It is said in this wikipedia article (in the 7th paragraph) that where there exists huge masses and very large gravitational forces (like around binary pulsars), general relativistic effects can be observed better:

By cosmic standards, gravity throughout the solar system is weak. Since the differences between the predictions of Einstein's and Newton's theories are most pronounced when gravity is strong, physicists have long been interested in testing various relativistic effects in a setting with comparatively strong gravitational fields. This has become possible thanks to precision observations of binary pulsars.

But here in whystringtheory.com (in the last paragraph), it is said that

For small spacetime volumes or large gravitational forces Einstein has little to offer

I know that in singularities, GR fails and this is a motivation for quantum gravity theories. But the second quote above says in small spacetime volumes or large gravitational forces.

Is there any problem with general relativity in conditions with very large gravitational forces (in big enough volumes of spacetime)?

  • $\begingroup$ The text no longer seems to be in the article. It doesn't sound right to me, although maybe it would make more sense with context. If you're interested in pursuing this, try clicking on View history and finding the version of the article that had that text. If you point us to it, we'll have context. $\endgroup$ – user4552 Jul 6 '13 at 0:05
  • $\begingroup$ @BenCrowell It exists! As I said in the question, in the 7th paragraph of section #Experimental tests. I copied the text in the question. $\endgroup$ – Zorich Jul 6 '13 at 0:25
  • $\begingroup$ Maybe you need to clear your browser's cache? It's not there for me. I'm using my browser's search function to search for the text "For small spacetime volumes," and it doesn't find it anywhere in the article. By the 7th paragraph, do you mean the one beginning with "By cosmic standards...?" $\endgroup$ – user4552 Jul 6 '13 at 0:30
  • $\begingroup$ @BenCrowell The second quote is from whystringtheory.com , not the wikipedia article! I modified the question. $\endgroup$ – Zorich Jul 6 '13 at 0:37
  • $\begingroup$ Maybe the question of "are there any problems with GR" might be better put as "are there any experimental results which tell against or which could be inconsistent with GR". I'd like to know the answer to that one from a real astronomer. $\endgroup$ – WetSavannaAnimal Jul 6 '13 at 2:38

The whystringtheory page is written in a popularized style that makes it impossible to tell what they really have in mind. Their statement doesn't make sense if interpreted according to the standard technical definitions of the terms. GR doesn't describe gravity as a force. In the system of units normally used in GR, with G=c=1, force and power are unitless, so there is also no natural motivation for defining something like a Planck force by analogy with the Planck length, etc. Possibly their "force" really means curvature, in which case this could be interpreted as a correct statement that GR breaks down when the Riemann tensor corresponds to a radius of curvature comparable to the Planck length.


I think what they are simply saying is that at those (energy of the order of Planck scales and distance of the order of Planck length) quantum effects come into play and GR being a classical theory is no longer an adequate description of physics. One would need a quantum theory of gravity to describe physics at such scales, and string theory is one such candidate.

To understand what they mean by "weak", "strong" and "large gravitational forces", I give you some numbers. Newtonian gravity is a good approximation at the surface of the Earth. At the surface of the sun, however, GR effects are more pronounced. Quantum effects of GR are visible in regions near (around the event horizon) a black hole.

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    $\begingroup$ "Quantum effects of GR are visible in regions near (around the event horizon) a black hole." Not really. They're relevant at distances within one Planck length of the singularity. $\endgroup$ – user4552 Jul 6 '13 at 1:11
  • $\begingroup$ I see. It's not even at one Planck length of the singularity. Quantum effects are important when the radius of curvature is of the order of the Planck Length. $\endgroup$ – Prahar Jul 6 '13 at 2:43

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