole, the Morris-Thorne wormhole, and the Alcubierre warp drive, elucidating the nature of the observer in determining physical quantities. Building on this knowledge, students will understand Einstein's motivation in determining the field equations, relating the distribution of mass and energy to the properties of space-time. Students will apply the field equations, including deriving the cosmological Friedmann-Robertson-Walker metric from the assumption of constant curvature, and using this to determine the universal expansion history and key observables. Students will obtain a complete picture of our modern cosmological model, understanding the constituents of the universe, the need for inflation in the earliest epochs, and the ultimate fate of the cosmos.

Unit details and rules

Academic unit	Physics Academic Operations
Credit points	6
Prerequisites ?	An average of at least 65 in 144 cp of units
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	A major in physics and knowledge of special relativity
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Bruce Yabsley, bruce.yabsley@sydney.edu.au
Lecturer(s)	Geraint Lewis, geraint.lewis@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam (Take-home short release)	Final exam Exam	60%	Formal exam period	3 hours
Outcomes assessed:
Assignment	Assignment 1 Assignment (worked problems)	13.33%	Week 05 Due date: 29 Aug 2022 at 23:59	Variable
Outcomes assessed:
Assignment	Assignment 2 Assignment (worked problems)	13.33%	Week 08 Due date: 19 Sep 2022 at 23:59	Variable
Outcomes assessed:
Assignment	Assignment 3 Assignment (worked problems)	13.34%	Week 10 Due date: 10 Oct 2022 at 23:59	Variable
Outcomes assessed:
= Type D final exam ?

Assessment summary

Assignment 1: This assignment will require you to apply information from lectures and your reading to solve worked problems.
Assignment 2: This assignment will require you to apply information from lectures and your reading to solve worked problems.
Assignment 3: This assignment will require you to apply information from lectures and your reading to solve worked problems.
Exam: This exam will cover all material in the unit. The exam will have a mixture of short-answer questions and worked problems.

Final exam: If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.”

Assessment criteria

Result Name	Mark Range	Description
High Distinction	85-100	At HD level, a student demonstrates a flair for the subject as well as a detailed and comprehensive understanding of the unit material. A ‘High Distinction’ reflects exceptional achievement and is awarded to a student who demonstrates the ability to apply their subject knowledge and understanding to produce original solutions for novel or highly complex problems and/or comprehensive critical discussions of theoretical concepts.
Distinction	75-84	At DI level, a student demonstrates an aptitude for the subject and a well-developed understanding of the unit material. A ‘Distinction’ reflects excellent achievement and is awarded to a student who demonstrates an ability to apply their subject knowledge and understanding of the subject to produce good solutions for challenging problems and/or a reasonably well-developed critical analysis of theoretical concepts.
Credit	65-74	At CR level, a student demonstrates a good command and knowledge of the unit material. A ‘Credit’ reflects solid achievement and is awarded to a student who has a broad general understanding of the unit material and can solve routine problems and/or identify and superficially discuss theoretical concepts.
Pass	50-64	At PS level, a student demonstrates proficiency in the unit material. A ‘Pass’ reflects satisfactory achievement and is awarded to a student who has threshold knowledge.
Fail	0-49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Weekly schedule

WK	Topic	Learning activity
Week 01	Special relativity revisited (4-vectors, boosts, observers)	Lecture and tutorial (2 hr)
Week 01	Description of curved surfaces (manifolds, local cartesian, pseudo-Rioemannian)	Lecture and tutorial (2 hr)
Week 02	Motion in curved space-time (vector calculus, geodesics)	Lecture and tutorial (3 hr)
Week 02	Tensor calculus on manifolds (index manipulation, tensor equations) (Weeks 2 - 3)	Lecture and tutorial (3 hr)
Week 03	The equivalence principle and spacetime curvature (Weeks 3 - 4)	Lecture and tutorial (3 hr)
Week 04	Schwarzchild geometry	Lecture and tutorial (2 hr)
Week 04	Experimental tests of relativity (Weeks 4 - 5)	Lecture and tutorial (2 hr)
Week 05	Schwarzchild black holes	Lecture and tutorial (2 hr)
Week 05	Other geometries (Kerr, Alcubierre)	Lecture and tutorial (1 hr)
Week 06	Gravitational waves	Lecture and tutorial (2 hr)
Week 06	The gravitational field equations	Lecture and tutorial (2 hr)
Week 07	FRW geometry	Lecture and tutorial (2 hr)
Week 07	Cosmological models	Lecture and tutorial (2 hr)
Week 08	Inflationary cosmologies	Lecture and tutorial (2 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

The text for this course is

J. Hartle, “Gravity: An introduction to Einstein’s General Relativity”

and set readings from this text will be specified on Canvas. The following text is also suggested for reference:

M.P. Hobson, G.P. Efstathiou, A.N. Lasenby, “General Relativity: An Introduction for Physicists”

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. Synthesise knowledge of Newtonian gravity and special relativity from the undergraduate syllabus.
LO2. Demonstrate understanding of the physics of space-time and its interaction with matter and light in the General Theory of Relativity, and contrast the theory with earlier descriptions of gravity.
LO3. Apply physics knowledge and mathematical skills to solve problems, including applying the field equations with different metrics.
LO4. Analyse gravitational phenomena in nature including black holes, wormholes, warp drives, and the cosmological history of the Universe.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

The number of assessments has been reduced. No other changes have been made since this unit was last offered.

Additional information

EQUITY, ACCESS AND DIVERSITY STATEMENT

The School of Physics recognises that biases, bullying and discrimination, including but not limited to those based on gender, race, sexual orientation, gender identity, religion and age, continue to impact parts of our community disproportionately. Consequently, the School is strongly committed to taking effective steps to make our environment supportive and inclusive and one that provides equity of access and opportunity for everyone.

The School has three Equity Officers as a point of contact for students who may have a query or concern about any issues relating to equity, access and diversity. If you feel you have been treated unfairly, discriminated against, bullied or disadvantaged in any way, you are encouraged to talk to one of the Equity Officers or any member of the Physics staff.

More information can be found at https://sydney.edu.au/science/schools/school-of-physics/equity-access-diversity.html

Any student who feels they may need a special accommodation based on the impact of a disability should contact Disability
Services: https://sydney.edu.au/study/academic-support/disability-support.html who can help arrange support.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect

Current students

PHYS4123: General Relativity and Cosmology

Semester 2, 2022 [Normal day] - Remote

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect