The Shapiro delay and falling into a black hole

In summary: So, if an object is in a gravitational field, its speed is decreased. However, an observer outside the gravitational field would still see the object as travelling at the same speed.In summary, the speed of an object is related to the strength of the gravitational field. Objects will be slowed down in a gravitational field, but a distant observer will still see them travelling at the same speed.
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Any particle or system with non-zero rest mass follows a time-like path through space-time. If you imagine the system being a stop-watch, the difference between the readings on the stop watch as it follows the time-like path would be the proper time associated with that section of the path. So we can think of proper time as what would be measured by a very small stop-watch, ideally a point-like stopwatch.

This observer-independent quantity, the change in reading on the stop-watch, can be computed by some formulae from observations made in a different frame in which the stop-watch may be (and usually is) moving. So we'd assign coordinates (usually t,x,y,z) to every point along the clock's path through space-time, and we can relate the changes in the clock reading to the changes in the coordinates via some mathematical formula (I'll avoid the details for now) involving the changes in coordinates.

Wiki has a writeup of proper time and the necessary formulas, <<link>> but I doubt it's the best place to start learning about the concept.

If you grasp the principle of computing the proper time in SR, you can read about the relatively minor modifications (involving the metric coefficients) that are needed to compute proper time in GR. If you take these formula as a given, using the Schwarzschild metric coefficients, you can compute the proper time interval that experienced by a stop-watch falling into a black hole - unfortunately, you need also to either know or be able to figure out which path a free-falling clock takes. You can find some paths that are not free-fall that do take an infinite time, so it's not a trivial question.

Most GR textbooks will do some version of this problem, though, and you can fact-check the result that the time on the clock is finite.
 
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<h2> What is the Shapiro delay and how does it relate to black holes?</h2><p>The Shapiro delay is a phenomenon in which the time taken for light to travel through a gravitational field is longer than expected due to the curvature of space-time. This effect was predicted by physicist Irwin Shapiro and has been observed in the vicinity of massive objects such as black holes.</p><h2> How does the Shapiro delay affect objects falling into a black hole?</h2><p>The Shapiro delay causes the light emitted from an object falling into a black hole to appear to slow down and stretch out, making it appear redder. This is due to the strong gravitational pull of the black hole, which causes the light to travel through a curved path, resulting in a longer travel time.</p><h2> Can the Shapiro delay be used to study black holes?</h2><p>Yes, the Shapiro delay can be used as a tool to study the properties of black holes. By measuring the delay in light from objects orbiting a black hole, scientists can determine the mass and size of the black hole, as well as the strength of its gravitational field.</p><h2> Is the Shapiro delay the same for all black holes?</h2><p>No, the Shapiro delay can vary depending on the size and mass of the black hole, as well as the distance of the object from the black hole. The closer an object is to the black hole, the stronger the gravitational pull and the longer the Shapiro delay will be.</p><h2> How does the Shapiro delay impact our understanding of space and time?</h2><p>The Shapiro delay is one of the many effects of Einstein's theory of general relativity, which describes the relationship between space, time, and gravity. This phenomenon helps us better understand the curvature of space-time and how it is affected by massive objects like black holes.</p>

FAQ: The Shapiro delay and falling into a black hole

What is the Shapiro delay and how does it relate to black holes?

The Shapiro delay is a phenomenon in which the time taken for light to travel through a gravitational field is longer than expected due to the curvature of space-time. This effect was predicted by physicist Irwin Shapiro and has been observed in the vicinity of massive objects such as black holes.

How does the Shapiro delay affect objects falling into a black hole?

The Shapiro delay causes the light emitted from an object falling into a black hole to appear to slow down and stretch out, making it appear redder. This is due to the strong gravitational pull of the black hole, which causes the light to travel through a curved path, resulting in a longer travel time.

Can the Shapiro delay be used to study black holes?

Yes, the Shapiro delay can be used as a tool to study the properties of black holes. By measuring the delay in light from objects orbiting a black hole, scientists can determine the mass and size of the black hole, as well as the strength of its gravitational field.

Is the Shapiro delay the same for all black holes?

No, the Shapiro delay can vary depending on the size and mass of the black hole, as well as the distance of the object from the black hole. The closer an object is to the black hole, the stronger the gravitational pull and the longer the Shapiro delay will be.

How does the Shapiro delay impact our understanding of space and time?

The Shapiro delay is one of the many effects of Einstein's theory of general relativity, which describes the relationship between space, time, and gravity. This phenomenon helps us better understand the curvature of space-time and how it is affected by massive objects like black holes.

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