CPT (M?) symmetries in Kerr-Newman metric

  • Context: Graduate 
  • Thread starter Thread starter michael879
  • Start date Start date
  • Tags Tags
    Metric Symmetries
Click For Summary

Discussion Overview

The discussion revolves around the discrete symmetries of the Kerr-Newman metric, particularly focusing on parity inversion in spherical coordinates. Participants explore different methods of applying parity transformations and their implications on the symmetries of the metric, including charge (C), parity (P), time (T), and a proposed mass (M) symmetry. The scope includes theoretical considerations and potential implications for the nature of antimatter.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Mike describes two methods of parity inversion that yield different results regarding the independence of C, P, and T symmetries in the Kerr-Newman metric.
  • Method #1 suggests that C, P, and T are independent symmetries, while Method #2 indicates that they are not independent and introduces an MCPT symmetry.
  • Mike expresses confusion over the stark differences in outcomes from the two methods and questions what he might be missing.
  • A later reply corrects the parameters resulting from Method #2, stating it would represent a Kerr-Newman black hole with parameters (-M, -Q, J).
  • Another participant introduces Method #3, which also leads to a Kerr-Newman black hole with parameters (-M, -Q, J), suggesting it is similar to Method #2 but involves a reflection in the x-y plane.
  • One participant proposes that the different parity transformations affect how points are moved through space, particularly in relation to the ring singularity of the Kerr metric.
  • Another participant suggests testing the same transformations on a rotating charged star to see if the results differ, questioning the known solutions for such objects.
  • Concerns are raised about the classical validity of the transformations, particularly regarding the transformation of the radial coordinate r, which is not typically allowed to be negative in classical physics.
  • There is a discussion about the semantics of the transformations and whether they can be considered classically indistinguishable under certain conditions.

Areas of Agreement / Disagreement

Participants express differing views on the validity and implications of the various methods of parity transformation. There is no consensus on the correct interpretation of the transformations or their physical significance, indicating ongoing debate and uncertainty.

Contextual Notes

Limitations include the dependence on the definitions of the transformations and the assumption that r must be non-negative in classical contexts. The discussion also highlights the ambiguity introduced by the ring singularity in the Kerr-Newman metric.

  • #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...
 
Last edited:
Physics news on Phys.org
  • #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.
 

Similar threads

Graduate Kerr Metric Time Dilation Formula: Deriving Absolute Form
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad What are the effects on a stationary observer for Kerr metric?
  • · Replies 43 ·
2
Replies
43
Views
5K
Graduate Understanding Kerr Black Holes: Metric, Killing Vectors & Event Horizons
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Principal and Gaussian curvature of the FRW metric
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Propagation Vector of Light in Kerr Spacetime: Reference Needed
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Coordinates for diagonal metric tensors
  • · Replies 12 ·
Replies
12
Views
3K
Graduate Exact meaning of the mass M in the Kerr metric event horizon formula?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Speed of Light for Bonnor Beam
  • · Replies 26 ·
Replies
26
Views
2K
Graduate Compute Induced Metric on Kerr Event Horizon
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Kerr-Newman Metric Equation Solution | Verified by Experts
  • · Replies 2 ·
Replies
2
Views
3K