Challenges to global solutions in Horndeski's theory

Abstract

We explore the question of obtaining global solutions in Horndeski's theories of gravity. Towards this end, we study a relevant set of the theory and, by employing the Einstein frame we simplify the analysis by exploiting known results on global solutions of wave equations. We identify conditions for achieving global solutions as well as obstacles that can arise to spoil such goal. We illustrate such problems via numerical simulations.

arXiv comment15 pages, 5 figures. v2: Matches published version

References in corpus (44)

• Cosmological Imprint of an Energy Component with General Equation of State
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• The galileon as a local modification of gravity
• Essentials of k-essence
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Chameleon Cosmology
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• Covariant Galileon
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Dark Energy after GW170817 and GRB170817A
• Tensor-scalar gravity and binary-pulsar experiments
• The conformal frame freedom in theories of gravitation
• Neutron-star mergers in scalar-tensor theories of gravity
• Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models
• Black holes and binary mergers in scalar Gauss-Bonnet gravity: scalar field dynamics
• Coalescence of binary neutron stars in a scalar-tensor theory of gravity
• Dynamical scalarization of neutron stars in scalar-tensor gravity theories
• Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order
• Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
• No-go theorem for k-essence dark energy
• On the local well-posedness of Lovelock and Horndeski theories
• The Paths of Gravity in Galileon Cosmology
• Black Hole Dynamics in Einstein-Maxwell-Dilaton Theory
• Dynamics of compact binary systems in scalar-tensor theories: I. Equations of motion to the third post-Newtonian order
• Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces
• Fixing extensions to General Relativity in the non-linear regime
• Hyperbolicity in Spherical Gravitational Collapse in a Horndeski Theory
• Summation by parts and dissipation for domains with excised regions
• Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An Overview
• Constraints on general second-order scalar-tensor models from gravitational Cherenkov radiation
• Towards the nonlinear regime in extensions to GR: assessing possible options
• Novel finite-differencing techniques for numerical relativity: application to black hole excision
• On the hyperbolicity of the most general Horndeski theory
• Two-body problem in Scalar-Tensor theories as a deformation of General Relativity : an Effective-One-Body approach
• The nonlinear dynamical stability of infrared modifications of gravity
• Gravitational collapse of k-essence
• Shock Formation in Lovelock Theories
• Recent works on the Strauss conjecture
• Well-posedness of cubic Horndeski theories
• The global stability of the Minkowski space-time in harmonic gauge
• Einstein frame or Jordan frame ?
• Do unbounded bubbles ultimately become fenced inside a black hole?

Cited by in corpus (37)

• Post-Newtonian dynamics and black hole thermodynamics in Einstein-scalar-Gauss-Bonnet gravity
• Scalarized Black Hole dynamics in Einstein dilaton Gauss-Bonnet Gravity
• Nonlinear/non-iterative treatment of EFT-motivated gravity
• No evidence of kinetic screening in simulations of merging binary neutron stars beyond general relativity
• Kinetic screening in nonlinear stellar oscillations and gravitational collapse
• Modelling self-consistently beyond General Relativity
• Black Hole Binaries in Cubic Horndeski Theories
• Numerical relativity for Horndeski gravity
• Dynamics of Screening in Modified Gravity
• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Fixing the dynamical evolution in scalar-Gauss-Bonnet gravity
• UV completions, fixing the equations and nonlinearities in $k$-essence
• Gravitational Collapse in Cubic Horndeski Theories
• Hairy rotating black holes in cubic Galileon theory
• Testing gravitational wave propagation with multiband detections
• $d+1$ formalism in Einstein-scalar-Gauss-Bonnet gravity
• K-dynamics: well-posed 1+1 evolutions in K-essence
• Nonperturbative gedanken experiments in Einstein-dilaton-Gauss-Bonnet gravity: nonlinear transitions and tests of the cosmic censorship beyond General Relativity
• Scalar Fields Near Compact Objects: Resummation versus UV Completion
• What is the fate of Hawking evaporation in gravity theories with higher curvature terms?
• Properties of scalar wave emission in a scalar-tensor theory with kinetic screening
• Fixing the dynamical evolution of self-interacting vector fields
• Nonlinear dynamics of oscillating neutron stars in scalar-tensor gravity
• Scalarization of isolated black holes in scalar Gauss-Bonnet theory in the fixing-the-equations approach
• Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics
• Critical collapse in K-essence models
• Numerical Relativity as a New Tool for Fundamental Cosmology
• Scalar emission from neutron star-black hole binaries in scalar-tensor theories with kinetic screening
• Master field equations for spherically symmetric gravitational fields beyond general relativity
• Non-linear electrodynamics non-minimally coupled to gravity:symmetric-hyperbolicity and causal structure
• A new nonlinear instability for scalar fields
• Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity
• Two-body problem in theories with kinetic screening
• Dynamical dimensional reduction in multi-valued Hamiltonians
• Gravitational collapse in Quadratic Gravity
• Stable non-linear evolution in regularised higher derivative effective field theories
• The well-posedness of the Cauchy problem for self-interacting vector fields