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Chapter 22: Problem 25

According to the general theory of relativity, why can't some sort of yet- undiscovered degenerate pressure prevent the matter inside a black hole from collapsing all the way down to a singularity?

Short Answer

Expert verified
According to the General Theory of Relativity, no yet-undiscovered form of 'degenerate pressure' could prevent the matter inside a black hole from collapsing into a singularity. This is because in a black hole, gravitational forces are so extreme that all forms of energy, including those related to pressure, contribute to the gravitational field and thus encourage collapse rather than preventing it. Any repulsive force that could potentially arise at quantum scales ultimately contributes to the gravitational collapse in the framework of general relativity.

Step by step solution

01

Understand the Black Hole Singularity

A singularity, in the context of black holes, refers to a point where gravitational forces are so intense that spacetime curves infinitely and the laws of physics as we know them cease to operate. This is generally accepted as the final point of matter collapsed inside a black hole, forming an infinitely dense point.
02

Understand Degenerate Pressure

\('Degenerate pressure' is a term used in quantum physics to describe a pressure exerted by matter when it is tightly compressed. For example, electron degeneracy pressure prevents white dwarfs from collapsing, and neutron degeneracy pressure keeps neutron stars stable. However, these pressures have limits and when those limits are surpassed (for instance, Chandrasekhar limit for white dwarfs), the object collapses into a denser state.
03

Argument against Degenerate Pressure Preventing Singularity

It's important to note, however, that those kinds of pressures act against gravity, and in a black hole, gravitational force is so strong that no known pressure could possibly withstand it. Quantum physics allows for repulsive forces at extremely small scales (Planck length), but in general relativity, all forms of energy, including those related to pressure, contribute to the gravitational field. Thus, even the highest possible degenerate pressure would ultimately contribute to the gravitational collapse rather than prevent it.

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Most popular questions from this chapter

What is the mass in kilograms of a black hole whose Schwarzschild radius is \(11 \mathrm{~km}\) ?

Is it possible to tell which chemical elements went into a black hole? Why or why not?

Speculate on the effects you might encounter on a trip to the center of a black hole (assuming that you could survive the journey).

What is the Schwarzschild radius of a black hole whose mass is that of (a) the Earth, (b) the Sun, (c) the supermassive black hole in NGC 4261 (Section 22-5)? In each case, also calculate what the density would be if the matter were spread uniformly throughout the volume of the event horizon.

Search the World Wide Web for information about a stellarmass black hole candidate named V4641 Sgr. In what ways does it resemble other black hole candidates such as Cygnus X-1 and V404 Cygni? In what ways is it different and more dramatic? How do astronomers explain why V4641 Sgr is different?
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