Schwarzenchild vs Minkowski: 4-Space & EigenValues

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In summary, the conversation discusses the relationship between the Schwarzschild metric and the Minkowski tensor in 4-space. It is mentioned that the Schwarzschild metric can be transformed into the Minkowski metric at a specific point, but this does not mean that the entire space-time is flat. The spectral theorem is also mentioned as a way to put the Schwarzschild metric in Minkowski form.
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The Schwarzenchild Metric can be the Minkowski Tensor with the correct terms in 4-Space. If not Schwarzenchild Metric must have EigenValues are all real and the Matrix is symmetrical.
 
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I'm not really sure what it is you're saying but if you're asserting that there exists a coordinate system in which the Schwarzschild metric becomes the Minkowski metric everywhere on the open subset the chart is defined on then that's obviously false; Schwarzschild space-time is not flat. What you can do is put the Schwarzschild metric in Minkowski form at a given point; this is a simple consequence of the spectral theorem.
 

1. What is the difference between Schwarzenchild and Minkowski space?

Schwarzenchild space is a solution to Einstein's field equations that describes the space around a non-rotating, spherically symmetric mass. It is characterized by a singularity at the center, known as the event horizon. Minkowski space, on the other hand, is a flat, four-dimensional space that serves as the foundation for Einstein's theory of special relativity.

2. How do the Eigenvalues of these spaces differ?

The Eigenvalues of Schwarzenchild space are determined by the mass of the object at the center, with larger masses resulting in larger Eigenvalues. In Minkowski space, the Eigenvalues are constant and equal to 1, as the space is flat and not influenced by mass or energy.

3. Can both spaces coexist in the same universe?

Yes, it is possible for both Schwarzenchild and Minkowski space to exist within the same universe. Schwarzenchild space is often used to describe the space around massive objects like black holes, while Minkowski space is used to describe the space between objects in the universe.

4. How are these spaces relevant to modern physics?

Both Schwarzenchild and Minkowski space are important concepts in modern physics as they are used to describe the effects of gravity and the structure of spacetime. They are also fundamental to our understanding of general relativity and play a crucial role in many cosmological theories.

5. Are there any practical applications for understanding these spaces?

Yes, understanding these spaces can have practical applications in fields such as astrophysics, cosmology, and aerospace engineering. Knowledge of Schwarzenchild space is essential for understanding and predicting the behavior of massive objects like black holes, while Minkowski space is used in the calculations and simulations of spacecraft trajectories and gravitational effects on satellites.

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