Gravitational Collapse in Cubic Horndeski Theories

Abstract

We study spherically symmetric gravitational collapse in cubic Horndeski theories of gravity. By varying the coupling constants and the initial amplitude of the scalar field, we determine the region in the space of couplings and amplitudes for which it is possible to construct global solutions to the Horndeski theories. Furthermore, we identify the regime of validity of effective field theory as the sub-region for which a certain weak field condition remains small at all times. We evolve the initial data using the CCZ4 formulation of the Einstein equations and horizon penetrating coordinates without assuming spherical symmetry.

Dynamics of Screening in Modified Gravity

“…3), the characteristic propagation speeds of the scalar-field equation eventually diverge, even before apparent/black-hole horizons form. This behavior, known to plague K-essence also in vacuum (for initial data close to critical collapse) [28,41,42], resembles that of the Keldysh equation t∂ 2 t φ(t, r) + ∂ 2 r φ(t, r) = 0, which is hyperbolic with characteristic speeds ±(−t) −1/2 for t < 0.…”

K-dynamics: well-posed 1+1 evolutions in K-essence

“…In this paper, we show that a broad class of K-essence theories yields a strongly hyperbolic and thus well-posed Cauchy problem in vacuum and spherical symmetry, for initial data sufficiently far from critical black hole collapse [33,34]. With the exception of this (small) set of initial data (which we identify with a precise criterion), we manage to avoid most of the pathologies previously found in the literature [26][27][28][29], at least outside apparent black hole horizons. Moreover, we show that one can write the scalar equation as a conservation law, which allows for using shock capturing methods to evolve the scalar field.…”

“…In more detail, if det(γ µν ) becomes zero (positive), the system becomes parabolic (elliptic). An example of such mixed type [50] systems is given by the Tricomi equation [28,29,51]…”

“…Having recognised that a Tricomi type behaviour can never occur for this class of K-essence theories, let us note, however, that the characteristic speeds V ± can in principle still diverge. An example of this behaviour is provided by the Keldysh equation [28,29,51]…”

“…Recently, several papers have tackled this problem by using numerical simulations [26][27][28], concluding that well-posedness is not always guaranteed. However, a quantitative estimation of the regime of well-posedness is still unavailable (see [29] for a recent attempt). Moreover, caustics in the scalar field characteristics, and therefore scalar shocks, are known to form generically in these theories [28,[30][31][32], which makes numerical evolutions even more challenging.…”