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Das apashanka
My question is why is the lagrangian density term in the action is equal to ricci scaler for gravitational field
The Einstein-Hilbert action, also known as the Einstein action or Hilbert action, is a mathematical expression used in Einstein's theory of general relativity to describe the gravitational field and its interactions with matter. It is a fundamental equation that summarizes the relationship between space-time curvature and the distribution of matter and energy.
The Einstein-Hilbert action is derived from the Einstein field equations, which relate the curvature of space-time to the energy and momentum of matter. It is derived using the principle of least action, which states that the physical laws governing a system can be described by minimizing the action, a mathematical quantity that describes the dynamics of the system.
The Einstein-Hilbert action is significant because it provides a mathematical framework for understanding the theory of general relativity. It allows for the calculation of the curvature of space-time and the prediction of the behavior of objects in the presence of a gravitational field. It has been extensively tested and is considered one of the most successful theories in physics.
The Einstein-Hilbert action differs from other theories of gravity in that it is a geometric theory, meaning it describes gravity as the curvature of space-time rather than a force between objects. This is a fundamental difference from Newton's theory of gravity, which describes gravity as a force of attraction between objects.
The Einstein-Hilbert action includes a term for the cosmological constant, a parameter that represents the energy density of the vacuum of space. This term was initially introduced by Einstein to maintain a static universe, but it is now used to explain the observed acceleration of the expansion of the universe. It plays a crucial role in modern cosmology and is a subject of ongoing research and debate in the scientific community.