metricGet_WarpShellComoving
Last updated
Last updated
Create the Warp Shell metric in a defined spacetime grid.
For more details on the Warp Shell metric and its numerical process, please read:
The metric is constructed using the parameters of ADM mass, shell radii, smoothing factor, and shift-vector. The metric relies on several helper functions that solve the necessary terms for the lapse and spatial contraction. Note that by setting the shift vector amount to zero this function will return a stable matter shell (or setting doWarp
to 0).
This metric is only available in a comoving frame.
For the metric to satisfy the energy conditions, three important factors must be considered:
The amount of shift vector, along with its spatial change, must be balanced by the total ADM mass parameter selected. Adding more shifts or sharp changes in the shift vectors' radial distribution will cause an increase in momentum flux that can exceed the positive energy density in that region supplied by the ADM mass parameter.
The mass shell smoothing factor must be chosen to not cause energy violations on the inner boundary due to excessive pressures. Select the smoothing factors to adjust this amount, along with the inner and outer radius.
The mass added into the region of the warp shell should not exceed the Schwarzchild radius limit to become a black hole.
See the Constant Velocity paper for a more detailed discussion of these aspects.
The code for the specific instance of the metric discussed in the Constant Velocity paper is provided in the example W1.
[
metric
] = metricGet_WarpShellComoving(
gridSize
,
worldCenter
,
M
,
R1
,
R2
,
Rbuff
,
sigma
,
smoothfactor
,
v
,
doWarp
,
gridScale
)
blue are required inputs.
orange are optional inputs with native default values.
gridSize
1x4 array
integer
The size of the world specified as:
worldCenter
1x4 array
double
M
1x1 array
double
The ADM mass of the shell
R1
1x1 array
double
Inner radius of the shell
R2
1x1 array
double
Outer radius of the shell
Rbuff
1x1 array
double
Defines the buffer between radii and the start of the sigmoid transition.
v
1x1 array
double
Speed of the warp drive, given as a factor of c. This sets the magnitude of shift on the inside of the bubble.
sigma
1x1 array
double
Transition factor for the sigmoid.
smoothfactor
1x1 array
double
The smoothing factor used by the solver to compute the lapse and spatial terms.
doWarp
1x1 array
double
Setting to apply shift vector to the metric. Has values of 0 or 1 The default value is 1
gridScale
1x4 array
double
Unit scaling factor of the grid dimensions defined relative to gridSize
. This determines the resolution of the grid along each dimension. Specified as:
The default value is [1, 1, 1, 1].
metric
struct
object
Warp Shell solution returned as the metric tensor object.
The center of the world, which defines the center of as a 4-vector, specified as: