CPT (M?) symmetries in Kerr-Newman metric

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SUMMARY

The discussion centers on the discrete symmetries of the Kerr-Newman metric, specifically examining parity inversion in spherical coordinates. Three methods of parity transformation are analyzed, revealing that Method #1 supports independent C, P, and T symmetries, while Methods #2 and #3 suggest the presence of an additional M symmetry, indicating that the metric only possesses MCPT symmetry. The confusion arises from the implications of these transformations on the nature of gravitational mass, particularly concerning antimatter. Ultimately, the discussion highlights the complexities of symmetry transformations in the context of general relativity.

PREREQUISITES
  • Understanding of Kerr-Newman metric properties
  • Familiarity with parity transformations in physics
  • Knowledge of spherical coordinates and their applications in general relativity
  • Basic concepts of black hole physics and singularities
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  • Research the implications of the Kerr-Newman metric on black hole thermodynamics
  • Study the role of ring singularities in general relativity
  • Explore the concept of analytic continuation in spacetime metrics
  • Investigate the relationship between gravitational mass and inertial mass in the context of antimatter
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The discussion is beneficial for theoretical physicists, cosmologists, and students of general relativity who are exploring the nuances of black hole metrics and the implications of symmetry transformations in high-energy physics.

  • #61
yea but a = R to an observer at infinity, where R is the radius of the ring singularity. And yea, I missed a factor of 1/2 :-p.

But anyway, the point I was trying to make way back was that most physicists start with the assumption that QFT is correct, and we are just lacking the correct model to describe the universe (i.e. the quantum gravity terms, and whatever extra terms are needed to solve the various problems). This boils down to using QFT to recreate gravity as an "emergent" macroscopic approximation. There is, however, the other route of assuming GR is correct and trying to recreate QFT with it. I'd say the experimental confirmation of GR is much more convincing than the experimental confirmations of QFT (which isn't to say they aren't convincing, but all of the experiments are riddled with unknowns and tiny invisible "objects").

If you remove the cosmic censorship hypothesis (which is complete speculation IMO), you can include naked singularities in GR. These objects possesses many of the qualities present in quantum particles (non-determinism being the main one). Additionally, I don't know how true this is but I read in a paper on the subject that an infinitesimal number of initial conditions will lead to a direct interaction with the naked singularity, making it virtually invisible. Clearly a many-body naked singularity solution is intractable, so proving or disproving that GR can recreate quantum effects is not an easy task. I was trying to make some progress with CPT symmetry, but it turns out I've shown nothing. Black holes obey C, P, and T symmetries independently, and so do fundamental particles if you ignore the strong and weak forces. It would be interesting to try to give a black hole charge in an SU(3) gauge field though...
 
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  • #62
michael879 said:
It would be interesting to try to give a black hole charge in an SU(3) gauge field though...

This is one thing I've always wondered about: shouldn't conserved charges for other fields besides the electromagnetic field count as additional "hair" that a black hole could have? And therefore shouldn't there be a generalization of the Kerr-Newman metric that includes the additional charges as well as Q (and J, or a, for angular momentum)?
 
  • #63
Yea I wondered this myself a while back. I derived the classical "Maxwell's" equations for an SU(N) gauge field, but they were so much more complicated than the U(1) case I gave up trying to apply them to a black hole. Hypothetically a black hole should be capable of holding any charge. However I read a paper that claimed to prove that a black hole couldn't be charged with respect to a massive vector field (weak force), or a massive scalar field (nuclear strong force), although I couldn't really follow it. Their conclusion was that a black hole couldn't interact weakly or have baryonic charge. However a black hole could probably have charge in a massless SU(2) field (which is what the weak force is before the Higgs field is applied), and a color charge (which would just be hadronized away in the macroscopic case).

Now that I was reminded of it I'm actually going to try to work out what the metric of a black hole charged under an SU(N) gauge field would be.
 

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