GRG Editor's Choice: The existence of smooth solutions in q-models

© SpringerOsorio Morales, J. & Santillán, O.P., The existence of smooth solutions in q-models, Gen Relativ Gravit (2019) 51: 29.

Editor's Choice (Research Article)

First Online: 09 February 2019

"This article is concerned with the question of whether a certain alternative metric theory of gravity (the so-called q-models) admits a well-posed initial value problem. This is an important issue which is often overlooked in the context of alternative theories of gravities and a necessary step for the systematic study of the solutions to the theory using numerical methods. The presentation of the analysis is careful and pedagogical and with the adequate level of rigour. Care is taken to verify that the technical conditions in Ringström's theorem are satisfied and important issues like the propagation of harmonic coordinates are addressed."


The q-models are scenarios that may explain the smallness of the cosmological constant (Klinkhamer and Volovik in Phys Rev D 77:085015, 2008; Phys Rev D 78:063528, 2008; JETP Lett 88:289, 2008; Mod Phys Lett A 31(28):1650160, 2016; JETP Lett 91:259, 2010; Phys Rev D 79:063527, 2009; J Phys Conf Ser 314:012004, 2011). The vacuum in these theories is presented as a self-sustainable medium and include a new degree of freedom, the q-variable, which establishes the equilibrium of the quantum vacuum. In the present work, the Cauchy formulation for these models is studied in detail. It is known that there exist some limits in which these theories are described by an F(R) gravity model, and these models posses a well posed Cauchy problem. This paper shows that the Cauchy problem is well posed even not reaching this limit. By use of some mathematical theorems about second order non linear systems, it is shown that these scenarios admit a smooth solution for at least a finite time when some specific type of initial conditions are imposed. Some technical conditions of Ringström (The Cauchy problem in general relativity, European Mathematical Society, Warsaw, 2000) play an important role in this discussion.

The authors: 

Juliana Osorio Morales is working with Osvaldo P. Santillán in the Department of Mathematics Luis Santaló (IMAS) at the University of Buenos Aires. 

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.