Object Types

Describes the major object types used in Warp Factory

Description

Core to the analysis in Warp Factory is the metric and stress-energy tensors. Both of these tensors are stored as a .struct which has several fields that contain the data. These structs have certian required fields which are used by the various functions in Warp Factory to ensure that operations are conducted properly when manipulating data. These fields are also helpful references to the user.

The term "Internal use" means that the value is used to determine logic within the analysis functions in Warp Factory. These fields should be overwritten and only modified by appropriate function calls.

The term "Reserved field" means that this struct field has certian values that Warp Factory will understand and use. It also means that changing these values outside of the appropriate functions that also change the tensor data will result in data type mismatches.

Metric Tensor Structure

The metric tensor is a unitless object which defines the curvature of spacetime. In Warp Factory the metric tensor is a special object stored as a .struct type, which includes several important fields that are used by several functions across the toolkit.

blue are required fields. These fields interact with different functions inside Warp Factory.

orange are optional fields. These fields act as a helpful reference for the user and are sometimes used by Warp Factory, but are not required for proper data handling.

Field	Values	Format	Type	Comment
.type	Object type	1x1 array	string	The string is a reserved field for internal use, only to be "metric".
.tensor	Value of the metric components at each spacetime point	4x4 cells containing 4x4 arrays	double	Tensor is in the standard form stored as a cell: $g_{\mu\nu} = \begin{pmatrix} g_{00} & g_{01} & g_{02} & g_{03} \\ g_{01} & g_{11} & g_{12} & g_{13} \\ g_{02} & g_{12} & g_{22} & g_{23} \\ g_{03} & g_{13} & g_{23} & g_{33} \\\end{pmatrix}$ The index of this tensor can be all types and is specified by the .index field.
.scaling	Scaling factor used for the dimensions	1x4 array	double	Specified in $[x_0, x_1, x_2, x_3]$. Smaller values mean higher resolution grids, relative to the gridSize input. Scaling is used by the solver in the finite element method.
.index	Tensor index	1x1 array	string	Can be either "covariant" or "contravariant". This is a reserved field for internal use and should not be manually changed.
.coords	Name of the used coordinate system	1x1 array	string	Only the Cartesian coordinate system has been implemented in Warp Factory in the current release. Other systems can be used but have not been tested or adapted in the solver and analysis functions
.name	Name of the metric	1x1 array	string	Standard names are used in the metric library but can be overwritten.
.date	Date created	1x1 array	string	In the metric library, the MATLAB internal date function is used. The format is "dd-MMM-yyyy".
.params	Contains sub-fields depending on the parameters used by the metric to construct it	.struct fields	double	The metric library functions assign the values passed into them as subfields. For example, this would be the radius and sigma factor for the Alcubierre bubble. Users can adapt this field as they see fit for custom metrics.

Stress-energy Tensor Structure

The stress-energy tensor is the physical content in the spacetime which is associated with the curvature in the metric tensor. In Warp Factory the stress-energy tensor is a special object stored as a .struct type, which includes several important fields that are used by several functions across the toolkit.

blue are required fields. These fields interact with different functions inside Warp Factory.

orange are optional fields. These fields act as a helpful reference for the user.

Field	Values	Format	Type	Comment
.type	Object type	1x1	string	The string is a reserved field for internal use, only to be "stress-energy".
.tensor	Value of the stress-energy components at each spacetime point	4x4 cells containing 4x4 arrays	double	Tensor is in the standard form stored as a cell: $T_{\mu\nu} = \begin{pmatrix} T_{00} & T_{01} & T_{02} & T_{03} \\ T_{01} & T_{11} & T_{12} & T_{13} \\ T_{02} & T_{12} & T_{22} & T_{23} \\ T_{03} & T_{13} & T_{23} & T_{33} \\\end{pmatrix}$ The index of this tensor can be all types and is specified by the .index field.
.scaling	Scaling factor used for the dimensions	1x4 array	double	Inherents the value from the metric .scaling field, specified in $[x_0, x_1, x_2, x_3]$. This is a reference field for internal use in the solver and should not be manually changed.
.index	Tensor index	1x1 array	string	Can be either "covariant", "contravariant", "mixedupdown", or "mixeddownup". This is a reserved field for internal use and should not be manually changed.
.coords	Name of the used coordinates	1x1 array	string	Only the Cartesian coordinate system has been implemented in Warp Factory in the current release. Other systems can be used but have not been tested or adapted in the solver and analysis functions
.frame	Name of the frame of the tensor	1x1 array	string	The frame is an optional field that is modified by doing frame transformations. Currently, only Eulerian transformations are implemented. This is a reserved field and should not be manually changed, but is not required unless a transformation is done.
.date	Date created	1x1 array	string	The getEnergyTensor assigns this using the MATLAB internal date function when generating the stress-energy tensor. Format is "dd-MMM-yyyy".
.name	Name of the tensor	1x1 array	string	Inherents the name from the metric .name field.
.order	Solver order used	1x1 array	string	This is assigned by the getEnergyTensor function, where the solver order is specified as either "second" or "fourth". This is a reserved field and should not be manually changed.