Text k předmětu SPECIÁLNÍ TEORIE RELATIVITY:

POZNÁMKY:

• Text pokrývá víceméně přesně látku vyučovanou v kursu Speciální teorie relativity (NOFY023).
• Omlouvám se, že stále chybějí obrázky, snad brzy doplním...

Lecture notes to GENERAL THEORY OF RELATIVITY, RELATIVISTIC PHYSICS I and RELATIVISTIC PHYSICS II:

REMARX:

• Notes cover the first two semesters of GR (Obecná teorie relativity, NTMF111; and Relativistická fyzika I, NTMF037) and some topics of the third semester (Relativistická fyzika II, NTMF038). They do not (yet) include most of the topics usually covered by student talks. Will try to also add these gradually.
  Text has not "suffered" any serious check, so will be grateful for corrections, suggestions...
  Some references to other sections are not working (?? being displayed) -- it is typically because the respective sections do not yet exist.
  Bibliography is by far not complete, it has been included in an opportune way.
  Figures 2.1 and 6.2 are slightly misplaced; have been fighting with that without success. Apparently bounding box (they are eps) is not recognized correctly (though it IS there and correct).
• 5th November 2020: Section 13.7.1 and Reissner-Nordström added.
• 16th November: Kerr and "More on motion in black-hole fields" chapters added, together with Appendix B.
18th November: Section 17.2.7 added, plus a few corrections.
• 4th January 2021: Chapter on Black holes & gravitational collapse added (see Fig. 18.2 on energy extraction employing a perfect Bosch dynamo!), plus part of the chapter on Relativistic stellar models (as far as the TOV equation). Beware, I changed notation for the Killing vector fields in stationary and axisymmetric space-times: instead of "eta" and "xi", am now denoting them "t" and "phi" (with respective index) -- hope it is suggestive.
• 11th January: Chapter on Relativistic stellar models written as far as Equation for energy transfer (still missing is the section on Radial oscillations).
  I have changed notation for cyclic permutation of indices from the cumbersome [...]cycl to {...}. It is described in Preface / notation part.
• 1st February: Chapter on Relativistic stellar models finished, and chapters on Final stages of stellar evolution and on Lagrangian formulation added. Therefore, all lectures of the first two GR semesters have been covered.
  Besides that, short (but important) section 7.6 has been added, also something at the end of A.1.1. And hope you will like new figures (e.g. in Preface).
  Thanks go to Matěj Mezera for several corrections.
• 23rd February: Chapter on Fermi-Walker transport added (applications are not compulsory; may use them next semester for seminar), plus several minor corrections.
  Thanks to Jan Střeleček and Richard Ivánek for corrections.
• 15th March: Chapters 23 (Vector fields and their integral congruences) and 24 (3+1 splitting of space-time) added. Plus minor corrections throughout.
  Thanks to Valerie Tynianski for noticing a mistake.
• 18th March: correcting misprints in the chapter on geodesics (thanks to Jonáš Dujava).
• 25th March: Chapter 25 (Hamiltonian formalism in GR) included, and section on surface term in Chapter 22 (Lagrangian formalism) added. New figure 24.1 in the (3+1)-splitting Chapter.
• 6th April: Chapter on Linearised theory and gravitational waves added (now it is Chapter 22), with its last (-but-one possibly) section yet to be done. Plus occassional editing at various places.
• 12th April: Chapter on Linearised theory and gravitational waves continued, just would like to finish its "Gravitoelectromagnetism" section. Thanking again Matěj Mezera for several corrections.
• 19th April: Chapter on Linearised theory and gravitational waves finished.
• 23rd April: Section 23.1 (Action and the functional derivative) added and, at the beginning of Chapter 26 (Hamiltonian formulation), the generic name for configuration variables (fields) changed from "q" to "psi", in order to be consistent with Section 23.1.
• 7th May: Many minor modifications, plus Kandinsky ("Weighing down", featuring the "=" sign) added after the Einstein equations. Thanks to Jonáš Dujava for comments.
• 11th May: Section on Shapiro time delay added after apsidal advance and light bending. And paragraph on principal null directions (17.3.7) modified in normalization of the principal fields. (Thanks to Valerie Tynianski for discussion and checking.)
• 25th May: Have simplified derivation in the Frobenius-theorem section, and also (thanks to Jonáš Dujava) "proof" of the planarity of geodesic motion in Schwarzschild.
• 2nd June: Algebraic classification of tensor fields started. Plus minor corrections elsewhere (mainly in the Frobenius-theorem section).
• 11th October: Several corrections at various places, mainly due to Jonáš Dujava.
• 7th January 2022: Algebraic classification continued (Goldberg-Sachs theorem still remains to be proven), "Palatini's" variational method (hopefully) treated in a simpler way, certain extension in the null-congruence section. Plus various minor corrections -- thanks go mainly to Róbert Jurčík. "Bez názvu" by Václav Boštík added at the end by obvious reason.
• 14th February 2022: Edit in "Effect of gravitational waves on test particles" section, thanks to Michael Vávra.
• 31st March 2022: Minor error corrected in "d'Alembert gamma_{0j}" equation above eq. (22.37) (and, consequently, in 22.37 itself) in the Gravitoelectromagnetism section, thanks to Šimon Pajger. Plus minor edit in the Newtonian limit of Einstein equations. Plus still fighting with (simple proof of) the Goldberg-Sachs theorem... (standardly it is being proved in Newman-Penrose formalism, which I however do not want to employ).
• 8th May 2022: Several corrections of minor mistakes, otherwise nothing new.
• 31st October 2022: Several corrections of minor mistakes, nothing really new.
• 23rd December 2022: Minor corrections, somewhat more concise "Palatini's variational method".
• 20th January 2023: "Palatini's variational method" improved even more thanks to Jonáš Dujava.
• 4th April 2023: There are always mistakes to correct...
• 12th October 2023: Several improvements thanks to Marek Milička.
• 21st November 2023: Few corrections thanks to Karel Balej. A short paragraph on acceleration of circular motion (specifically on the "repulsive" effect at the very centre) in Kerr added. The (summer) long list of comments from Jonáš Dujava still to be tackled...
• 18th March 2024: Quite some changes: new chapter on Conservation laws added. (Note: still certain details on Lie derivative should be fixed, also in the Lie-derivative chapter. -Thanks to Pavel Krtouš for discussions.) Part of a new chapter on Initial (Cauchy) problem added (GR case still to be covered). And, few corrections thanks to Viktor Vařeka (mainly on Carter observers, in the Kerr section).
• 25th March 2024: Cauchy problem for GR finished, just a "summarizing theorem" yet to be added.
• 15th April 2024: Various improvements in the Conservation-laws chapter (also adjusting signs in definitions to match the rest of the notes), the "Pseudotensor" section yet to be done. Cauchy problem for GR finished completely.
• 30th April 2024: Various improvements in the Conservation-laws chapter (the section on Landau-Lifshitz pseudotensor rewritten), several changes in the Hamiltonian-formalism chapter. Some additions to the chapter on Lie derivative (Lie derivative of the affine connection etc.) A short section on Geometrical objects added to the chapter on fundamental principles.
• 14th May 2024: Slight improvements mainly in chapters on Hamiltonian formalism and Algebraic classification. Heroic section 28.2.5. corrected and completed!
• 21st May 2024: Slight additions in the Algebraic classification chapter.
• 29th November 2024: VERY helpful remarks by Jonáš Dujava "implemented", at last! Plus a few minor improvements.
• 9th December 2024: Another incredible progress: hyperreferences. Have had to delete all the maths in section titles, now it should work. Enjoy :-)
• 3rd February 2025: Again incredible: the Goldberg-Sachs theorem proved at last! Who invents shorter way will be punished somehow. (Just being obstinate, the whole chapter on algebraic classification is not in fact covered within the course.) And thanks to Karel Kraus, David Podrápský and mainly Marek Milička for comments.
• 25rd February 2025: Many minor changes, I think useful at times.

Notes on black-hole horizons in circular space-times (part of BLACK-HOLE THERMODYNAMICS course in 2025):