/Tensor_toolkit

In summary, this program performs computations involving tensors that are fundamental to the mathematical formulation of general relativity. These tensors capture the geometric and energetic properties of spacetime, providing insights into the gravitational behavior of massive objects and the dynamics of the universe.

Primary LanguagePython

Stress-Energy Tensor Visualization

This project provides a visualization tool for the stress-energy tensor of a given metric tensor in General Relativity. The visualization allows users to adjust input values and dynamically see the changes in the tensor components. Python4

Features

  • Compute the stress-energy tensor analytically for a given metric tensor.
  • Visualize multiple components of the stress-energy tensor.
  • Adjust input parameters using a graphical user interface (GUI) built with Tkinter.
  • Interactive plots using Matplotlib.

Requirements

  • Python 3.x
  • SymPy
  • NumPy
  • Matplotlib
  • Tkinter

Installation

  1. Clone the repository:

    git clone https://github.com/LeetHappyfeet/Tensor_toolkit/stress-energy-tensor-visualization.git
cd stress-energy-tensor-visualization

  2. Install the required Python packages:

    pip install sympy numpy matplotlib

Usage

  1. Run the visualizer.py script to start the GUI:

    python visualizer.py

  2. Adjust the input parameters (t amplitude, x amplitude, y amplitude, z amplitude, xy coupling) using the provided entry fields.

  3. Click the "Update Plot" button to see the changes in the stress-energy tensor components.

Project Structure

  • analyticalEnergyTensor.py: Contains the function to compute the stress-energy tensor analytically.
  • visualizer.py: Main script to run the GUI and visualize the tensor components.
  • README.md: Project documentation.

Example

Here's an example of how to use the analyticalEnergyTensor function directly in Python:

import sympy as sp
from analyticalEnergyTensor import analyticalEnergyTensor

# Define symbolic variables
t, x, y, z = sp.symbols('t x y z')

# Define a simple metric tensor
g = sp.zeros(4, 4)
g[0, 0] = -1
g[1, 1] = 1 + 0.1 * sp.sin(x) * sp.sin(t)
g[2, 2] = 1 + 0.1 * sp.sin(y) * sp.sin(t)
g[3, 3] = 1 + 0.1 * sp.sin(z) * sp.sin(t)
g[1, 2] = 0.05 * sp.cos(x) * sp.cos(y) * sp.cos(t)
g[2, 1] = g[1, 2]  # Symmetric component

# Define the coordinates
coords = [t, x, y, z]

# Compute the stress-energy tensor
T_out = analyticalEnergyTensor(g, coords)

# Print the stress-energy tensor
print(T_out)

License

This project is licensed under the MIT License. See the LICENSE file for more details.

Contributing

Contributions are welcome! Please open an issue or submit a pull request for any changes.