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Event horizons are (relativistic) classical predictions of general relativity and theories of gravity. How can, in principle, to detect an event horizon and elucidate to what kind of black hole it belongs to? Or are event horizons undetectable with astronomical tools?

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  • $\begingroup$ Maybe that's interessting for you. The scientists from the EHT work on such measurmenst: eventhorizontelescope.org $\endgroup$
    – Alpha001
    Aug 11, 2018 at 18:23

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In a Schwarzschild (static and spherically symmetric) black hole a stationary observer measures the frequency of a photon depending on the radial coordinate $r$. For a photon emitted radially at $r_1$ and observed at $r_2$ we have:
$$\dfrac{\omega_2}{\omega_1} =\left(\frac{1 - 2M/r_1}{1 - 2M/r_2}\right)^{1/2}$$ where:

  • $c = G = 1$ natural units
  • $\omega$ photon frequency
  • $M$ black hole mass

If you are in a spacecraft at radial distance $r_2$ and you drop a beamer, you may detect the frequency emitted by the beamer approaching the black hole. You will measure a progressive redshifting of the frequency and a progressive dilation of the time interval between a pulse and the next one. A plot of $r_1$ vs. the measured frequency and the dilated time interval allows to estimate the radial coordinate of the horizon. As the beamer is moving you have also to consider a superimposing relativistic Doppler effet.

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