metricGet_ModifiedTime

Description

Create the Modified Time warp solution from Introducing Physical Warp Drives in a defined spacetime grid.

Modified Time Metric

This solution modifies an Alcubierre geometry by the addition of an extra factor $A$ acting on the time component:

$ds^2 = -((1-f(r_s)+A^{-1}) dt)^2+ (dx^2 - v_s(t) f(r_s)^2 \ dt)^2 + dy^2 + dz^2$

For more details on the Modified Time metric, please read (section 4.5):

Introducing Physical Warp DrivesarXiv.org

Method

The shape function of $A$ takes on the same value as the shift vector in Alcubierre.

The comoving version of this metric called metricGet_ModifiedTimeComoving has the same inputs but requires that the gridSize along t = 1 and will return the metric in the Galilean comoving frame.

Syntax

[Metric] = metricGet_ModifiedTime(gridSize,worldCenter,v,R,sigma,A, gridScale)

[Metric] = metricGet_ModifiedTimeComoving(gridSize,worldCenter,v,R,sigma,A, gridScale)

Input Arguments

blue are required inputs.

orange are optional inputs with native default values.

Inputs	Format	Type	Description
gridSize	1x4 array	integer	The size of the world specified as: $[t, x, y, z]$
worldCenter	1x4 array	double	The center of the world, which defines the center of $r_s$ as a 4-vector, specified as: $[t,x,y,z]$
v	1x1 array	double	Speed of the warp drive, given as a factor of c.
R	1x1 array	double	Radius of the warp bubble.
sigma	1x1 array	double	Thickness factor for the warp bubble.
A	1x1 array	double	Lapse rate modification.
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: $[t_{scale}, x_{scale}, y_{scale}, z_{scale}]$ The default value is [1, 1, 1, 1].

Output Arguments

Outputs	Format	Type	Description
metric	struct	object	Modified Time solution returned as the metric tensor object.