615.748.81 - Introduction to Relativity

Expanded Course Description

This course begins with the special theory of relativity, tensor calculus in Minkowski space-time, and the covariant formulation of the electromagnetic field and its stress-energy-momentum tensor and the associated conservation laws.  Relativistic perfect fluids and their energy-momentum tensor as the source of gravitation are defined.  Tensor calculus and geodesics in curved pseudo-Riemannian manifolds is presented and Einstein's field equations are studied.  Gravitational waves and their detection are described.  The Schwarzschild and the Kerr black holes will be thoroughly investigated.

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu.   Each module may be divided into multiple videos, and includes a homework assignment. Course modules are released on Saturdays and allow nearly 10 days for assignment submission. 

Course Topics

• Module 01:  Introduction
• Module 02:  The Special Theory of Relativity (SR)
• Module 03:  Vector calculus in SR
• Module 04:  Tensor calculus in SR
• Module 05:  The Electromagnetic Field
• Module 06: Sources of the Gravitational Field:  Perfect fluids and their Energy-Momentum Tensor; Tensor calculus in curvilinear coordinates of flat space
• Module 07:  Curved manifolds: covariant derivative, geodesics, the curvature tensor, and parallel transport
• Module 08:  Physics in a Curved Space-Time, the Einstein Field Equations
• Module 09:  Gravitational radiation I 
• Module 10:  Gravitational radiation II     
  
• Module 11:  Spherically symmetric space-times
  
• Module 12:   The Schwarzchild (black hole) solution
• Module 13:   Rotating black holes and the Kerr Solution I
• Module 14:  Rotating black holes and the Kerr Solution II
  

Course Goals

A thorough understanding of the physical and the mathematical foundations of Einstein's theory of relativity (the special and the general theories) and their applications to the most modern developments including black holes and gravitational waves.

Course Learning Outcomes (CLOs)

• • Explain the physical basis for the special and the general theories of relativity.
• • Draw and use space-time diagrams and perform tensor calculations.
• • Explain the significance of the Einstein field equations and interpret them in astrophysical and cosmological contexts.
• • Derive and explain the important tests of GR: gravitational deflection of light and the perihelion shift of Mercury’s orbit.

Textbooks

"A First Course in General Relativity", by B. Schutz
Second or third edition.
Cambridge University Press, ISBN:  978-1-108-49267-6

Student Coursework Requirements

This course will consist of two basic student requirements:

• Weekly Assignment (85% of final grade)

Weekly assignments task you to apply the concepts that are covered in the weekly readings and lectures. There are 14 assignments (one each week) and they are equally weighted toward your final grade.  Late assignment policy:  maximum grade is limited to 90% if 3 days late, and 80% if 6 days late, and 50% if later than 6 days.

• Discussion Forums (15% of final grade)

Each week, you are required to complete a discussion post explaining point(s) or concept(s) that challenged you during the week. These will help the instructor to offer guidance and feedback as the course progresses. There may be a small number of additional discussion forums related to applications for the material being presented in which case they will become the topic of discussion for that week. All discussion forums are weighted equally. Please refer to the Rubric posted in Canvas for grading criteria related to discussion forums.

Grading Policy

Course Policies

All assignment must be submitted as PDF files in Canvas.  All assignments must be well presented and readable.  Most students use LaTeX to produce their PDF outputs.  Handwritten work must be tidy and readable and contain no ``scratch work''.  Scanned documents must be readable; cell phone photos on your kitchen table are usually insufficient.  Late submissions will be reduced only if prior arrangements have not been made.  If the work is late and you have not spoken with any of us prior to submitting your work, the maximum grade you could achieve on the late assignments will be lowered by 5 points for every day the assignment has been late.  Grades will be available within 7-9 days after submission.  A second attempt may be granted when deserved.  Should you be asked to make a second attempt then you must submit your second attempt within 3 days so as to receive a maximum of 90 points. 

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.