Special and General Relativity - year IV

ToDo

when/where

• lecture 13:00-14:30 Friday
  • face-to-face (f2f): @KRA main seminar room (sala 20)
  • online: BigBlueButtonHints
• tutorial (cwiczenia) - 14:30-16:00 Friday
  • f2f: @KRA room 48
  • online: BigBlueButtonHints
• extra exercise sessions up to and including Fri XX June may be negotiated
• egzamin: exam TBD XX June/July 2025 09:00-15:00 @Institute of Astronomy, Piwnice Room 48 - 6 hours = maximum time; a good student can finish in 2 hours

communication

• main communication - small-group non-public email
• you may want to join the cosmo-pl list for circulating cosmology announcements interesting to the PL cosmology community

what

• lectures: pdf
  • • full lectures (free-licensed versions):
      • sr_240412.pdf gr_140407.pdf
      • add this file to gifmovie/ locally | LorentzImage - transform some image files
      • twins0606559.pdf: pdf for astro-ph/0606559
      • Wikimedia community managed versions at: http://en.wikiversity.org/wiki/Special_relativity_and_steps_towards_general_relativity
        • SR git source: https://codeberg.org/boud/SRandGR_lectures
• SR (=STW): WikipediaEn:Minkowski_space
  • • WikipediaEn:World_line
• GR (=OTW): WikipediaEn:General_relativity
  
  ((C) 2011 CC-BY-NC, xkcd.com/895 )
  • Bertschinger notes: https://web.mit.edu/edbert/GR/ (SRandGRBertschingerArchived)
  • Concepts:
    • WikipediaEn:Riemannian_geometry (and pseudo-Riemannian geometry)
      • coordinate basis, gradient of vector field, Christoffel symbols https://web.mit.edu/edbert/GR/gr1.pdf
      • directional derivative, parallel transport, geodesics https://web.mit.edu/edbert/GR/gr2.pdf
      • Riemann tensor, curvature, Ricci identity, Ricci tensor, Einstein tensor https://web.mit.edu/edbert/GR/gr2.pdf
      • WikipediaEn:Stress–energy_tensor https://web.mit.edu/edbert/GR/gr2b.pdf
      • WikipediaEn:Einstein_field_equations https://web.mit.edu/edbert/GR/gr5.pdf
      • Exact solutions:
        • WikipediaEn:Schwarzschild_metric
        • WikipediaEn:Friedmann-Lema%C3%AEtre-Robertson-Walker_metric
    • WikipediaEn:Equivalence_principle - can be thought of as consequence of model
  • Equations:
    • WikipediaEn:Intermediate_treatment_of_tensors

advanced level

• Approximation methods:
  • WikipediaEn:ADM_formalism
• software:
  • maxima - component tensor packet ctensor
  • ArXiv:1111.3344 - The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics - Frank Löffler, et al - built on Cactus - http://cactuscode.org

summary of modern cosmology

• AstroPh:0602280 - George Ellis - Issues in the Philosophy of Cosmology - this is a proper scientific approach, i.e. serious philosophy explained in simple (scientific) words

online intros to cosmology

• http://theory.physics.helsinki.fi/~cosmology/
• ArXiv:gr-qc/9712019

wims - wersja online

• http://cosmo.torun.pl/wims -> students' area
• Dlaczego coś jak wims? http://wims.unice.fr/paper/pqt.pdf - a paper explaining the principle of tests with open-question sets. WIMS can be used to implement this principle.
• WimsDyskusja

traditional exercises

• John Peacock has some nice online exercises: http://www.roe.ac.uk/~jap/teaching/cos5.html

how

who

• się dodaj do listy, np Main.PiotrNowak
• BoudRoukema (lecturer)

zaliczenie

• 5 points from relativity exercises on http://cosmo.torun.pl/wims
  • you can do the exercises from outside the spacetime region of the exercise sessions, but without getting points
  • you accumulate points during the official exercise sessions

exam

• calibration: lecturer should be able to do full exam in 60 minutes with a score of at least 4.5 (out of 5)
• fixed day/time, expected up to 3 hours, allowed up to 5 hours, at KRA as in a traditional exam; repeat exam possible in September as in official program
• exam uses a selection of wims exercises used during the exercise sessions, i.e. the questions are different but statistically drawn from the same distribution in a multi-dimensional parameter space with N >> 1 parameters
• same as for exercises: score rounded to nearest number in the set {0, 2, 3, 3.5, 4, 4.5, 5}
• The examination for this subject requires verification that the students are working through examination questions using verifiable tools. Purely online methods of verifying the students' knowledge are insufficient for this course, so a face-to-face "traditional" exam is required. Experience has shown that some students use scientifically invalid methods.
• differences wrt exercises
  • stronger prerequisite relation between exercises - you must do the easier exercises before being allowed to try the harder ones
  • more severe scoring system: instead of
  • no internet acccess
  • fresh shell account - no access to personal notes or scripts; the lecture pdf will be available
  • physics/astro/maths constants: exact: metre-to-second conversion (p129) 1 s = 299792458 m; 1 AU = 149597870700 m; approximate: π 3.14159265359

5.0 grade points on WIMS - how it's calculated

• You can get a grade of up to a maximum of 5.0 points from WIMS exercises:
  • where
    • is the percentage done for a given "sheet" - let us normalise this to the range from 0.0 i 1.0
    • is the "quality" - in the range from 0.0 to 1.0; the power of 0.3 implies that the effect of is weak unless the "quality" parameter is very low
  • how to check your current score:
    • home
      • My scores
        • Global average: something out of 5. Here, something is your total amount of points
• The formula for a single exercise done m times, is po m razy, gdzie , which is in the range from 0.0 to 1.0. This is a decaying average, with . In other words, the most recent tries at a realisation of an exercise have the most influence on the score for that exercise.
• Chromium/Chrome bug: As of 2020 to 2024, chromium/chrome browser software has a bug that prevents the display of some of the exercises. Firefox is one browser without the bug.

old

• SRandGRwhatwhen - possible timing of what is in pdfs + wims on each lecture date