# GR Verification for a Charged Black Hole

For a charged ($Q$) rotating ($L$) mass ($M$), the Kerr-Newman equations give the angular deflection of light. Has there been observational verification (I would prefer to use only the angular deflection of light) that all three $QLM$ parameters are needed?

I am wondering if all observed light deflection could be fit just as well with the simpler Schwarzschild model (or, if not, with the Kerr model). I have some doubt about the way that electromagnetic field energy bends spacetime in General Relativity.

## 1 Answer

I don't think there has even been observational evidence of Kerr-specific effects. While gravitational lensing is well known these days I don't think any of the objects studied have been rotating fast enough for the difference between the Kerr and Schwarzschild metrics to be apparent. Well, not in lensing anyway - Gravity Probe B did measure frame dragging.

The chances of us ever finding an astronomical object with a net charge big enough to have any measurable effect on the geometry are essentially zero. There is no known way for a charge imbalance that big to develop and too many ways for it to neutralise. I doubt there will be observational evidence for the effect of charge on spacetime any day soon.

Observational evidence of black holes remains rather indirect even these days.

• Is it fair to say that, if the spin and charge of all stars/planets outside of our solar system were magically doubled, we couldn't notice the difference? – bobuhito Jun 7 '16 at 16:55
• We have no idea what the charges of astronomical objects are, so if you double them we staill have no idea what they are. We've been able to measure the rotation rates of galaxies using Doppler shifts, and even measure the rotation rates of a few stars by directly imaging them, so we'd be able to tell if those rotation rates were doubled. However as far as lensing goes we have no evidence for the effects of rotation rates on lensing. – John Rennie Jun 7 '16 at 17:00
• Thanks, if I extend my observations beyond lensing to orbital precession too (or to anything short of galaxy rotation), I assume that there still is no evidence. – bobuhito Jun 7 '16 at 17:04
• Precession isn't due to rotation (of the central body). I suspect you're thinking of frame dragging. As far as I know the only measurement of frame dragging ever done was by Gravity Probe B. – John Rennie Jun 7 '16 at 17:15