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Methods for exact solutions of gravity theories: isometries and classification of tensors - NTMF081

Title:	Methods for exact solutions of gravity theories: isometries and classification of tensors
Guaranteed by:	Institute of Theoretical Physics (32-UTF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Marcello Ortaggio Mgr. Vojtěch Pravda, Ph.D.

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2022)

Part 1: Isometries, Killing equation, conformal Killing equation, isometry groups. Spaces of constant curvature. Stationary and static spacetimes. Spherically symmetric spacetimes. Birkhoff's theorem in GR. Static black holes. Near horizon limits. Basic notions on Bianchi models. Part 2: Petrov classification, Newman-Penrose formalism, Goldberg-Sachs theorem. Higher dimensions: black holes/strings/rings. Basics of Lovelock gravity, f(R) gravity, quadratic gravity, critical gravity and examples of solutions. Kundt spacetimes. Scalar-tensor gravities.

Course completion requirements -

Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2022)

Oral exam.

Literature -

Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2022)

L. P. Eisenhart, Riemannian Geometry. Princeton University Press, Princeton, 2nd ed., 1949.

J. B. Griffiths and J. Podolsky, Exact Space-Times in Einstein's General Relativity. Cambridge University Press, Cambridge, 2009.

H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein's Field Equations. Cambridge University Press, Cambridge, 2nd ed., 2003.

M. P. Ryan and L. C. Shepley, Homogeneous Relativistic Cosmologies. Princeton University Press, Princeton, 1975.

Papers in scientific journals.

Requirements to the exam -

Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2022)

The course is concluded by an oral exam, which may include both theoretical questions and problems (excercises) on topics from lectures.

Syllabus -

Last update: doc. RNDr. Karel Houfek, Ph.D. (12.05.2022)

Part 1: Isometries and applications (M. Ortaggio)

Isometries, Killing equation, conformal Killing equation, isometry groups. Spaces of constant curvature. Stationary and static spacetimes. Spherically symmetric spacetimes. Birkhoff's theorem in GR. Static black holes. Near horizon limits. Basic notions on Bianchi models.

Part 2: Classification of tensors and applications (V. Pravda)

Petrov classification, Newman-Penrose formalism, Goldberg-Sachs theorem. Higher dimensions: black holes/strings/rings. Basics of Lovelock gravity, f(R) gravity, quadratic gravity, critical gravity and examples of solutions. Kundt spacetimes. Scalar-tensor gravities.