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A charged particle on a straight line does not emit synchrotron radiation. What happens if it is on a geodesic? Do electrons that circle around a black hole emi

by fxj 2y ago

A charged particle on a straight line does not emit synchrotron radiation. What happens if it is on a geodesic? Do electrons that circle around a black hole emit synchrotron radiation?

db48x 2y ago
That’s beyond my level of expertise, but yes. Quoting from the abstract of The Motion of Point Particles in Curved Spacetime <https://web.archive.org/web/20151203142700/http://relativity.livingreviews.org/Articles/lrr-2011-7/download/lrr-2011-7Color.pdf https://web.archive.org/web/20151203142700/http://relativity...> > This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. Note especially that the charged particle won’t actually follow the geodesic. Because the synchrotron radiation carries away some energy, the particle will be continually pushed off of the geodesic; it will spiral inwards instead of orbiting forever.
- fxj 2y ago
  Does this mean that when the geodesic is a straight line then the particle stays on the geodesic, but when the geodesic is curved the particle interacts with its own e.m. field and deviates from the geodesic because it feels a deflecting force? Then there would be a fundamental difference between curved and straight geodesics which would be a contradiction to the Einstein Equivalence Principle. How do physicists explain that contradiction?
  - db48x 2y ago
    The equivalence principle only applies to uniform fields and uniform motion. A charged particle in orbit is not in a uniform field and is not experiencing uniform motion.

by fxj 2y ago

A charged particle on a straight line does not emit synchrotron radiation. What happens if it is on a geodesic? Do electrons that circle around a black hole emit synchrotron radiation?

db48x 2y ago

That’s beyond my level of expertise, but yes. Quoting from the abstract of The Motion of Point Particles in Curved Spacetime <https://web.archive.org/web/20151203142700/http://relativity.livingreviews.org/Articles/lrr-2011-7/download/lrr-2011-7Color.pdf https://web.archive.org/web/20151203142700/http://relativity...> > This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. Note especially that the charged particle won’t actually follow the geodesic. Because the synchrotron radiation carries away some energy, the particle will be continually pushed off of the geodesic; it will spiral inwards instead of orbiting forever.

fxj 2y ago
Does this mean that when the geodesic is a straight line then the particle stays on the geodesic, but when the geodesic is curved the particle interacts with its own e.m. field and deviates from the geodesic because it feels a deflecting force? Then there would be a fundamental difference between curved and straight geodesics which would be a contradiction to the Einstein Equivalence Principle. How do physicists explain that contradiction?
- db48x 2y ago
  The equivalence principle only applies to uniform fields and uniform motion. A charged particle in orbit is not in a uniform field and is not experiencing uniform motion.