Newtonian and GR Friedman equation

In summary, the energy of a test mass at a certain radius from the center of a spherical universe is given by:E_{tot} = E_{kin} + E_{pot} = \frac{1}{2} m \dot{R}^2(t) - \frac{4 \pi}{3} Gm \mathcal{\rho}_M R^2(t)
  • #36
PAllen said:
But the if the approach is valid, since the center is arbitrary, it should work if I choose a different center for each point.

Try this with ri=rj and you will see why choosing different centers in the same calculation is not allowed. In #34 g0 replaces the integration constant in #24 and like the integration constant it needs to be normalized with the same condition for the whole calculation (e.g. by definition of the acceleration at a specific position).
 
<h2> What is the difference between Newtonian and GR Friedman equation?</h2><p>The main difference between Newtonian and GR Friedman equation is the underlying theory they are based on. Newtonian equation is based on classical mechanics, whereas GR Friedman equation is based on Einstein's theory of general relativity. Additionally, GR Friedman equation takes into account the effects of gravity on the expansion of the universe, while Newtonian equation does not.</p><h2> How do Newtonian and GR Friedman equations describe the expansion of the universe?</h2><p>Both Newtonian and GR Friedman equations describe the expansion of the universe in terms of the scale factor, which represents the relative size of the universe at a given time compared to its size at an initial time. However, GR Friedman equation also takes into account the effects of dark energy and dark matter, which play a significant role in the expansion of the universe.</p><h2> Can Newtonian and GR Friedman equations be used interchangeably?</h2><p>No, Newtonian and GR Friedman equations cannot be used interchangeably. While they both describe the expansion of the universe, they are based on different theories and take into account different factors. Using one equation in place of the other would lead to incorrect results.</p><h2> What are the limitations of Newtonian and GR Friedman equations?</h2><p>Newtonian equation is limited in its ability to accurately describe the expansion of the universe on a large scale, as it does not take into account the effects of gravity. On the other hand, GR Friedman equation is limited in its ability to accurately describe the universe on a small scale, as it does not take into account quantum effects.</p><h2> How are Newtonian and GR Friedman equations used in cosmology?</h2><p>Newtonian and GR Friedman equations are used in cosmology to study the evolution and behavior of the universe. They are used to make predictions about the expansion of the universe, the distribution of matter and energy, and the formation of structures such as galaxies and galaxy clusters. They are also used to test and refine our understanding of fundamental theories such as general relativity and the standard model of cosmology.</p>

FAQ: Newtonian and GR Friedman equation

What is the difference between Newtonian and GR Friedman equation?

The main difference between Newtonian and GR Friedman equation is the underlying theory they are based on. Newtonian equation is based on classical mechanics, whereas GR Friedman equation is based on Einstein's theory of general relativity. Additionally, GR Friedman equation takes into account the effects of gravity on the expansion of the universe, while Newtonian equation does not.

How do Newtonian and GR Friedman equations describe the expansion of the universe?

Both Newtonian and GR Friedman equations describe the expansion of the universe in terms of the scale factor, which represents the relative size of the universe at a given time compared to its size at an initial time. However, GR Friedman equation also takes into account the effects of dark energy and dark matter, which play a significant role in the expansion of the universe.

Can Newtonian and GR Friedman equations be used interchangeably?

No, Newtonian and GR Friedman equations cannot be used interchangeably. While they both describe the expansion of the universe, they are based on different theories and take into account different factors. Using one equation in place of the other would lead to incorrect results.

What are the limitations of Newtonian and GR Friedman equations?

Newtonian equation is limited in its ability to accurately describe the expansion of the universe on a large scale, as it does not take into account the effects of gravity. On the other hand, GR Friedman equation is limited in its ability to accurately describe the universe on a small scale, as it does not take into account quantum effects.

How are Newtonian and GR Friedman equations used in cosmology?

Newtonian and GR Friedman equations are used in cosmology to study the evolution and behavior of the universe. They are used to make predictions about the expansion of the universe, the distribution of matter and energy, and the formation of structures such as galaxies and galaxy clusters. They are also used to test and refine our understanding of fundamental theories such as general relativity and the standard model of cosmology.

Similar threads

A Synchronous to Newtonian gauge
Replies
1
Views
630
A Obtaining the Orbit equation (Effective Potential) from the Newtonian metric
Replies
12
Views
2K
I Compute Gradient in GR: Step-by-Step Guide
Replies
3
Views
1K
I Null energy condition constrains the metric
Replies
5
Views
776
I Linearised gravity approach to Lense Thirring metric
Replies
7
Views
970
I Conserved Quantity Along Affine Parameter
Replies
8
Views
1K
Newtonian Limit of GR: Exploring Einstein Equations
2
Replies
35
Views
4K
A What is the Expression for the Waveform of an In-Spiralling Compact Binary?
Replies
1
Views
1K
I Einstein brother-in-law elevator
Replies
11
Views
938
GR Relation Reduces to Newtonian: Limits Explained
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top