# XXIV SIGRAV Conference on General Relativity and Gravitation

Sep 7 – 9, 2021
Urbino/Palazzo Battiferri
Europe/Rome timezone

## Canonical Analysis of Brans-Dicke Theory Addresses Hamiltonian Inequivalence between Jordan and Einstein Frames

Sep 7, 2021, 10:30 AM
30m
Urbino/Palazzo Battiferri

#### Urbino/Palazzo Battiferri

Via Aurelio Saffi, 42, 61029 Urbino PU
Gravity theory

### Speaker

Gabriele Gionti, S.J. (Vatican Observatory (Specola Vaticana))

### Description

We analyze the Brans-Dicke theory with a Gibbons-Hawking-York(GHY) boundary term and perform ADM decomposition both in Jordan and Einstein frames. For ω≠-3/2, we show that, at the Hamiltonian level, the Weyl (conformal) transformations from the Jordan to Einstein frames are not canonical transformations (in Hamiltonian sense). A set of canonical transformations is found. These are Anti-Gravity or Anti-Newtonian transformations and are different respect to the transformations from the Jordan to the Einstein frames. The case for ω=-3/2 with GHY boundary term is studied as well. The presence of the conformal invariance too in the Jordan frame, the Dirac’s constraint algebra of secondary first-class constraints is different in the Jordan frame respect to the Einstein frame. This inequivalence of the Dirac’s algebra between the two frames addresses, more strongly respect to the case ω≠-3/2, the non (Hamiltonian)-canonicity of the transformations from the Jordan to the Einstein Frames.