Does a linearly accelerated observer inside an inertial spherical charged shell detect an electric field? The electric field inside a charged spherical shell moving inertially is, per Gauss's law, zero.
If the spherical shell is accelerated, the field inside is not zero anymore, but it gains a non-null component along the direction of the acceleration, as mentioned, for example, in this paper.
The following picture from the above paper shows the field lines in the xy-plane in the instantaneous rest frame. The shell is undergoing rigid hyperbolic motion along the x-axis (toward the right)

The question I have is the following:
Assuming that a charged spherical shell is moving inertially, would an accelerated observer (test charge) inside of it detect an electric field like in the image above?
This question is also equivalent to asking the following ones:
Is there an electric field inside the shell if it is accelerating in an homogenous gravitational field?  Will an observer (test charge) in the center of the shell that is not falling along with it, detect an electric field?
I read in a couple of papers that there won't be any field detected by such observer, but this is not demonstrated and sounds strange to me.
The reasoning of these papers is that the electromagnetic tensor is invariant, so if it is zero in the inertial frame it will be zero also in the non-inertial one.
But here we are talking about the electric field only, which is a component of the electromagnetic tensor, so I don't see any a priori reason why it could not be made non-zero thanks to a frame transformation
 A: 
I read in a couple of papers that there won't be any field detected by such observer, but this is not demonstrated and sounds strange to me. The reasoning of these papers is that the electromagnetic tensor is invariant, so if it is zero in the inertial frame it will be zero also in the non-inertial one.
But here we are talking about the electric field only, which is a component of the electromagnetic tensor, so I don't see any a priori reason why it could not be made non-zero thanks to a frame transformation

Right, the correct argument is as follows: if all components of the electromagnetic tensor are zero in one frame, then the same will be true in any other frame. Also, it does not matter whether one frame or the other or both is non-inertial.
The nonzero components of the electromagnetic tensor are the 3 components of the electric field, the 3 components of the magnetic field, and the same with their signs flipped. So if the electric and magnetic fields both vanish in the first frame, then we can be assured that an accelerated observer at the same location will also agree that they both vanish.
A stationary, uniformly charged spherical shell in an inertial frame has no interior electric field and no interior magnetic field, as measured in such frame. So, an accelerated observer would agree.
A: After thinking a bit now I think there should be an electric field inside: electromagnetic tensor depends on the charge density, and this changes in the reference frame of the sphere due to the fictious force drive, so should not be invariant: hope I'm not saying blasphemies. Anyway, for a mechanical reasoning I should expect that electrons are driven in the direction opposite to the acceleration until they reach a point in which electrostatic force equals $m\boldsymbol{a}$. You fundamentally have now a capacitor and the figure you posted seems to confirm this. You also have emission by Larmor formula due to low-mass charged electrons, while nuclei don't almost emit, but I really can't tell if the phases of all photon emitted by all points of the sphere make electrodynamic field cancel out inside the sphere: electrostatic field should be present for the capacitor effect I told you before. I really can't imagine more than this; if I didn't say anything wrong I'll wait for a more conscious and claryfing answer since it's an interesting question.
