On March 18, Pablo Guilleminot defended his doctorate thesis titled “First-order Lagrangian of Lovelock gravity and applications”. His work was guided by Dr. Rodrigo Olea (UNAB – HolographyCL) and Dr. Nelson Marino (UNAP), and his comitee was formed by Dra. Olivera Miskovic (PUCV – HolographyCL), Dr. Rodrigo Aros (UNAB), Dr. Alberto Faraggi (UNAB – HolographyCL) and Dr. Cristóbal Corral (UNAP).
Much of the Physics we know is described by first-order functionals (actions), i.e., that depend at most on the speed squared. The action for General Relativity, on the other hand, does not fit into this category. In fact, the dynamics of Einstein’s gravitation is given by a Lagrangian that depends linearly on acceleration. Such a Lagrangian can consistently be put into its first-order form by adding a boundary term, without changing the dynamics.
The first part of this Thesis replicates the previous idea to a gravitational Lagrangian given by the Lovelock functional, which contains higher powers in the curvature and still gives rise to second order equations in the derivatives. [Guilleminot et al., Class.Quant.Grav. 38, 10 (2021)]
The second part of the work considers an application of the first-order equivalent Lagrangians to joining conditions. When a thin shell of matter separates space into two regions, the geometry presents a discontinuity between inside and outside. In the present development, the leap in geometry is characterized by the discontinuity in the canonical moment of the theory (taking the radial coordinate as the one generated by the evolution of the system). This uniquely characterizes the collapse of this self-gravitating bubble. [Guilleminot, Merino and Olea, manuscript in preparation]
