Why didn’t the Universe collapse into a black hole in the past when there was so

much matter in such a small space?

(a) Most of the particles in the early Universe were unstable and decayed before a black
hole could form. By the time only stable particles were left (protons, electrons, etc.),
the Universe had expanded to be large enough so that it would not collapse into a black
hole.
(b) Quantum gravity—which is relevant at high energies and small distances—stabilized the
Universe and prevented a collapse into a black hole.
(c) Particles in the early Universe had a lot of kinetic energy (the temperature was very
high!), preventing them from becoming gravitationally bound and collapsing into a black
hole.
(d) It actually could have collapsed into a very giant black hole that we are now living inside
of.

c) universe is rapidly expanding with very high speed and temperature thus it didn't collapse into a black hole. The Schwarzschild solution of the gravitational equations is static and demonstrates the limits placed on a static spherical body before it must collapse to a black hole. The Schwarzschild limit does not apply to rapidly expanding matter.

Nice try to solve the final exam of course of profesor Murayama...

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The correct answer is (c) Particles in the early Universe had a lot of kinetic energy (the temperature was very high!), preventing them from becoming gravitationally bound and collapsing into a black hole.

To understand why the Universe didn't collapse into a black hole in the past, let's consider the conditions of the early Universe. In the early stages of the Universe, it was extremely hot and dense, with an enormous amount of matter packed into a very small space.

At these high temperatures, particles in the early Universe had a lot of kinetic energy. This kinetic energy prevents the particles from being gravitationally bound to each other. In other words, the fast-moving particles counteract the gravitational attraction and prevent the collapse into a black hole. Think of the kinetic energy as the "push" that counterbalances the "pull" of gravity.

As the Universe expanded and cooled down, the kinetic energy decreased, allowing for the formation of stable particles like protons and electrons. At this point, the Universe had expanded to a size where the gravitational attraction between particles was not strong enough to cause a collapse into a black hole.

So, the combination of high temperatures and an expanding Universe prevented the collapse into a black hole during the early stages. It's important to note that the formation of a black hole requires not only a large amount of matter, but also a critical density and size to overcome the kinetic energy and gravitational repulsion between particles.