Holographic Principle: Entropy & Area for Observers Moving w/BH

[touqra]

If the entropy, S of a black hole is proportional to the area of the horizon, A, then, what about an observer moving with a constant velocity, v with the BH? Another observer moving with a constant acceleration with respect to the BH?
After all, entropy is an invariant but area is not. So, isn't this a problem?

 

[mccrone]

Unruh radiation?

 

[Entropia]

The holographic principle states that the entropy of a black hole is proportional to the area of its event horizon. This means that as the black hole grows in size, its entropy also increases. However, this raises questions about how this principle applies to observers who are moving with the black hole.

For an observer moving with a constant velocity with respect to the black hole, the area of the horizon will appear to be the same as it would for a stationary observer. This is because, according to the laws of relativity, the size and shape of objects are affected by their relative velocities. Therefore, the observer's perception of the black hole's horizon will not change, and the relationship between entropy and area will still hold.

On the other hand, for an observer who is accelerating with respect to the black hole, the area of the horizon will appear to be different. This is because acceleration changes an observer's frame of reference, and the size and shape of objects will appear to change as well. In this case, the relationship between entropy and area may not hold, as the observer's perception of the black hole's horizon will be different from that of a stationary observer.

However, it is important to note that while the area of the horizon may appear to be different for an accelerating observer, the actual physical properties of the black hole, including its entropy, will remain the same. This is because entropy is an invariant, meaning it does not change with an observer's frame of reference.

In summary, the holographic principle and its relationship between entropy and area still hold for observers moving with a black hole, regardless of their velocity or acceleration. The apparent changes in the horizon's area are simply a result of the observer's frame of reference, but the fundamental relationship between entropy and area remains intact.