Particle falling radially into a black hole

In summary, the conversation discusses the need to finish a class for graduation and the desire for a safety net of a passing grade. The concept of the Schwarzschild metric in spherical coordinates is then introduced, which involves a particle's movement and proper time. The relevant equation is mentioned as a starting point for understanding the topic.
  • #1
Cythermax
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New poster has been reminded to show their work on schoolwork problems
Homework Statement
Attached it below
Relevant Equations
Not sure which equations necessary here.
I've been stuck starting anywhere with this. I need to finish this class for graduation and i'd like a safety net of a passing grade with this.
 

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  • #2
Well, do you know what the Schwarzschild metric is? In Schwarzschild (spherical) coordinates, if a particle starts at the point ##r, \theta, \phi## at time ##t## and travels a small distance to the point ##r+\delta r, \theta + \delta \theta, \phi + \delta \phi## by time ##t+\delta t##, then the the change in proper time ##\delta \tau## satisfies:

##(\delta \tau)^2 = (1 - 2GM/(c^2 r))^{-1} (\delta t)^2 - (1 - 2GM/(c^2 r)) (\delta r)^2 - r^2 \delta \theta^2 - r^2 sin^2(\theta) (\delta \phi)^2##

You have to start with that as a "relevant equation".
 
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Related to Particle falling radially into a black hole

1. What is a black hole?

A black hole is a region in space where the gravitational pull is so strong that nothing, including light, can escape from it. It is formed when a massive star collapses in on itself.

2. How does a particle fall into a black hole?

A particle falls into a black hole when it enters the region of space where the black hole's gravitational pull is stronger than any other force acting on the particle. This causes the particle to accelerate towards the black hole, eventually crossing the event horizon and entering the black hole.

3. What happens to a particle as it falls into a black hole?

As a particle falls into a black hole, it experiences extreme gravitational forces. The closer it gets to the black hole, the stronger the gravitational pull becomes. At the event horizon, the gravitational pull is so strong that the particle is stretched and squeezed, eventually becoming infinitely long and infinitely thin. This is known as "spaghettification". Once the particle crosses the event horizon, it is pulled towards the center of the black hole, known as the singularity, where it is crushed to an infinitely small point.

4. Can anything escape from a black hole?

No, once something crosses the event horizon and enters a black hole, it cannot escape. This is because the escape velocity (the speed needed to escape the gravitational pull) of a black hole is greater than the speed of light, making it impossible for anything to escape.

5. How does a particle falling into a black hole affect the black hole itself?

As a particle falls into a black hole, it adds mass to the black hole, making it more massive and increasing its gravitational pull. This can affect the behavior of objects around the black hole, such as other particles or even entire stars. The more mass a black hole has, the stronger its gravitational pull becomes.

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