Computing trajectories in Schwarzschild spacetime

Thread starter bcrowell
Start date Apr 13, 2015
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Computing Schwarzschild Spacetime Trajectories

In summary: Sorry, typo. The last line is$$\frac{d\phi}{d \lambda} = \frac{p}{r^2}$$The procedure in post #16 works for the timelike case; I have used it.Can you explain how that works? I didn't see a clear explanation in post #16. Also, can you explain what you mean by "the turning points are handled"?

Apr 20, 2015

m4r35n357

I was away yesterday, but glad to see you have all got it working. BTW I consider the program finished in terms of what I set out to do, so feel free to fork/fix/improve as you wish, it's GPL after all ;).

<h2>1. What is Schwarzschild spacetime?</h2><p>Schwarzschild spacetime is a mathematical model that describes the curvature of space and time around a non-rotating, uncharged black hole. It was first proposed by German physicist Karl Schwarzschild in 1916.</p><h2>2. How does computing trajectories in Schwarzschild spacetime differ from computing trajectories in flat spacetime?</h2><p>In Schwarzschild spacetime, the presence of a massive object causes the fabric of space and time to curve, leading to the bending of light and the motion of objects. This curvature must be taken into account when computing trajectories, whereas in flat spacetime, objects move in straight lines according to Newton's laws of motion.</p><h2>3. What is the significance of computing trajectories in Schwarzschild spacetime?</h2><p>Computing trajectories in Schwarzschild spacetime allows us to understand the behavior of objects in the vicinity of a black hole, including the effects of gravitational lensing and the possibility of objects falling into the black hole's event horizon.</p><h2>4. What are some challenges in computing trajectories in Schwarzschild spacetime?</h2><p>One major challenge is that the equations for computing trajectories in Schwarzschild spacetime are highly complex and require advanced mathematical techniques. Additionally, the presence of a singularity at the center of the black hole makes it difficult to accurately predict the behavior of objects near it.</p><h2>5. How do scientists use computing trajectories in Schwarzschild spacetime in their research?</h2><p>Scientists use computing trajectories in Schwarzschild spacetime to study the behavior of matter and energy in extreme gravitational fields, such as those found near black holes. This research can help us better understand the nature of gravity and the universe as a whole.</p>

1. What is Schwarzschild spacetime?

Schwarzschild spacetime is a mathematical model that describes the curvature of space and time around a non-rotating, uncharged black hole. It was first proposed by German physicist Karl Schwarzschild in 1916.

2. How does computing trajectories in Schwarzschild spacetime differ from computing trajectories in flat spacetime?

In Schwarzschild spacetime, the presence of a massive object causes the fabric of space and time to curve, leading to the bending of light and the motion of objects. This curvature must be taken into account when computing trajectories, whereas in flat spacetime, objects move in straight lines according to Newton's laws of motion.

3. What is the significance of computing trajectories in Schwarzschild spacetime?

Computing trajectories in Schwarzschild spacetime allows us to understand the behavior of objects in the vicinity of a black hole, including the effects of gravitational lensing and the possibility of objects falling into the black hole's event horizon.

4. What are some challenges in computing trajectories in Schwarzschild spacetime?

One major challenge is that the equations for computing trajectories in Schwarzschild spacetime are highly complex and require advanced mathematical techniques. Additionally, the presence of a singularity at the center of the black hole makes it difficult to accurately predict the behavior of objects near it.

5. How do scientists use computing trajectories in Schwarzschild spacetime in their research?

Scientists use computing trajectories in Schwarzschild spacetime to study the behavior of matter and energy in extreme gravitational fields, such as those found near black holes. This research can help us better understand the nature of gravity and the universe as a whole.