Numerical solutions for the $f(R)$-Klein-Gordon system

Abstract

We construct a numerical relativity code based on the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation for the gravitational quadratic $f(R)$ Starobinsky model. By removing the assumption that the determinant of the conformal 3-metric is unity, we first generalize the BSSN formulation for general $f(R)$ gravity theories in the metric formalism to accommodate arbitrary coordinates for the first time. We then describe the implementation of this formalism to the paradigmatic Starobinsky model. We apply the implementation to three scenarios: the Schwarzschild black hole solution, flat space with non-trivial gauge dynamics, and a massless Klein-Gordon scalar field. In each case, long-term stability and second-order convergence is demonstrated. The case of the massless Klein-Gordon scalar field is used to exercise the additional terms and variables resulting from the $f(R)$ contributions. For this model, we show for the first time that additional damped oscillations arise in the subcritical regime as the system approaches a stable configuration.

arXiv comment34 pages, 7 figures, corrigendum included

References in corpus (26)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• On the Numerical Integration of Einstein's Field Equations
• Planck 2013 results. XXII. Constraints on inflation
• Can modified gravity explain accelerated cosmic expansion?
• Gauge conditions for long-term numerical black hole evolutions without excision
• New Formalism for Numerical Relativity
• Extended Gravity Theories and the Einstein-Hilbert Action
• Cosmological dynamics of R^n gravity
• Numerical Relativity and Compact Binaries
• Dark Matter from R^2-gravity
• On neutron stars in f(R) theories: small radii, large masses and large energy emitted in a merger
• Covariant formulations of BSSN and the standard gauge
• Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation
• BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes
• Formulations of the 3+1 evolution equations in curvilinear coordinates
• BSSN in Spherical Symmetry
• Black hole critical behaviour with the generalized BSSN formulation
• Critical Collapse of Scalar Fields Beyond Axisymmetry
• Bona-Masso slicing conditions and the lapse close to black-hole punctures
• On the Hyperbolicity and Stability of $3+1$ Formulations of Metric $f(R)$ Gravity
• A Note on the Strong Hyperbolicity of $f(R)$ Gravity with Dynamical Shifts
• Gravitational Theories with Torsion

Cited by in corpus (1)

• Toward a realistic Buchdahl limit in f(R) theories of gravity