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Geometry of the light-front and its application to dynamics of gravitational field, Ph.D. thesis:
- Geometric tools describing the structure of a null-like surface S (wave front) are constructed. Geometry of isolated horizons (surfaces surrounding black holes) is analyzed in terms of the constructed tools.
- Hamiltonian dynamics of gravitational field contained in a spacetime region with null boundary S is discussed. Complete Hamiltonian formula generating its dynamics is derived.
- A quasi-local proof of the first law of black holes thermodynamics is obtained as a consequence, in case when S is an isolated horizon.
- A complete Lagrangian and Hamiltonian description of the theory of self-gravitating light-like matter shells is given in terms of gauge-independent geometric quantities.
- The results are applied to a special case and dynamics of a spherically symmetric self-gravitating shell of light-like matter is solved.
Multipole moments in Kaluza-Klein theories, MS thesis:
Thesis contains discussion of the problem of motion of extended, i.e. non point test bodies in multidimensional space.Extended bodies are described in terms of so called multipole moments. Using approximated form of equations of motion for extended bodies deviation from geodesic motion is derived. Results are applied to special form of space-time. Using the same formalism the relation between space extension and the law of charge conservation is also discussed and revised.
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