1
$\begingroup$

In lecture, I am told that if a photon is initiated outside the event horizon of a black hole, from the laboratory frame of reference, it will never reach the event horizon. What is confusing is that the professor said if I have a photon initiated in a direction perpendicular to the radial direction and the photon is in between the photon sphere and the event horizon, then the photon will spiral into the singularity of the black hole (he did not mention from which reference frame), but I don't even think it will pass through the event horizon from laboratory frame of reference.

So why did he claim that the photon will spiral into the singularity?

$\endgroup$
2
  • $\begingroup$ In the first case the photon still enters the event horizon even if in the lab frame all we see is infinitely red shifting light $\endgroup$
    – Triatticus
    Jan 8, 2019 at 19:00
  • $\begingroup$ Your intuition is correct. There is no frame, in which any photon ever crosses the horizon. In fact, the same applies to massive particles, because nothing has a frame at the horizon while in any other frame they never cross. $\endgroup$
    – safesphere
    Jan 10, 2019 at 8:30

1 Answer 1

1
$\begingroup$

There are no global frames of reference in general relativity. These descriptions in terms of the "frame of reference" of a distant observer are just incorrect pop sci. What is true is that if a distant observer tries to get a signal sent to him from the event horizon when something crosses the event horizon, he will never receive the signal. But this is just trivially true, since the definition of the event horizon is that it's a place that you can't transmit a signal from.

If the photon crosses the horizon, it will hit the singularity, and if it hits the singularity, then it had to enter through the horizon. General relativity just doesn't offer a notion of simultaneity that allows a distant observer to say that these events happen "now."

$\endgroup$
7
  • $\begingroup$ But what happen if the photon just crosses the photon sphere? Will it cross the event horizon? $\endgroup$ Jan 9, 2019 at 1:59
  • $\begingroup$ @Jerry: If it crosses the photon sphere on a radial inward trajectory, then certainly it will cross the event horizon and later reach the singularity. $\endgroup$
    – user4552
    Jan 9, 2019 at 2:22
  • $\begingroup$ What happen if the photon is inside the photon sphere and its initial direction is perpendicular to the radial direction? $\endgroup$ Jan 9, 2019 at 2:27
  • $\begingroup$ A photon at the photon sphere with a direction tangential to the sphere's surface will orbit the black hole. If it's between the photon sphere and the horizon with direction perpendicular to radial direction, then it cannot maintain that orbit and the orbit will degrade (the photon spirals inward), inevitably crossing the horizon. $\endgroup$ Jan 9, 2019 at 2:45
  • $\begingroup$ Is it true from my observation point of view, the photon will spiral asymptotically to the event horizon? $\endgroup$ Jan 9, 2019 at 2:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.