1

I imagine a swinging pendulum being held outside a black hole supported by the normal foce of a jet propelled rocket. The rocket's velocity is approaching light speed, therefore hovering the swinging pendulum right above the event horizon in the strong gravitational potential outside of the black hole.

My first question is: what would the frequency be of this pendulum and would this be the natural limit to swinging frequencies? How could the frequency possibly increase more in potential in nature (besides by shortening length)?

And following the consequences of this: I believe photons and pendulums behave identically under the influence of a gravitational potential; does this then imply photons also have a natural cut-off limit for their frequency?

Apsteronaldo
  • 109
  • A pendulum is a massive system, a photon is merely an amount of field energy. They are not even in the same category. – FlatterMann Jun 04 '23 at 20:58
  • Does this answer your question? - Does a pendulum violate general relativity? – mmesser314 Jun 05 '23 at 01:21
  • my answer to this question may help you understand the complexity of the photon https://physics.stackexchange.com/questions/273032/what-exactly-is-a-photon/273180#273180 – anna v Jun 05 '23 at 03:53
  • @FlatterMann The pendulum will increase in frequency, and the photon will blueshift in equal manner under influence of the gravitational field (when it is identical to the gravitational potential), and both can be 'accelerated' limited to light speed. It takes mass infinite energy though indeed, for photons it doesn't. Their behavior seems identical though and we have no valid reason for UV-cutoff in QFT. I was wondering if they were related. – Apsteronaldo Jun 05 '23 at 14:17
  • @mmesser314 Thanks for the link, I had already looked at that one, and the question is related but not the same. It's not about time or time dilation, it's about blueshifting behavior in photons which seems identical to pendulum behavior under the same gravitational field – Apsteronaldo Jun 05 '23 at 14:20
  • You are simply laboring under the wrong assumption that things are obtaining infinite mass-energy. The mass-energy of the entire volume of space (black hole plus whatever is above it) is always the same. – FlatterMann Jun 05 '23 at 17:58
  • @Apsteronaldo Photons don’t blueshift in gravity. The apparent blueshift is an effect of looking at them from a different (time dilated) frame of reference. When you properly measure from the same frame before and after, the total energy of free falling objects (including photons) is conserved (does not change). In this way massless and massive particles do behave the same. The pendulum is just not a proper example to see this similarity. – safesphere Jun 06 '23 at 15:19

1 Answers1

1

A hovering observer will feel a local gravitational acceleration $$g_{\rm eff} = \frac{GM}{r^2}\left(1 - \frac{r_s}{r}\right)^{-1/2}\ ,$$ where $r_s$ is the Schwarzschild radius. This expression diverges to infinity as $r \rightarrow r_s$ (as does the force required to maintain your observer at fixed $r$) and so the period of the pendulum, which goes as $\sqrt{l/g_{\rm eff}}$ will become arbitrarily small.

However, a distant observer viewing the pendulum would disagree. There would be an additional time dilation factor of $(1- r_s/r)^{-1/2}$, which means that observer would see the pendulum period become arbitrarily longer as $r \rightarrow r_s$.

Objects with mass (a pendulum) do not behave in the same way as massless particles (photons) near a black hole.

ProfRob
  • 130,455