Thesis

Energetics and thermodynamics of black holes

• Call:

  IDPASC Portugal - PHD Programme 2014

• Academic Year:

  2014 /2015

• Domain:

  General Relativity

• Supervisor:

  José Sande Lemos

• Co-Supervisor:

  Vitor Cardoso

• Institution:

  Instituto Superior Técnico

• Host Institution:

  Instituto Superior Técnico

• Abstract:

  Black holes are of great importance in studies in astrophysics, gravitation and fundamental physics. One part of the thesis will involve purely classical investigations of black holes, in particular, black holes in strong magnetic fields and physics of particles and fields in their vicinity. Solutions of the Einstein-Maxwell are available by Ernst and other authors, which describe such configurations exactly. They are quite involved. However, in case of almost extremal black holes without external magnetic fields it is known that one can approximate the geometry around horizons by simpler metrics. One would like to see how such descriptions may be generalized for the cases when strong magnetic fields are present. Further points of interest involve other recent results like the presence of ergoregions far from rotating black holes in magnetic fields, as envisaged recently by Gibbons et al in 2013, or charged clouds of particles or fields which can be supported by just near-extremal Kerr-Newman black holes as discussed by Hod in 2014. Near extremal black holes are of utmost importance also from their thermodynamical and quantum properties. In addition, similar effects in case of weak but non-axisymmetric (not-aligned with hole's rotation axis) fields around black holes are of considerable interest. Other parts of the thesis involve the black hole interior, the black hole horizon, and its relation to fundamental physics. For instance, one would like to find new regular interior black hole solutions and test their stability. In relation to the horizon one could combine both the Euclidean action and membrane paradigm approaches and obtain a direct derivation of the black hole entropy in the case there are electric and magnetic fields present. In the vicinity of the horizon one could also study important physical phenomena like generalized Banados-Silk-West effect, discovered in 2009, where black holes can act as particle accelerators with collisions, in principle, at arbitrarily high center-of-mass energies, or Meissner-type effects of the expulsion of the flux of axisymmetric magnetic fields from the horizons of extreme black holes which was demonstrated by Bicak et al some time ago and has been revived most recently. Finally, although black holes are objects not fully understood yet, from some of their generic properties one can extract important indications to a fundamental theory. Such a theory should include in a unified way, gravitation and quantum mechanics. We know from quantum calculations that black holes have a well defined entropy and temperature, the Bekenstein-Hawking entropy, proportional to the area of the black hole, and the Hawking temperature. Through several physical arguments one can deduce that the black hole entropy is the maximum entropy in a given region of space. This in turn led to the holographic principle as proposed by ’t Hooft and Susskind which states that, associating the entropy with the logarithm of the number of possible quantum states of the system, one is led to the conclusion that the fundamental degrees of freedom of a given region of space are in the area A of the region, and not in its volume, as one would expect a priori. Certainly, the fundamental theory has to take this into account. In this part of the thesis one wants to further develop the notion of black hole entropy, by studying instances and cases in which classical and quantum arguments mesh in the understanding of the fundamental degrees of freedom.