## Abstract

The Palatini formalism, which assumes the metric and the affine connection as independent variables, is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, as done in the usual teleparallel theories, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither curvature nor torsion, so that all the geometrical information is encoded in the non-metricity. We discuss how this geometrical framework leads to a purely inertial connection that can thus be completely removed by a coordinate gauge choice, the coincident gauge. From the quadratic theory we recover a simpler formulation of General Relativity in the form of the Einstein action, which enjoys an enhanced symmetry that reduces to a second linearised diffeomorphism at linear order. More general theories in both geometries can be formulated consistently by taking into account the inertial connection and the associated additional degrees of freedom. As immediate applications, the new cosmological equations and their Newtonian limit are considered, where the role of the lapse in the consistency of the equations is clarified, and the Schwarzschild black hole entropy is computed by evaluating the corresponding Euclidean action. We discuss how the boundary terms in the usual formulation of General Relativity are related to different choices of coordinates in its coincident version and show that in isotropic coordinates the Euclidean action is finite without the need to introduce boundary or normalisation terms. Finally, we discuss the double-copy structure of the gravity amplitudes and the bootstrapping of gravity within the framework of coincident General Relativity.

## Full Text

### Topics from this Paper

- Boundary Terms
- Teleparallel Equivalent Of General Relativity
- General Theories
- Choices Of Coordinates
- Palatini Formalism + Show 5 more

Create a personalized feed of these topics

Get Started#### Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call### Similar Papers

- Journal of Cosmology and Astroparticle Physics
- Mar 27, 2018

- International Journal of Modern Physics A
- Nov 20, 2002

- Physical Review D
- Apr 19, 2022

- Physical Review D
- Aug 6, 2019

- Physics Letters B
- Dec 1, 2017

- Journal of Cosmology and Astroparticle Physics
- May 29, 2018

- Journal of Cosmology and Astroparticle Physics
- Sep 1, 2018

- The European Physical Journal C
- Oct 3, 2022

- The European Physical Journal C
- Dec 28, 2021

- Classical and Quantum Gravity
- May 9, 2023

- Physical Review D
- Nov 19, 2021

- Physical Review D
- Sep 3, 2013

### Journal of Cosmology and Astroparticle Physics

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023

- Journal of Cosmology and Astroparticle Physics
- Nov 1, 2023