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.

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.