Newtonian Limit of GR: Exploring Einstein Equations

Thread starter pseudoriemann
Start date Aug 14, 2015
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Gr Limit Newtonian

In summary, the Newtonian limit of General Relativity involves neglecting terms that are smaller by orders of magnitude in the energy-momentum tensor, leading to the Poisson equation in the Einstein equation. However, some components of the Einstein tensor may also be neglected in this limit, which raises questions about the validity of the equations. It is important to consider the assumptions and approximations made in the derivation of the Newtonian limit in order to understand why these components are neglected.

Aug 19, 2015

Markus Hanke

PeterDonis said:

But this isn't really a "boundary condition".

Ok, point taken, and I think I understand what you are attempting to say. These are the finer subtle points that I, as an amateur, are often missing. Thank you !

<h2>1. What is the Newtonian Limit of General Relativity?</h2><p>The Newtonian Limit of General Relativity (GR) refers to the approximation of GR in situations where velocities are much smaller than the speed of light and gravitational fields are weak. In this limit, GR reduces to Newton's law of gravitation.</p><h2>2. How is the Newtonian Limit derived from Einstein's Equations?</h2><p>The Newtonian Limit is derived by taking the non-relativistic limit of the Einstein Field Equations, which describe the relationship between the curvature of spacetime and the distribution of matter and energy. This involves assuming that the velocities involved are much smaller than the speed of light and that the gravitational fields are weak.</p><h2>3. What are the implications of the Newtonian Limit in terms of gravity?</h2><p>The Newtonian Limit implies that in situations where velocities are much smaller than the speed of light and gravitational fields are weak, gravity can be described by Newton's law of gravitation. This means that the force of gravity is proportional to the masses of the objects and inversely proportional to the square of the distance between them.</p><h2>4. Are there any situations where the Newtonian Limit does not hold?</h2><p>Yes, the Newtonian Limit does not hold in extreme situations such as near black holes or in the early universe where velocities are close to the speed of light and gravitational fields are strong. In these cases, the full equations of General Relativity must be used to accurately describe gravity.</p><h2>5. How does the Newtonian Limit of GR compare to Newton's law of gravitation?</h2><p>The Newtonian Limit of GR is a more accurate and comprehensive theory of gravity than Newton's law of gravitation. It takes into account the effects of space and time on the curvature of spacetime and the distribution of matter and energy. It also predicts additional phenomena such as gravitational time dilation and gravitational waves, which are not accounted for in Newton's theory.</p>

1. What is the Newtonian Limit of General Relativity?

The Newtonian Limit of General Relativity (GR) refers to the approximation of GR in situations where velocities are much smaller than the speed of light and gravitational fields are weak. In this limit, GR reduces to Newton's law of gravitation.

2. How is the Newtonian Limit derived from Einstein's Equations?

The Newtonian Limit is derived by taking the non-relativistic limit of the Einstein Field Equations, which describe the relationship between the curvature of spacetime and the distribution of matter and energy. This involves assuming that the velocities involved are much smaller than the speed of light and that the gravitational fields are weak.

3. What are the implications of the Newtonian Limit in terms of gravity?

The Newtonian Limit implies that in situations where velocities are much smaller than the speed of light and gravitational fields are weak, gravity can be described by Newton's law of gravitation. This means that the force of gravity is proportional to the masses of the objects and inversely proportional to the square of the distance between them.

4. Are there any situations where the Newtonian Limit does not hold?

Yes, the Newtonian Limit does not hold in extreme situations such as near black holes or in the early universe where velocities are close to the speed of light and gravitational fields are strong. In these cases, the full equations of General Relativity must be used to accurately describe gravity.

5. How does the Newtonian Limit of GR compare to Newton's law of gravitation?

The Newtonian Limit of GR is a more accurate and comprehensive theory of gravity than Newton's law of gravitation. It takes into account the effects of space and time on the curvature of spacetime and the distribution of matter and energy. It also predicts additional phenomena such as gravitational time dilation and gravitational waves, which are not accounted for in Newton's theory.