On the emergence of Lorentzian signature and scalar gravity

TL;DR

This paper proposes a model where Lorentzian signature and scalar gravity emerge from fundamental objects, leading to a form of Nordstrom gravity and demonstrating how spacetime properties can arise from simpler underlying dynamics.

Contribution

It introduces a novel emergent gravity model where Lorentzian signature and scalar gravity arise from fundamental dynamics starting with a Riemannian manifold and scalar fields.

Findings

Time emerges as a property of perturbations around specific solutions.

Perturbations give rise to a spin-0 gravity resembling Nordstrom gravity.

Diffeomorphism invariance can emerge from simpler systems.

Abstract

In recent years, a growing momentum has been gained by the emergent gravity framework. Within the latter, the very concepts of geometry and gravitational interaction are not seen as elementary aspects of Nature but rather as collective phenomena associated to the dynamics of more fundamental objects. In this paper we want to further explore this possibility by proposing a model of emergent Lorentzian signature and scalar gravity. Assuming that the dynamics of the fundamental objects can give rise in first place to a Riemannian manifold and a set of scalar fields we show how time (in the sense of hyperbolic equations) can emerge as a property of perturbations dynamics around some specific class of solutions of the field equations. Moreover, we show that these perturbations can give rise to a spin-0 gravity via a suitable redefinition of the fields that identifies the relevant degrees of freedom. In particular, we find that our model gives rise to Nordstrom gravity. Since this theory is invariant under general coordinate transformations, this also shows how diffeomorphism invariance (albeit of a weaker form than the one of general relativity) can emerge from much simpler systems.