4 research outputs found
Constraint propagation equations of the 3+1 decomposition of f(R) gravity
Theories of gravity other than general relativity (GR) can explain the
observed cosmic acceleration without a cosmological constant. One such class of
theories of gravity is f(R). Metric f(R) theories have been proven to be
equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term.
Using this equivalence and a 3+1 decomposition of the theory it has been shown
that metric f(R) gravity admits a well-posed initial value problem. However, it
has not been proven that the 3+1 evolution equations of metric f(R) gravity
preserve the (hamiltonian and momentum) constraints. In this paper we show that
this is indeed the case. In addition, we show that the mathematical form of the
constraint propagation equations in BD-equilavent f(R) gravity and in f(R)
gravity in both the Jordan and Einstein frames, is exactly the same as in the
standard ADM 3+1 decomposition of GR. Finally, we point out that current
numerical relativity codes can incorporate the 3+1 evolution equations of
metric f(R) gravity by modifying the stress-energy tensor and adding an
additional scalar field evolution equation. We hope that this work will serve
as a starting point for relativists to develop fully dynamical codes for valid
f(R) models.Comment: 25 pages, matches published version in CQG, references update
Simulating magnetized neutron stars with discontinuous Galerkin methods
Discontinuous Galerkin methods are popular because they can achieve high order where the solution is smooth, because they can capture shocks while needing only nearest-neighbor communication, and because they are relatively easy to formulate on complex meshes. We perform a detailed comparison of various limiting strategies presented in the literature applied to the equations of general relativistic magnetohydrodynamics. We compare the standard minmod/ limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite-difference hybrid method. The ultimate goal is to understand what limiting strategies are able to robustly simulate magnetized TOV stars without any fine-tuning of parameters. Among the limiters explored here, the only limiting strategy we can endorse is a discontinuous Galerkin-finite-difference hybrid method