Thesis

Critical phenomena in gravitational collapse and black hole formation

• Call:

  IDPASC Portugal - PHD Programme 2015

• Academic Year:

  2015 / 2016

• Domains:

  General Relativity | Astrophysics

• Supervisor:

  Filipe Mena

• Co-Supervisor:

  José Sande Lemos

• Institution:

  Universidade do Minho

• Host Institution:

  Instituto Superior Técnico

• Abstract:

  Many physical systems can suffer phase transitions, i.e., the state of the system changes abruptly when a relevant parameter characterizing the system changes continuously. A common example is given by a normal metal turning into a ferromagnetic metal when the temperature decreases past a critical temperature. Unexpectedly, the same type of phenomenon happens in the gravitational collapse of matter. For low density matter, the collapse rebounds and disperses to infinity, whereas for large density the collapse forms a black hole. There is a critical value, parametrized by a parameter p that separates the two possibilities. The solution at the critical value is self-similar, discrete and universal, hinting that there are similarities with thermodynamic phase transitions. In these transitions, the important parameter is the order parameter (it gives a measure of the order in the system in a phase transition). In the ferromagnet case the order parameter is the magnetization of the metal. In simple gravitational collapse the order parameter can be the mass of the collapsing system. However, other parameters can feature in the collapse system. For instance, electric charge, angular momentum in the usual general relativity or even other conserved charges that appear in modified gravity theories and, in particular, in brane world models. In this thesis we want to fully understand the role of the conserved charges in the critical stage phenomenon using analytical and numerical methods. This will provide a bridge to the well know black hole thermodynamic properties at classical and quantum levels. [1] M. W. Choptuik, "Universality and scaling in the gravitational collapse of a massless scalar field", Physical Review Letters 70, 9 (1993). [2] J. P. S. Lemos, "Naked Singularities: Gravitationally Collapsing Configurations of Dust or Radiation in Spherical Symmetry - A Unified Treatment", Physical Review Letters 68, 1447 (1992). [3] C. R. Evans, J. S. Coleman, "Observation of Critical phenomena and self-similarity in the gravitational collapse of radiation fluid", Physical Review Letters 72, 1782 (1994); arXiv:gr-qc/9402041. [4] C. Gundlach, C., "Critical phenomena in gravitational collapse", Advances in Theoretical and Mathematical Physics 2, 1 (1998); arXiv:gr-qc/9712084. [5] D. Garfinkle, "Choptuik scaling in null coordinates", Physical Review D 51, 5558 (1995); arXiv:gr-qc/9412008. [6] P. Bizon, "Critical collapse of Skyrmions", Physical Review D 58, 041501 (1998); arXiv:gr-qc/9801012. [7] T. Harada, H. Maeda, B. Semelin, "Criticality and convergence in Newtonian collapse", Physical Review D 67, 084003 (2003); arXiv:gr-qc/0210027. [8] J. Bland, B. Preston, M. Becker, G. Kunstatter, V. Husain, "Dimension dependence of the critical exponent in spherically symmetric gravitational collapse", Classical and Quantum Gravity 22, 5355 (2005); arXiv:gr-qc/0507088 [9] E. Sorkin, Y. Oren, "On Choptuik's scaling in higher dimensions", Physical Review D 71, 124005 (2005); arXiv:hep-th/0502034. [10] M. Mars, F. C. Mena, R. Vera, "First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models", Physical Review D 78, 084022 (2008); arXiv:0805.4179 [gr-qc]. [11] L. Alvarez-Gaume, C. Gomez, A. Sabio Vera, A. Tavanfar, M. A. Vazquez-Mozo "Critical gravitational collapse: towards a holographic understanding of the Regge region", Nuclear Physics B 806, 327 (2009); arXiv:0804.1464 [hep-th]. [12] J. M. Torres, M. Alcubierre, "Gravitational collapse of charged scalar fields", General Relativity and Gravitation 46, 1773 (2014); arXiv:1407.7885 [gr-qc]. [13] X. Zhang, H. Lu, "Critical Behavior in a Massless Scalar Field Collapse with Self-interaction Potential", Physical Review D 91, 4 (2015); arXiv:1410.8337 [gr-qc].