The escape velocity from a common gravtational attractor means that a body lounched away from the attractor will never turn back. But in the case of a BH at the event horizon this escape velocity is $c$ and as even light cannot move away in these circumstances it is likely that a body should also be stopped from moving away even a little bit. But what about a spot close to the BH but far enough for the escape velocity not to be $c$? Would a body,at least theoretically,pushed away from the BH at that spot travel a piece of space before it eventually encounter the BH core after passing through the event horizon? And what about light that would point away from the BH at that spot? Would it act differently than the material body? Would it just change its own wavelength or it could be changing its velocity as frame-dragging suggests that space-time could be dynamic near the BH so the overall velocity of a photon of light should be put in aggregation with the motion of space-time near the BH. Even the fact that light as just a vibration that travels in straight trajectories inside the space-time tissue bends near the BH could suggest about eventual dynamic behaviour of space-time near the BH?
1 Answers
Krešimir Bradvica asked: "But what about a spot close to the BH but far enough for the escape velocity not to be c? Would a body,at least theoretically,pushed away from the BH at that spot travel a piece of space before it eventually encounter the BH core after passing through the event horizon?"
Since the gravitational time dilation is finite above the horizon, the shapirodelayed velocity (in the frame of the far away observer) of the escaping object which moves radially outwards relative to a local stationary observer might be small, but not zero, so yes, it will move away from the black hole also in the frame of the far away observer aka the Schwarzschild coordinate bookkeeper, but slower than in the frame of the local stationary observer.
Krešimir Bradvica asked: "what about light that would point away from the BH at that spot? Would it act differently than the material body? Would it just change its own wavelenght or it could be changing its velocity"
The light would escape if it is directed radially outwards, the shapirodelayed velocity will also be small if it is close to the horizon but it will escape to infinity and arrive there with the corresponding gravitational redshift.
Also its relative velocity to every local oberver that it flies past, be it a free falling or a stationary one and regardless of r, will be always c, only relative to a distant observer the velocity will shapirodelay by the gravitational time dilation factor.
If the light is not pointed radially outwards, but tangential, it needs to be above the photon sphere at 1.5 times the radius of the horizon in order to escape (under Newton the radial and tangential escape velocity would be the same, while under Einstein they are not, but that goes for particles and photons).
Below the horizon in the frame of free falling observers the radially outward directed photons (relative to the free falling observers) also move inward relative to the black hole, though not as fast as those who are also directed inwards relative to the free fallers, see here.
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