Thank-you for asking. Of course, I have mentioned some of the GR flaws before, but I continually refine my list and so here it is now. The recent papers about event horizon firewalls and eternally collapsing matter are very interesting new perspectives on GR flaws.
Georgina Woodward replied on Apr. 27, 2015 @ 05:29 GM with "...you keep saying there are flaws with GR, Now you suggest some areas to consider. Do you wish to share your insight?"
Although there have been notable successes for GR, that are also many notable flaws embedded within general relativity and quantum action. Along with a better understanding of the universe, the flaws of GR are now becoming more and more obvious. Not all of the flaws, of course, are with GR. Quantum action carries its own flaws as well as GR.
Black holes are inconsistent with quantum action
Probably the most famous of all of relativity's progeny is the notion of a black hole. Given enough mass, gravity will eventually become sufficient to capture light and stop time, two well worn predictions that simply cannot be the complete story.
Black hole event horizons are inconsistent with quantum action[\b]
A particle of matter is subject to two quite different fates once it encounters the event horizon of a black hole. According to much of the historical black hole research, such a particle simple joins the mass accretion and loses all of its information. More recent calculations find that, prior to reaching the event horizon, a particle is ripped into smaller and smaller pieces that are smaller than the Planck limit. Those tiny pieces of matter begin collapsing and therefore never actually enter the primary black hole. These eternally collapsing objects, eco's, take the place of the primary black hole. Great, just what we wanted to hear.
Quantum calculations show, on the other hand, that the exact same particles of matter are torn into matter and antimatter, emitting so-called Hawking radiation. This seems to turn the black hole event horizon equivalent into a firewall and just like with the eco, all action stops. There just cannot be two different fates for the same neutral particle.
Proper time inconsistent with quantum time
Proper time is a key notion of GR and that proper time becomes a fourth dimension spacetime. Ironically, this in effect does away with time because all motion in GR occurs along determinate geodesics by gravity and so the GR future is completely determined.
Quantum time, on the other hand, is reversible and there is no sense to a quantum time stoppage at an event horizon or any where else for that matter. Time is simply a quantum progress variable and there is therefore no expectation value for a time duration.
The future simply cannot be both deterministic and probabilistic and it is likely that both GR and quantum time need some kind of adjustment for time.
Dark matter and dark energy not explained
Dark matter is an extra gravity term that explains the stabilities of galaxies and galaxy clusters while dark energy is yet another gravity term needed to hold the universe together as the CMB. The absence these extra gravity terms in GR is a little disconcerting. If we expect anything at all from our gravity models is that the model all of the effects of gravity.
Determinate geodesics inconsistent with quantum action
Another of the basic results of GR is that gravity action distorts or curves the 4D spacetime and that objects simply follow certain predetermined geodesics as minimum energy paths. Of course, quantum action does not distort 4D spacetime and yet quantum action results in likely but not certain futures. In a future quantum gravity, there will have to be a number of futures instead of a determinate one.
Lack of amplitude and phase coherence and interference
All of our quantum reality depends on both the phase as well as the amplitude of matter. This is what gives us coherence and interference and entanglement. However, gravity force in GR only deals with the norms of matter and time and so there is no coherence or interference or entanglement. Since all of these notions figure prominently in quantum action, it is a major flaw that GR has no corresponding quantum gravity.
Planck limit inconsistent with quantum uncertainty principle
Once a particle gets small enough, it will collapse into a microscopic event horizon where its time stops. But quantum action functions everywhere in the universe and there is no stopping quantum time, even at the Planck limit. Quantum action limits the divisibility of matter and space to the uncertainty principle.
Quantum time is not consistent with proper time of GR
But there are flaws to quantum time as well as GR time. Why can't we all just get along?
Quantum space and motion are inconsistent with GR space and motion
Quantum action is obsessed with space and motion just as GR is. However, the two notions of space and motion have certain intrinsic contradictions. Therefore, restructuring each of quantum and GR with alternate conjugates such as matter and time, resolves the contradictions and allows unification.
