![]() We also investigate the case where the source falls from rest at a finite distance from the black hole. It is found that, as in the electromagnetic and gravitational cases, at high initial velocities the energy spectrum for each multipole with \(l \ge 1\) approximately is constant up to the fundamental quasinormal frequency and then drops to zero. Higher multipoles become dominant at high initial velocities. When the source falls from infinity, the monopole radiation is dominant for low initial velocities. Obviously, despite an order one prefactor, is the same, but I am confused.We investigate the radiation to infinity of a massless scalar field from a source falling radially towards a Schwarzschild black hole using the framework of the quantum field theory at tree level. here In the paper, at the end the calculation provides a time Remark: The above time differs (I would want to know why or where is the contradiction if any) asking about the free fall into the event horizon from a external $r>R_g$, solved e.g. Obviousle at the singularity (the only real problem) we need another theory, but as far as I see, I find problematic to understand free falling as constant acceleration, obviously it can not be constant.I think.ī) Obviously, at $r=0$, where the hypothetical singularity is, we have a divergent (infinite gravitational finite, even when that is completely nonsense), so I wonder what it means if we adopt the picture that there is no "black hole interior", as suggested by some holographic approaches. Free falling is tricky in the sense a free falling observer, according to Einstein, does not experience "locally" gravity, but obviously it feels tidal forces, so I can not see if at one point we should assume GR falls. The gravitational "field" is not uniform inside the black hole, so I can not understand:Ī) The role of the equivalence principle. Moreover, I don't understand a point I want to understand before I will recalculate all this for the time we need to reach the ring singularity in the Kerr black hole. My question is simple: since GR is only effective, I don't think this calculation is meaningful. According to general relativity, we can compute the (finite) free fall time in which we travel from the Schwarzschild radius to the singularity (we ASSUME by the moment GR holds, the point is to what extend is this valid both in General Relativity and the real world, but we can do it as an exercise): ![]() Suppose we fall into a Schwarzschild black hole. So the proper time interval inside the event horizon is meaningful. Note: As a general comment a classical theory breaks down at a physical singularity, in Schwarzschild at $r = 0$, but it is applicable until close to that point. Remark: The formula above applies whether you start to measure the proper time interval from outside the event horizon, $r \gt r_s$, or from inside the horizon, $r \lt r_s$. Note that in terms of proper time a finite interval is requested to reach the singularity.Ī) The principle of equivalence applies locally, that is in a limited region of spacetime.ī) The singularity $r = 0$ can not be described by a classical theory. ![]() This relation is consequent to the Schwarzschild metric. In Schwarzschild a free falling particle from infinity, starting with zero kinetic energy and zero angular momentum, and plunging radially into the black hole measures a proper time $\Delta \tau$ to reach the singularity, function of the initial radial coordinate $r$, as
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