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**Physics, Astronomy & Cosmology / Is there an error in this relativistic thought experiment?**

« **on:**14/11/2018 19:12:06 »

Suppose you have a Schwarzschild black hole with an event horizon.

I presume that a light beam shone upward from an event horizon would be infinitely redshifted before it travels any distance above the event horizon. The redshift from an event horizon up to any point in space is infinite. This is because the gravitational potential energy difference between an event horizon and any point above the event horizon is infinite.

Conservation of energy requires that gravitational redshift is reversible. Infinite redshift up mean infinite blueshift down. The blueshift a light beam will undergo when traveling from any point in space to an event horizon is infinite.

Thought experiment: Place a laser at some point outside of the event horizon, stationary with respect to the black hole. Point the laser radially downward toward the center of gravity of the black hole. Turn on the laser.

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted. The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.

This is true no matter where in space the laser is located. Before light can travel from any point in space to an event horizon, infinite time must pass at that point in space. This is also true for every point in space that the light beam travels through on the way to the event horizon. Each of those points can be considered as a light source and infinite time must pass in those points before the light can travel to the event horizon.

If light cannot travel a path in finite time, nothing can. Not matter or energy or information.

It seems to me that this sort of reasoning could be why Einstein insisted black hole event horizons are impossible.

I presume that a light beam shone upward from an event horizon would be infinitely redshifted before it travels any distance above the event horizon. The redshift from an event horizon up to any point in space is infinite. This is because the gravitational potential energy difference between an event horizon and any point above the event horizon is infinite.

Conservation of energy requires that gravitational redshift is reversible. Infinite redshift up mean infinite blueshift down. The blueshift a light beam will undergo when traveling from any point in space to an event horizon is infinite.

Thought experiment: Place a laser at some point outside of the event horizon, stationary with respect to the black hole. Point the laser radially downward toward the center of gravity of the black hole. Turn on the laser.

By the time the front of the laser beam intersects the event horizon, the beam is infinitely blueshifted. The light beam will contain infinitely many wave cycles. This means that, before the front of the beam reaches the event horizon, the laser must generate a sequence of infinitely many wave cycles. Before the front of the light beam can reach the event horizon, infinite time must pass at the laser.

This is true no matter where in space the laser is located. Before light can travel from any point in space to an event horizon, infinite time must pass at that point in space. This is also true for every point in space that the light beam travels through on the way to the event horizon. Each of those points can be considered as a light source and infinite time must pass in those points before the light can travel to the event horizon.

If light cannot travel a path in finite time, nothing can. Not matter or energy or information.

It seems to me that this sort of reasoning could be why Einstein insisted black hole event horizons are impossible.