Is the Horizon r=2GM a Null Surface?

In summary, the horizon in General Relativity (GR) is a defining boundary that separates the observable region of spacetime from the unobservable region. It is a crucial characteristic of black holes, as it represents the point of no return where even light cannot escape. The horizon can change over time and differs for different observers, but its existence is consistent for all observers. Once an object crosses the horizon, it is no longer visible and experiences extreme gravitational forces.
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quasar987
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In my GR final, there was a question that asked to show that the horizon r=2GM is a null surface, i.e. [itex]d\tau^2=0[/itex]. How does that work, since just plugging r=2GM and dr=0 in the Schwarzschild metric yields

[tex]d\tau^2=-(2GM)^2d\Omega^2[/tex]

which is obviously not zero. :confused:
 
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A null surface has the property that its normal vector is null. What's a normal covector to the surface defined by r-2GM=0? Is it null?
 

FAQ: Is the Horizon r=2GM a Null Surface?

What is the horizon in GR?

The horizon in General Relativity (GR) is a boundary that separates the region of spacetime that can be observed from the region that cannot be observed. It is a null surface, meaning that light rays cannot escape from the region beyond the horizon.

How is the horizon related to black holes?

The horizon is a defining characteristic of black holes in GR. It is the point of no return, beyond which the gravitational pull is so strong that nothing, including light, can escape. The size and shape of the horizon determine the properties of the black hole, such as its mass and spin.

Can the horizon change over time?

Yes, the horizon can change over time. In GR, the horizon is not a fixed boundary but can expand or contract depending on the amount of matter and energy present. For example, the horizon of a black hole can grow larger as it consumes more matter.

What happens when an object crosses the horizon?

Once an object crosses the horizon, it is no longer visible from the outside. Time and space are also distorted near the horizon, so an object crossing it would experience extreme gravitational forces. Additionally, objects crossing the horizon can never escape, even if they are moving at the speed of light.

Is the horizon the same for all observers?

No, the horizon is not the same for all observers. In GR, the perception of space and time is relative, so different observers can have different horizons depending on their location and motion. However, the existence of a horizon is a fundamental property of black holes that is consistent for all observers.

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