A. Gravity - a universal force in space

1. Historical development of knowledge about gravity

Ancient philosophy and natural science - Aristarchos, Aristotle, Ptolemy. The beginnings of European realistic science - Copernicus, Galilee, Kepler, Newton. Newton's and Galileo's basic laws of classical mechanics - law of inertia, law of force and acceleration, law of action and reaction, law of free fall, Newton's law of gravitation. LeS and Ge's hypothesis about the origin of gravity and its rejection.

2. Electromagnetic and gravitational fields in classical physics

Coulomb's law of electrostatics and Newton's law of gravitation - similarities and differences between electricity and gravity. Principle of superposition, laws of excitation of electromagnetic field by electric charges, currents and variable fields - Maxwell shear current (outline of analogy with Isaacson tensor of energy-momentum of gravitational waves), Maxwell's equations, retarded potentials, energy of electromagnetic field, electromagnetic waves.

3. Electromagnetism and gravity in the special theory of relativity

Inertial systems, the principle of relativity of Galileo and Einstein, the principle of constant speed of light. Interval, eigenvalue, Lorentz transformations - contraction of lengths, dilation of time, composition of velocities. Minkowski four-dimensional spacetime - metric tensor, 4-velocity, 4-momentum, energy-momentum tensor.

Relativistic electrodynamics - 4-potential, electromagnetic field tensor, 4-dimensional unification of Maxwell's equations. General principles of field theory. Incompatibility of Newton's theory of gravitation with special theory of relativity, attempts at relativistic formulation of Newton's gravity.


B. General theory of relativity - physics of gravity

1. Versatility - the basic key to understanding gravity

Universality of gravitational interaction - a characteristic feature distinguishing gravity from other types of interactions. Gravity ® inertia ® kinematics ® equivalence principle. Thoughtful experiments documenting the principle of equivalence. Weightlessness state => locally Euclidean geometry of spacetime.

2. Local principle of equivalence and curved spacetime

Principle of equivalence => local application STR => curved Riemann spacetime. Curvilinear coordinates - parallel transfer, metrics and connections, Christoffel coefficients of affine connection, covariant derivation, Riemann curvature tensor. Movement in geodesy, deviation of geodesics. Physical laws in the presence of gravity @ physical laws in curved spacetime - replacement of partial derivatives according to coordinates by covariant derivatives.

3. Einstein's equations of the gravitational field

Universal excitation of the gravitational field by all matter energies => fundamental nonlinearity of gravity. Derivation of Einstein's equations of gravitational field, basic general procedures for their solution, equations of motion of sources as a consequence of Einstein's equations of excited gravitational field. Linearized equations weak gravitational field effects of off-diagonal No L enes in the metric.

4. Gravitational energy and gravitational waves

Retarded potentials and final velocity of disturbance propagation in the gravitational field. Gravitational waves - generation of gravitational waves (quadrupole law), properties and propagation of gravitational waves, detection of gravitational waves, Isaacson's formalism and tensor of effective distributed energy-momentum of gravitational waves (geon, possibility of gravitational wave collapse). Pseudotenzor energy-momentum gravitational field - Bauer paradox nelokalizovatelnost ener g ie gravitational field, local vs global conservation laws in general relativity.


C. Black holes in space

1. Gravity and evolution of stars

Formation of protostars by condensation of the primordial cloud, gravitational collapse and contraction, thermonuclear reactions and stable phases of stellar life. The final stages of stellar evolution - the white dwarf and the Chandrasekhar limit, the formation of the neutron star and the Oppenheimer-Landau limit, the complete gravitational collapse.

2. Gravitational collapse and formation of black holes

Scenario of relativistic gravitational collapse and the formation of a black hole. Effect of narrowing the output light cone, event horizon, singularity. Confrontation of the description of the external and internal observer.

3. Schwarzschild non-rotating black holes

Schwarzschild geometry of spheres of cky -symmetric gravitational field. Spherically symmetric collapse, Birkhoff's theorem. Shapes of light cones, photon sphere, Schwarzschild sphere. Movement of particles and photons in a field of non-rotating black holes, diffraction of light, gravitational lensing effect. Kruskal p rostoročasový diagram Einstein-Rosen bridge to the second space Penrose conformal diagram.

4. Rotating Kerr-Newman black holes

Gravitational collapse scenario of a rotating star. Kerr-Newman geometry of space-time axially symmetric rotating black holes - entrainment of local inertial systems, static limit, ergosphere, Penrose process and superradiation. Motion of particles and photons in the field of a rotating black hole. Classification of black holes - Schwarzschild, Kerr, Reissner-Nordström and Kerr black holes, extreme black holes, nude singularities (cosmic censorship principle). Outer and inner horizon, Kerr and Penrose space-time diagrams, black holes as "tunnels" to other universes.

5. Laws of black hole dynamics and quantum evaporation of black holes

The " black hole has no hair " theorem - preservation of mass, momentum and electric charge of black holes, uniformity and indistinguishability of black holes of various origins, violation of prediction towards the past. 1st law of black hole dynamics. 2nd law of black hole dynamics - reversible and irreversible processes, indestructibility of black holes. 3rd law of black hole dynamics. Analogies and connections with thermodynamics. Hawking effect of quantum evaporation of black holes - vacuum polarization and production of particle- and antiparticle pairs around the horizon, tunneling phenomenon. Violation of the 2nd Act of Black Hole Dynamics. Thermal character of quantum radiation, thermodynamics of black holes. Quantum black hole explosion, primordial black holes. Violation of conservation laws and determinism u during collapse and quantum evaporation of black holes.

6. Astrophysical significance of black holes

Possibilities of black holes - collapse of stars isolated, in binary and multiple systems, black holes in star clusters, gigantic black holes in the cores of galaxies, primordial black minidires. Interaction of black holes with the surrounding matter and with each other. Accretion of matter into a black hole - thin and thick accretion disks, mass and energy transfer, efficiency of conversion of accretion mass into radiated energy, collimation; quasars . Total gravitational collapse - the greatest catastrophe in nature and the deepest paradox in physics.


D. Relativistic cosmology

1. Historical development of cosmological ideas

Cosmological ideas of ancient and medieval - the "gap" between the laws of terrestrial nature and the "heavenly" laws of the universe. Newtonian cosmology - its successes and limitations (Olbers' photometric paradox, Seeliger's gravitational paradox).

2. Relativistic cosmological models

Basic starting points and principles of cosmology - uniqueness of the universe, Kop erník's principle, homogeneity and isotropy of the universe, static « dynamics of the universe, redshift and Hubble's constant, relic radiation. Procedures for constructing a relativistic cosmological model - symmetry and metrics of spacetime, cosmological matter, solution of Einstein's equations. Einstein's model of the static universe - cosmological constant, finiteness and closedness of the universe. Fridman dynamic models - Robertson-Walker metric, Fridman equations, Hubble constant and deceleration parameter, critical density of matter, evolution of closed and open space, influence of cosmological constant.

3. Standard cosmological model and physical comology

The concept of a hot early universe - the "big bang". Hadron Era - baryon asymmetry. The Lepton Era - Separation of neutrinos from other matter, helium formation, and primary nucleosynthesis. The era of radiation - the separation of radiation from matter, the origin of relic radiation. The era of matter - the formation of the large-scale structure of the universe (a cluster of galaxies and galaxies). Hidden matter in space - non-radiant gravitational matter in galaxies and galaxy clusters, baryon and non-baronic nature of hidden matter. Future space - diversity evolution closed and open space, "large bust," collapse galaxies quantum evaporation BLACK characterized ch holes, disintegration baryons "thermal death" universe.

4. Inflation model of a very early universe

Difficulties and problems of the standard cosmological model - the problem of singularity and finiteness of the universe in time (oscillating versus single cycle universe), local and global homogeneity and isotropy of the universe, the problem of horizon, the problem of flatness and precise "tuning" of expansion rate, the problem of germinal inhomogeneities, the problem of baryon asymmetry, problem of relic magnetic monopoles. Quantum unitary t EORI fields in the very early universe - phase transitions and false vacuum stage inflationary expansion of the universe, solving problems and difficulties of the standard model. Neoinflationary models, chaotic inflation, spontaneous emergence of the universe "out of nothing", irrelevance of initial conditions.

5. Anthropic principle and existence of multiple universes

Possibilities of the origin of life in different structure and evolution of the universe. Weak anthropic principle. Strong anthropic principle. Anthropic principle of many universes - physical, cosmological and philosophical aspects. Participatory anthropic principle - connections with quantum physics and gnoseology. The final anthropic principle and its unreality.


E. Philosophical aspects of relativistic astrophysics and cosmology

1. The relationship between philosophy and natural sciences

The concept of nature in the most important philosophical directions. Space and time : philosopher. categories « physical quantities « of basic substance (relation to geometrodynamics), geometry and topology (black holes, cosmology). Infinity : potential « current, extensive « intense (in cosmology and microworld). Matter : attributes and structure, origin of « extinction, matter « of energy, matter «of field, unitary theory of field and matter (matter formed from emptiness?). The essence and development of the world: evolution « project, chaos « self-organization (synergetics), the origin of life (evolution« Creation). Information « tangible wearer, the spirit of " mass. Causality and knowledge: determinism " indeterminacy (the macroscopic world, micro and megasvětě) coincidence " destiny, freedom of will " BC natural laws . Positive science " philosophy, ethics and aesthetics in science, altruism: inspiration of God, " the result of evolution driven by natural laws. Knowledge « wisdom.

2. The concept of God and science

Demonism - animism - polytheism - monotheism. Basic conception of God - theism, deism, pantheism. The search for God on a psychological and scientific level. Thought link of the most important religions - Hinduism, Buddhism, Taoism, Confucianism, Islam, Christianity. Physics and God : Classical Physics and Materialism; theory of relativity, quantum physics, field theory and transcendent; synergetics, unitary field theory and quantum cosmology - a new perspective on the concept and role of God.

The lecture or seminar is intended for 5th year students of
physics and mathematics at the Faculty of Science

Lecturer: RNDr. Vojtech Ullmann


Recommended literature:

Grygar J., Horsky Z., Mayer P .: Vesmir. MF, Prague 1979

Hawking S .: A Brief History of Time. Alfa, Bratislava 1992

Horský J .: Introduction to the Theory of Relativity. SNTL, Prague 1975

Kuchař K .: Basics of General Theory of Relativity. Academia, Prague 1968

Landau LD, Lifšic EM: Field Theory. Science, Moscow 1974

Ullmann V .: Gravity, Black Holes and the Physics of Spacetime. Cs. astronomer. company Č SAV, Ostrava-Prague 1986 (reprint 1990)

Ullmann V .: Anthropic Principle or Cosmic God. Syllabus. Cs. astronomer. spol. CSAV, Ostrava 1988

Vanýsek V .: Fundamentals of Astronomy and Astrophysics. Academia, Prague 1980

Weinberg S .: The first three minutes. MF, Prague 1983

Note : Only a few (mostly book) titles are listed that are easily accessible to students, either at school or in the research library. A more comprehensive list of literature is given, for example, in the monograph " Gravity, Black Holes and the Physics of Spacetime ", from which the whole seminar is thematically based. For informative follow-up of new findings, we can recommend the published journals "Advances in Mathematics, Physics and Astronomy", "Universe", "Cosmos" and "Realm of Stars".

Gravity, black holes and space-time physics :
Gravity in physics General theory of relativity Geometry and topology
Black holes Relativistic cosmology Unitary field theory
Anthropic principle or cosmic God
Nuclear physics and physics of ionizing radiation
AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy