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

Abstract

Testing General Relativity and exploring possible departures has received further input with the possibility to do so through gravitational waves emitted in strongly gravitating/highly dynamical scenarios and also through the availability of exquisitely sensitive cosmological observations. However, most extensions suffer from severe pathologies at the mathematical level which have stymied a thorough exploration of putative theories. With the aid of a model problem which captures typical pathologies, we explore suggested methods to control them. We find that the approach that modifies the equations to control higher-order gradients is both robust and efficient. arXiv:1808.07897v1 [gr-qc]

Well-posedness of cubic Horndeski theories

“…Another method is based on the Israel-Stewart process [37] which is widely used in relativistic hydrodynamics to deal with the ill-posedness of the Navier-Stokes equation. Roughly speaking, consider equations of motion of the form L(φ) = ǫS(φ) for a collection of fields denoted by φ, [35,36]. Here L is a differential operator such that the zeroth order equation of motion is L(φ) = 0; S(φ) is another differential operator playing the role of a correction term, suppressed with a small parameter ǫ.…”

“…The solution to this modified equation asymptotically approaches the solution to the original equation in a timescale τ . This procedure also restricts solutions to the infrared and it may also fix the hyperbolicity of the equations of motion [35,36].…”

Scalarized black hole dynamics in Einstein-dilaton-Gauss-Bonnet gravity

“…For our initial data for α and ζ, we set their values at the excision surface as in Eq. (25), and then integrate outwards in r. An example of such a case is shown in Fig. 7.…”

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]).…”