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TimeRip496
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How to solve EFE without using the vacuum solution like how you did in schwarzschild metric?
I am not sure why can we just use the vacuum solution to solve EFE? Why can't we use a nom zero stress momentum tensor to solve?DEvens said:Do you mean, how to solve the EFE for a general situation? If that is what you mean, probably using numerical methods and a computer.
If you mean something else, please say what.
TimeRip496 said:I am not sure why can we just use the vacuum solution to solve EFE? Why can't we use a non zero stress momentum tensor to solve?
Nugatory said:In other problems, for example a ball of dust collapsing under its own gravitational attraction to form a star or planet (google for "Oppenheimer-Snyder"), we don't have a vacuum and the stress energy tensor is not zero. Then we have to solve the field equation for a non-zero stress-energy tensor.
The Einstein Field Equation is a set of mathematical equations developed by Albert Einstein to describe the relationship between the curvature of space-time and the distribution of matter and energy in the universe. It is a fundamental equation in the field of general relativity and is used to understand the behavior of gravity.
Solving the Einstein Field Equation without a vacuum solution means finding a solution to the equation that does not involve the absence of matter or energy in the universe. This is important because it allows for a more complete understanding of the effects of gravity on the universe as a whole, rather than just in empty space.
The Einstein Field Equation is a complex set of equations that involve multiple variables and terms. It is difficult to solve without a vacuum solution because the presence of matter and energy adds additional complexity to the equations, making it challenging to find a solution that accurately describes the behavior of gravity in the universe.
Solving the Einstein Field Equation without a vacuum solution has significant implications for our understanding of the universe. It allows us to better understand the role of gravity in the formation and evolution of galaxies, the behavior of black holes, and the overall structure of the universe. It also has practical applications in fields such as astrophysics and cosmology.
Scientists use various mathematical and computational methods to solve the Einstein Field Equation without a vacuum solution. These may include numerical simulations, analytical approximations, and mathematical models. Additionally, experimental data from observations and experiments can be used to validate and refine the solutions. Collaboration and interdisciplinary approaches are also important in tackling this complex problem.