Geometry of the light-front 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 null-like surface S (wave front) are constructed. They are applied to analysis of interaction between a light-like 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 quasi-local proof of the first law of black holes thermodynamics is obtained as a consequence, in case when S is a non-expanding 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. 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 self-gravitating shell of light-like 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 (gr-qc/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) (gr-qc/0405073).
  • J. Jezierski, J. Kijowski and E. Czuchry, Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description, Phys. Rev. D 65 (2002) 064036 (gr-qc/0110018).
  • J. Jezierski, J. Kijowski and E. Czuchry, Geometry of null-like 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 self-gravitating shell of matter.
  • E. Czuchry and J. Kijowski, Dynamics of a spherically symmetric null shell of matter.