Henrique Gomes

Einstein gravity as a 3D conformally invariant theory

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3–diffeomorphisms and 3D conformal transformations that preserve the 3–volume (for the spatially compact case). Locally, this symmetry is identical to that of Hoyrava–Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.

Asymptotic analysis of the Engle―Pereira-Rovelli―Livine four-simplex amplitude

The semiclassical limit of a four-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a nondegenerate four-simplex geometry, the asymptotic formula contains the Regge action for general relativity. A canonical choice of phase for the boundary state is introduced and is shown to be necessary to obtain the results.

Asymptotics of 4d spin foam models

We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry.

Asymptotic analysis of the Ponzano–Regge model for handlebodies

Using the coherent state techniques developed for the analysis of the EPRL model we give the asymptotic formula for the Ponzano–Regge model amplitude for non-tardis triangulations of handlebodies in the limit of large boundary spins. The formula produces a sum over all possible immersions of the boundary triangulation and its value is given by the cosine of the Regge action evaluated on these. Furthermore the asymptotic scaling registers the existence of flexible immersions. We verify numerically that this formula approximates the 6j-symbol for large spins.

A Summary of the Asymptotic Analysis for the EPRL Amplitude

We review the basic steps in building the asymptotic analysis of the Euclidean sector of new spin foam models using coherent states, for Immirzi parameter less than one. We try to focus on conceptual issues and by so doing omit peripheral proofs and the original discussion on spin structures.

Classical gauge theory in Riem

In the geometrodynamical setting of general relativity in Lagrangian form, the objects of study are the Riemannian metrics (and their time derivatives) over a given 3-manifold M. It is our aim in this paper to study some geometrical aspects of the space M:=Riem(M) of all metrics over M. For instance, the Hamiltonian constraints by themselves do not generate a group, and thus its action on Riem(M) cannot be viewed in a geometrical gauge setting. It is possible to do so for the momentum constraints however. Furthermore, in view of the recent results representing GR as a dual theory, invariant under foliation preserving 3–diffeomorphisms and 3D conformal transformations, but not under refoliations, we are justified in considering the gauge structure pertaining only to the groups D of diffeomorphisms of M, and C, of conformal diffeomorphisms on M. For these infinite-dimensional symmetry groups, M has a natural principal fiber bundle structure, which renders the gravitational field amenable to the full range o...In the geometrodynamical setting of general relativity in Lagrangian form, the objects of study are the {it Riemannian} metrics (and their time derivatives) over a given 3-manifold

Asymptotics of recent spin foam models

M

The Dynamics of Shape

. It is our aim in this paper to study the gauge properties that the space Riem(M) of all metrics over

A geodesic model in conformal superspace.

M

The dynamics of shapes

possesses, specially as they relate to the constraints of geometrodynamics. For instance, the Hamiltonian constraint does not generate a group, and it is thus hard to view its action in Riem(M) in a gauge setting. However, in view of the recent results representing GR as a dual theory, invariant under foliation preserving 3--diffeomorphisms and 3D conformal transformations, but not under refoliations, we are justified in considering the gauge structure pertaining only to the groups