Gravitational Radiation: Falling Objects into Black Holes

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SUMMARY

Gravitational radiation is emitted when an object falls into a black hole, as demonstrated by the linearized approximation and the superposition principle. In the case of two identical objects falling simultaneously from opposite sides, the radiation emitted does not cancel due to the additive nature of their quadrupole moments. This confirms that gravitational waves are produced in such scenarios, providing insights into the dynamics of black hole interactions.

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keithdow
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If an object falls into a black hole, gravitational radiation is emitted. Suppose two identical objects from opposite sides fall into a black hole simultaneously, how do I show that:

a. Radiation is emitted.
b. Radiation is not emitted.
 
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Look at the linearized approximation, use the superposition principle and see that the radiation emitted by the two particles does not cancel. (It clearly doesn't, since their quadrupole moments add rather than canceling)
 
Thanks!
 

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