General Relativity, form of scale factor

In summary, we are given a set of Einstein's field equations with constants and variables representing energy density and rate of change. The general solution for R(t) is given as R(t) = A*[(t-ti)^(2/3)], but there seems to be a discrepancy between this solution and the given equations. It is possible that there is a mistake in the question, or that the solution given is for a different scenario.
  • #1
deadringer
33
0
We are given a form of Einstein's field equations:

3R'' = -pR
R''R + 2((R')^2) = p(R^2)

where p is a constant and R' = dR/dt

Assuimg that R and R' are both positive, we are asked to show that the general solution is R(t) = A*[(t-ti)^(2/3)]

I'm very confused about this. If we substitute the required expression into the given equations it doesn't solve them! This indicates to me that there might be a mistake, but it' an old Oxford exam paper from the Maths department, so it should be reliable. N.b if you solve the above equations simultaneously you should get an exponentially increasing function for R(t).
Either the quesion is wrong or there is something I'm not seeing.
 
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  • #2
Is p supposed to be an energy density? If so then they sort of resemble the Friedmann equations with no pressure if you adjust a coefficient or two. And if p is constant the solution is exponential alright. On the other hand the solution you've given is for matter driven expansion - which is pressureless alright. But energy density=p is not constant in that case p*R(t)^3 is. I'm confused too.
 
  • #3
We are given a form of Einstein's field equations:

3R'' = -pR
R''R + 2((R')^2) = p(R^2)

where p is a constant and R' = dR/dt
If p is constant the equations are independent and may not have a simultaneous solution. I'm confused too.
 

What is General Relativity?

General Relativity is a theory of gravity proposed by Albert Einstein in 1915. It describes how objects with mass and energy affect the fabric of space and time, known as the space-time continuum.

What is the form of scale factor?

The form of scale factor in General Relativity is a mathematical function that describes the expansion or contraction of the universe over time. It is represented by the letter "a" and can vary depending on the curvature of space-time and the distribution of matter and energy.

How does General Relativity explain gravity?

General Relativity explains gravity as a curvature of space-time caused by the presence of mass and energy. Objects with mass create a dent in the fabric of space-time, and other objects with mass follow this curvature, resulting in the force we experience as gravity.

What is the difference between General Relativity and Newton's law of gravitation?

General Relativity and Newton's law of gravitation both describe the force of gravity, but they have different foundations. Newton's law is based on the concept of a force acting at a distance, while General Relativity explains gravity as a curvature of space-time caused by the presence of mass and energy.

How has General Relativity been tested and proven?

General Relativity has been tested and proven through various experiments and observations, such as the bending of light by massive objects, the precession of Mercury's orbit, and the detection of gravitational waves. These observations have confirmed the predictions of General Relativity and validated its accuracy as a theory of gravity.

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