Fixing extensions to general relativity in the nonlinear regime

Abstract

The question of what gravitational theory could supersede General Relativity has been central in theoretical physics for decades. Many disparate alternatives have been proposed motivated by cosmology, quantum gravity and phenomenological angles, and have been subjected to tests derived from cosmological, solar system and pulsar observations typically restricted to linearized regimes. Gravitational waves from compact binaries provide new opportunities to probe these theories in the strongly gravitating/highly dynamical regimes. To this end however, a reliable understanding of the dynamics in such a regime is required. Unfortunately, most of these theories fail to define well posed initial value problems, which prevents at face value from meeting such challenge. In this work, we introduce a consistent program able to remedy this situation. This program is inspired in the approach to "fixing" viscous relativistic hydrodynamics introduced by Israel and Stewart in the late 70's. We illustrate how to implement this approach to control undesirable effects of higher order derivatives in gravity theories and argue how the modified system still captures the true dynamics of the putative underlying theories in 3+1 dimensions. We sketch the implementation of this idea in a couple of effective theories of gravity, one in the context of Noncommutative Geometry, and one in the context of Chern-Simons modified General Relativity.

Challenges to global solutions in Horndeski’s theory

“…A complementary or alternative approach would be to identify the set of behaviors which can be considered physical and, armed with a suitable justification, modify the non-linear equations of motion to control unphysical pathologies (e.g. [36,59]).…”

Towards the nonlinear regime in extensions to GR: assessing possible options

“…However, most such extensions typically involve pathological features that have hindered a thorough understanding of their implications, especially in regimes where deviations from GR would be largest. Recently, several different ideas have been suggested as possible paths forward in this endeavour [29,36,41] and first steps are being taken [41][42][43][44]. In this work, we exploited a toy-model which -from an EFT point of view-evidences many of such pathologies, but within a known UV-complete theory.…”

Numerical measurements of scaling relations in two-dimensional conformal fluid turbulence

“…The (2 + 1)-dimensional case is especially relevant to draw intuition for related phenomena in (3 + 1)-dimensional gravity with the help of the fluid-gravity correspondence (e.g. [12,16,25]). This work is largely a continuation and completion of [1], which contained a numerical study which was inconclusive at the time.…”

“…To see this, expand the left-hand side and use statistical symmetries to obtain 16) and then note that the second term on the right-hand side vanishes by incompressibility, isotropy, and regularity at r = 0 [36]. Thus eq.…”

“…[8,9]) and, through the fluid-gravity correspondence, it has found its way into the realm of fundamental gravity research [10,11]. Intriguingly, this correspondence has revealed that gravity can exhibit turbulent behavior, and studies of its possible consequences are gaining interesting momentum [12][13][14][15][16]. The understanding of turbulence in any regime is a difficult task given its intrinsic complexity, and despite a long history of efforts in the subject, our knowledge of this rich phenomenon is still incomplete.…”