Geometry of the lightfront and its application to dynamics of gravitational field
Ph.D. thesis in Mathematical Physics, Physics Department, University of Warsaw, 2002
Advisor: Prof. dr hab. Jerzy Kijowski
Abstract:
Geometric tools describing the structure of a nulllike surface S (wave front) are constructed. They are applied to analysis of interaction between a lightlike matter shell and the surrounding gravitational field. 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 for the dynamics is derived.  A quasilocal proof of the first law of black holes thermodynamics is obtained as a consequence, in case when S is a nonexpanding horizon.  A complete Lagrangian and Hamiltonian description of the theory of selfgravitating lightlike matter shells is given in terms of gaugeindependent geometric quantities. Finally, the Hamiltonian dynamics of the interacting system: "gravity + matter'' is derived from the total Lagrangian.  The results are applied to a special case and dynamics of a spherically symmetric selfgravitating shell of lightlike matter is solved.
Manuscript (in Polish):
Published as:
 E. Czuchry, J. Jezierski and J. Kijowski, Dynamics of gravitational field within a wave front and thermodynamics of black holes, Phys. Rev. D 70 (2004) 124010 (grqc/0412042).
 E. Czuchry, J. Jezierski and J. Kijowski, Null hypersurfaces in general relativity, Proceedings of the Thirteenth Workshop on General Relativity and Gravitation in Japan, Osaka, December 1–4, 2003; edited by H. Ishihara, K. Nakao, N. Kanda, H. Nakano, T. Nakamura, K. Tomita; pp. 68–71.
 E. Czuchry, J. Jezierski and J. Kijowski, in Relativity Today, Proceedings of the 7th Hungarian Relativity Workshop, edited by I. Racz (Akadémiai Kiadó, Budapest, 2004) (grqc/0405073).
 J. Jezierski, J. Kijowski and E. Czuchry, Dynamics of a self gravitating lightlike matter shell: a gaugeinvariant Lagrangian and Hamiltonian description, Phys. Rev. D 65 (2002) 064036 (grqc/0110018).
 J. Jezierski, J. Kijowski and E. Czuchry, Geometry of nulllike surfaces in General Relativity and its application to dynamics of gravitating matter, Rep. Math. Phys. 46 (2000) 397–418 (pdf).
In preparation:
 E. Czuchry and J. Kijowski, Dynamics of a selfgravitating shell of matter.
 E. Czuchry and J. Kijowski, Dynamics of a spherically symmetric null shell of matter.
