- #1

- 894

- 0

GR and EM are classical field theories, but later in the questions I wish to treat this in a semiclassical manner. For those helping to answer, please be specific which answers can be done in a purely classical manner, and which require quantum approaches (and please let me know if the semiclassical approach will not apply to some of these questions, such that we must wait for a consistent quantum gravity theory).

Let us consider a non-rotating blackhole with charge (Reissner-Nordström blackhole) and also consider another charge slightly above the event horizon. For roughly 4pi of the solid angle, geodesic lines for light starting from this external point will terminate at the singularity. Let's define F as the force on the singularity due to this external charge at this distance.

If I now move the external charge further away, so that the solid angle (of geodesic lines starting from this external point and terminating at the singularity) is now pi, will the force now be F/4 as intuition suggests? (a kind of "number of field lines" idea of electric field strength)

If so, does this mean the force on the singularity due to an external charge located at the event horizon is independent of the event horizon radius?

Now, while almost the entire solid angle of geodesics from a point above the horizon meet the singularity, only a small fraction of the total solid angle of geodesics meeting at the singularly actually go through the external point. So does this mean the electric force on the singularity will be greater than the electric force on the external charge?

This seems wrong to me. So, while making the explanation of the 1/r^2 in Coulomb's law seem obvious in flat space, the "number of field lines" idea of electric field strength probably doesn't work in curved space for some reason? If so, can someone explain this to me?

Now for the semiclassical part: How can we even know a blackhole is charged? In other words, how can the virtual photons escape the singularity and leave the event horizon? I realize they can have a spin-0 state or even non-zero invarient mass, unlike normal photons, so can they do other bizarre things like travel "faster" than the speed of light?

I have many other questions as well, but I need to clear up any of my possible misunderstandings of this first before I can hope to move on to the rest.

Let us consider a non-rotating blackhole with charge (Reissner-Nordström blackhole) and also consider another charge slightly above the event horizon. For roughly 4pi of the solid angle, geodesic lines for light starting from this external point will terminate at the singularity. Let's define F as the force on the singularity due to this external charge at this distance.

If I now move the external charge further away, so that the solid angle (of geodesic lines starting from this external point and terminating at the singularity) is now pi, will the force now be F/4 as intuition suggests? (a kind of "number of field lines" idea of electric field strength)

If so, does this mean the force on the singularity due to an external charge located at the event horizon is independent of the event horizon radius?

Now, while almost the entire solid angle of geodesics from a point above the horizon meet the singularity, only a small fraction of the total solid angle of geodesics meeting at the singularly actually go through the external point. So does this mean the electric force on the singularity will be greater than the electric force on the external charge?

This seems wrong to me. So, while making the explanation of the 1/r^2 in Coulomb's law seem obvious in flat space, the "number of field lines" idea of electric field strength probably doesn't work in curved space for some reason? If so, can someone explain this to me?

Now for the semiclassical part: How can we even know a blackhole is charged? In other words, how can the virtual photons escape the singularity and leave the event horizon? I realize they can have a spin-0 state or even non-zero invarient mass, unlike normal photons, so can they do other bizarre things like travel "faster" than the speed of light?

I have many other questions as well, but I need to clear up any of my possible misunderstandings of this first before I can hope to move on to the rest.

Last edited: