Event horizon

From Academic Kids

For the science fiction film, see Event Horizon

An event horizon is a boundary in spacetime for a given observer beyond which no electromagnetic energy, including light, can reach the observer.

Light emitted from inside the event horizon will never reach a stationary observer outside the horizon, hence the name black hole. Note the dependency on the observer of the concept of event horizon. For example, a free falling observer toward a black hole does not experience an event horizon (see e.g. catastrophic gravitational collapse).

The event horizon for an outside observer really acts as a horizon. He sees an object falling toward the horizon approaching it, but (in his own proper time) never reaching it. In his observations the object goes slower and slower toward the horizon and at the same time the redshift increases beyond bounds to infinity. Also the intensity of the falling object quickly becomes zero. In a finite time the outside observer will receive the last photon from the falling object. He will never see the falling object passing through the event horizon.

The event horizon is distinct from the particle horizon.

Contents

Sticking your hand through an event horizon

One can ask what happens, when a stationary observer is in orbit just outside the event horizon and (against all advice) sticks his hand through the horizon? The answer is: he won't succeed in doing so. Free orbits are only possible at a certain distance (for a non-rotating black hole, this figure is at least three times the Schwarzschild radius). Near the event horizon, an observer can only remain at a constant radius when he uses a force (e.g. from a rocket) to keep him there. The force needed grows to infinity when the observer wants to maintain a steady constant orbit approaching the event horizon. When he sticks out his hand, the tidal force (the difference in gravity between body and hand along his arm) also becomes infinitely high, so his hand will be chopped off before he manages to do so.

The physical consequences of the previous paragraph are drawn by Stephen Hawking. Everywhere in the vacuum of space virtual particle pairs are created and annihilate quickly. Near an event horizon, they can be separated. Effectively, a particle or photon will be emitted from the horizon, the so-called Hawking radiation.

Recently, however, Stephen Hawking has reversed his position regarding black holes, having claimed that an event horizon never actually forms around a black hole.

The Euclidean path integral over all topologically trivial metrics can be done by time slicing and so is unitary when analytically continued to the Lorentzian. On the other hand, the path integral over all topologically non-trivial metrics is asymptotically independent of the initial state. Thus the total path integral is unitary and information is not lost in the formation and evaporation of black holes. The way the information gets out seems to be that a true event horizon never forms, just an apparent horizon.

--GR Conference website (http://www.dcu.ie/~nolanb/gr17.htm) summary of Hawking's talk.

Event horizon in the absence of gravity

Event horizons also exist in the absence of gravity. A simple example is a uniform accelerated particle (whose speed will thus eventually approach the speed of light but will always be smaller). Light emitted at a certain distance in the direction of that particle will never reach the accelerated particle. It is beyond the event horizon for that particle. Such event horizons occur in particle accelerators.

Event horizon in the absence of gravity. World line of an accelerated observer (solid curved line) in a two dimensional spacetime representation (time vertical, space horizontal) will not observe anything to the left of his event horizon (marked as future horizon).
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Event horizon in the absence of gravity. World line of an accelerated observer (solid curved line) in a two dimensional spacetime representation (time vertical, space horizontal) will not observe anything to the left of his event horizon (marked as future horizon).

A part of spacetime forms an event horizon as observed from a constantly accelerated observer. The world line of the observer is given as the solid curve in a two dimensional spacetime representation with time x0 in the vertical direction and a one dimensional space coordinate x3 to the right. An angle of 45 indicates the speed of light, such as the world line of a photon traveling to the right and starting in a. The world line of the observer is described by a hyperbola. The parameter along his path is τ, his proper time. In 0 his speed is zero and eventually he will reach a speed close to the velocity of light, inclined at an angle of 45 degrees. This asymptotic line is his future event horizon. A photon emitted at any event to the left of it (such as the emission of a photon from event a) will never reach him (as long as the observer maintains a constant acceleration).

If someone at constant zero velocity (a static observer with a vertical line as worldline) would emit photons to the right, then the accelerated observer would see all photons below the event horizon, but in his proper time it would take longer and longer when these photons are emitted closer to the horizon. Also they are more and more redshifted. The accelerated observer would never see the static observer pass the event horizon.

Other examples of an event horizon

Hypothetically, an event horizon can also exist in a universe, for an observer at a given location in space-time, who remains at the same comoving spatial position. When a universe expands quickly enough, for example a de Sitter universe, it can be possible for an event horizon to exist.

See also

External link

cs:Horizont udlost es:Horizonte de sucesos it:Orizzonte degli eventi nl:Waarnemingshorizon ja:事象の地平面 pl:Horyzont zdarzeń sl:dogodkovno obzorje fi:Tapahtumahorisontti

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