In light of this analysis, we derive the resonant approximation for this system using 1) the method of multiple scales and 2) the renormalization group method with the aim of resumming the secular terms in the perturbative series in order to get a description of the relevant dynamics that is valid at long times. terms that grow without bounds, in the perturbative series, which were conjectured to be progenitors of a resonant mode mixing which causes the transfer of energy from lower to higher modes. The numerical evidence was corroborated by a weakly non-linear perturbation analysis which revealed the existence of secular terms, i.e. Friday, November 19th, 13:00 Lunch SeminarĪrgam Ohanyan (Vienna): The Hawking-Penrose singularity theorem for C^1-Lorentzian metricsĪbstract: In 2012, Maliborski gave numerical evidence for the non-linear instability of a portion of (3+1) dimensional Minkowski spacetime enclosed inside a timelike worldtube ℝ⨉B³ with a perfectly reflecting wall under arbitrarily small perturbations.> video of the talk, -> audio of the talk Visser, Holographic Thermodynamics Requires a Chemical Potential for Color. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. This leads to a new understanding of the Van der Waals behaviour of charged AdS black holes, where the phase changes are now governed by C instead of P. I will briefly review his argument, and rewrite the bulk first law in a new form containing both variations of P and C, the central charge of the dual CFT. While the natural unit G=1 was kept in previous studies, Visser argued that considering variations of G is necessary to achieve a duality between the bulk and boundary thermodynamic first laws. Recently, Visser reconsidered the situation in the context of holography. By studying the equation of state of AdS black holes in this extended phase space, many interesting phase transitions were found a prominent example is the Van der Waals like small-to-large phase transition of charged AdS black holes which takes place below a critical pressure. The thermodynamic phase space of AdS black holes has been extended to include a P-V term in. Abstract: Black holes have been accepted as thermodynamic systems ever since Hawking’s discovery of black hole radiation.