# Black Holes

by Ron Kurtus (updated 18 January 2022)

A Black Hole is a star or sun that has so much gravity that nothing can escape it, not even light. Because of this, it appears like a black blob or hole in space.

The creation of a Black Hole comes about when a sun or star has lost much of its fuel and starts to cool down. It may then may collapse on itself to become a Black Hole. The size of a Black Hole can be calculated from the escape velocity equation.

Black Holes have some unusual properties and are useful in finding out more about the nature of space and the Universe.

Questions you may have include:

• How is a Black Hole created?
• How big is a Black Hole?
• What are some special properties of a Black Hole?

This lesson will answer those questions.

## Creation of a Black Hole

A black hole is created when a star spends most of its fuel and collapses upon itself.

The heat and energy created in a star or sun typically comes from thermonuclear reactions where hydrogen nuclei combine to form helium nuclei. The thermal energy of the heat spreads out the particles, giving the sun its size. This is the typical expansion of a hot gas.

When the hydrogen fuel runs out, the sun starts to cool off and the force of gravity pulls the particles together. This causes the physical size of the sun to decrease.

The force of gravity is a function of the mass and distance, so with the collapse of the sun, its gravity increases. At some point the gravity becomes so great that not even light can escape and the sun becomes a Black Hole.

## Size of a Black Hole

The predicted radius of a Black Hole can be calculated from the equation for the escape velocity and the mass of the star. This is also called the Schwarzschild radius. The sphere of the radius of a Black Hole is called the event horizon.

One theory is that the event horizon is simply a boundary, while the mass may be concentrated in a single point or singularity.

### Escape velocity for light

The escape velocity is the speed required for a particle or object to escape the force of gravity of a planet or sun. With a Black Hole, the escape velocity is greater than the speed of light, thus preventing light from leaving the star. The equation is:

c < √(2GM/R)

where

• c is the speed of light (about 300,000 kilometers/second)
• < is the "less than" symbol
• G is Newton's universal gravitational constant; G = 6.67*10−20 km³/kg-s²
• M is the mass of the planet or sun in kilograms
• R is the radius of the planet or sun in kilometers
• √(2GM/R) is the square root of the quantity 2GM/R

### Finding the radius for a given mass

This equation can be changed to:

c2 < 2GM/R

Solving for R:

R < 2MG/c2

Substituting values, you get:

R < M*2*6.67*10−20/9*1010

R < M*1.48*10−30 km

### Black Hole with mass of our Sun

The mass of our Sun is about M = 2*1030 kg. Thus, if the Sun would become a Black Hole, its radius would be:

R < 2*1030*1.5*10−30 km = 3 km

In other words, a star with the mass of our Sun with its matter compressed to a radius of less than 3 km, would be a Black Hole, because the escape velocity would be greater than the speed of light.

## Properties

A Black Hole has some interesting properties.

### Gains energy

Although it is a sun and very hot, none of its light escapes. That means a Black Hole does not lose mass or energy like our Sun does. In fact, it gains energy and mass by sucking in nearby matter.

### Difficult to see

Since no light leaves the Black Hole, it does not shine like other objects in space. This makes it very difficult to find in the black background of space. Astronomers think they have found Black Holes by noticing background stars temporarily disappearing at different viewing angles. Still, they are not 100% sure that what they saw was a Black Hole or some obstruction in space.

### Horizon

Since gravity decreases as the square of the distance from an object, there is a distance where the escape velocity of a Black Hole becomes less than the speed of light. This is called the Black Hole's event horizon. Outside the horizon, light is allowed to escape, but inside the event horizon, nothing can escape. Scientists have visualized what would happen at and near the event horizon.

## Summary

A Black Hole has so much gravity that even light cannot escape it. After it loses its fuel, a star may collapse on itself to become a Black Hole. You can calculate the radius or size of the event horizon of a Black Hole, knowing its mass. Black Holes have interesting properties. Astronomers only think they have seen Black Holes in observations through their telescopes.

## Resources and references

Ron Kurtus' Credentials

### Websites

Black Holes Frequently-Asked-Questions by Ted Bunn - thorough explanation of Black Holes from the University of California-Berkeley

Virtual Trips to Black Holes and Neutron Stars by Robert Nemiroff - explanations and MPEG movies showing how things look from NASA (most computers can show these short animations)

Black Holes and Beyond - a more complex explanation of Black Holes from the University of Illinois

Astronomy Resources

### Books

(Notice: The School for Champions may earn commissions from book purchases)

Exploring Black Holes: Introduction to General Relativity by Edwin F. Taylor, John Archibald Wheeler, Benjamin/Cummings Publishing (2000) \$37.33 - top ranked book on the subject

Black Holes and Time Warps: Einstein's Outrageous Legacy by Kip S. Thorne, Frederick Seitz and Stephen Hawking, W.W. Norton & Company (1995) \$18.95 - popular book, including views of Hawking

## Students and researchers

www.school-for-champions.com/astronomy/
black_holes.htm

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