5 research outputs found
Equilibrium initial data for moving puncture simulations: The stationary 1+log slicing
We propose and explore a "stationary 1+log" slicing condition for the
construction of solutions to Einstein's constraint equations. For stationary
spacetimes, these initial data will give a stationary foliation when evolved
with "moving puncture" gauge conditions that are often used in black hole
evolutions. The resulting slicing is time-independent and agrees with the
slicing generated by being dragged along a time-like Killing vector of the
spacetime. When these initial data are evolved with moving puncture gauge
conditions, numerical errors arising from coordinate evolution are minimized.
In the construction of initial data for binary black holes it is often assumed
that there exists an approximate helical Killing vector that generates the
binary's orbit. We show that, unfortunately, 1+log slices that are stationary
with respect to such a helical Killing vector cannot be asymptotically flat,
unless the spacetime possesses an additional axial Killing vector.Comment: 20 pages, 3 figures, published versio
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