In this talk I will discuss several aspects of theories with curvature, torsion and non-metricity in the absence and presence of a cosmological constant, i.e. also in relation to holography. After an overview over the topic, I will in particular discuss a derivation of the universal Gibbons-Hawking-York boundary term necessary for the variational principle in all theories with curvature, torsion and non-metricity. The method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, a split formalism for differential forms is used, in which the boundary terms of the action are manifest by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. I observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. I furthermore confirm existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity, and obtain new results for Lovelock-Chern-Simons and metric-affine gravity. In the second part of this talk, I will discuss the correct treatment of the boundary terms in the geometric trinity of Einstein-Hilbert (curvature only), teleparallel (torsion only) and symmetric teleparallel (non-metricity only) gravity. I in particular show that the GHY term for both TEGR and STEGR must vanish for consistency of the variational problem. Furthermore, I discuss how this approach allows to extend the equivalence between GR, TEGR and STEGR beyond the Einstein-Hilbert action to any action built out of the curvature two-form, thus establishing the generalized geometrical trinity of gravity.

Biography

René Meyer received his Ph.D. from LMU Munich, in 2009. He conducted postdoctoral research at the University of Crete (2009-12), IPMU (2012-15) and Stony Brook U. (2015-16). Since 2016, he has been working at Julius-Maximilians-Universität Würzburg (Germany). His research primarily focuses on high-energy physics, AdS/CFT correspondence, string theory and quantum information theory.

Inviter: Li Li