All Questions
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Is there a deeper relationship between symmetry and gravitational potential comparing Newton's and Einstein's gravity?
In this question, see Why is general relativity in (2+1) dimensions different from cylindrical systems in (3+1) dimensional GR?, it is mentioned
"The gravitational potential Φ of an infinite rod ...
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1
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0
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Einstein's equation of gravitation field [duplicate]
I'm looking for the reason why there is the number eight $8$ at the r.h.s. of EI:
$$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^2}T_{\mu\nu}.$$
My attempt was to take the limit of this equation ...
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3
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When does Newtonian physics fail?
When does Newtonian physics fail?
The answer by Zo the Relativist to the question How accurate is Newtonian Gravity? includes the statement:
The key point is that Newtonian physics fails when, ...
2
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1
answer
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Physical relevance of the $ij$ components of the Einstein field equations in the Newtonian limit
In the weak field limit of general relativity (with matter described by a perfect fluid consisting only of dust), we have the following correspondences:
$00$-component of the Einstein field equations ...
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-3
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1
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How does Einstein's theory of relativity prove Newton's laws of gravitation (or is it incorrect)?
I have heard that at the speed of light the Newton's laws of gravitation stop working. Why does that happen or does that even happen? Is there any proof to it? From what I have heard It's related to ...
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2
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695
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General relativity when can we approximate to Newtonian gravity?
Lets consider this scenario in deep void of space where other curvatures of large objects are negligible in this case and we bring 2 objects lets say $A$ and $B$.
We give it a force slightly lower ...
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5
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1
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ONLY non-relativistic limit of general relativity
From my study of GR I learnt that to reach the “Newtonian” limit of the Einstein field equation we have to assume:
weak field $g_{\mu\nu} = \eta_{\mu\nu} + \epsilon h _{\mu\nu}$ with $\epsilon <&...
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How to derive Newton's law of gravitation from general theory relativity [duplicate]
Newton's law of gravitation must be a special case of the general theory of relativity. How can we derive it from field equations of GTR?
If the electric field F/q is equal to E, then does the ...
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15
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8
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What is the true nature of gravity? [closed]
In 17th century, Sir Isaac Newton gave us the universal law of gravitation which stated that gravity is an inverse square force. In 1915, Albert Einstein recognised gravity as a curvature of space-...
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Is it possible to make a tiny approximation in the equations of General Relativity so that they collapse to Newton's law of gravity? [duplicate]
GR and Newton give almost exactly the same result for the orbits of planets and the acceleration of falling bodies. Is it an incredible coincidence, or does GR have some tiny term (e.g., ict) that ...
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4
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At which distance $r$ from a black hole does its gravity become Newtonian?
The force near a black hole (outside event horizon $r=3r_s/2$) onto a mass $m$ can be calculated by General Relativity:
$$F=\frac{GMm}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}.$$
However, there must be ...
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3
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Newtonian Limit of Schwarzschild metric
The Schwarzschild metric describes the gravity of a spherically symmetric mass $M$ in spherical coordinates:
$$ds^2 =-\left(1-\frac{2GM}{c^2r}\right)c^2 \, dt^2+\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^...
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2
votes
1
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Rigorous derivation of non-relativistic limit in cosmology?
The standard way to derive the non-relativistic limit and its corrections in general relativity is to formally expand Einstein equation in powers of $1/c$ around a background space-time. The non-...
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Question about the Newtonian limit of general relativity
I ran into something peculiar while attempting to carefully derive the Newtonian limit of general relativity, specifically for the geodesic equation.
To set it up, we assume that the curve $q:[a,b]\...
3
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3
answers
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With calculations involving GR & gravity, when are Newtonian mechanics & Newtonian gravity sufficient and when are they not?
I understand that Newtonian mechanics is a good approximation of GR but at what extremities are the differences so great that GR must be used.
I assume it to not be suitable at velocities nearing ...
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