Tag Archives: The Special Theory of Relativity

GREAT OLD, BIG, HUGE BLACK HOLES

In 1905 Albert Einstein employed one of the most powerful brains on planet Earth to puzzle out an elusive concept called “The Special Theory of Relativity”.  Ten years later he used those same brain cells to develop his even more powerful “General Theory of Relativity”.

Figure 1 highlights his most dramatic proposal for proving – or disproving! – his General Theory of Relativity.  The test he proposed had to take place during a total eclipse of the sun.  For, according to The General Theory of Relativity, light from a more distant star would be bent by about one two-thousandths of a degree when it swept by the edge of the sun.

Four years later (in 1919) the talented British astronomer Arthur Eddington in pursuit of a total eclipse of the sun, ventured to the Crimean Peninsula to perform the test Einstein had proposed based on the idea that “starlight would swerve measurably as it passed through the heavy gravity of the sun, a dimple in the fabric of the universe.”*

A black hole comes into existence when a star converts all of its hydrogen into helium and collapses into a much smaller ball that is so dense nothing can escape from its gravitational pull, not even light.

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Figure 1:  In 1915, when he finally worked out his General Theory of Relativity, Albert Einstein proposed three clever techniques for testing its validity.  Four years later, in 1919 the British astronomer, Arthur Eddington, took advantage of one of those tests during a total eclipse of the sun to demonstrate that, when a light beam passes near a massive celestial body, it is bent by the local gravitational field as predicted by Einstein’s theory.  This distinctive bending is similar to the manner a baseball headed toward home plate is bent downward by the gravitational pull of the earth.

The existence of black holes was inadvertently predicted by a mathematical relationship Sir Isaac Newton understood and employed in 1687 in developing many of his most powerful scientific predictions, including the rather weird concept of escape velocity.  As Figure 2 indicates, it is called the Vis Viva equation.

Start by solving the Vis Viva equation for the radius Re, then plug in the speed of light, C, as a value for the escape velocity, Ve.  The resulting radius Re is the so-called “event horizon”, which equals the radius at which light cannot escape from an extremely dense sphere of mass, M.  As the calculation on the right-hand side of Figure 2 indicates, if we could somehow compressed the earth down to a radius of 0.35 inches – while preserving its total mass light waves inside the sphere would be unable to escape and, therefore, could not be seen by an observer.  The radius of the event horizon associated with a spherical body of mass, M, is directly proportional to the total mass involved.

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Figure 2:  The Vis Viva equation was developed and applied repeatedly by Isaac Newton when he was evaluating various gravity-induced phenomena.  Properly applied, the Vis Viva equation predicts that sufficiently dense celestial bodies generate such strong gravitational fields that nothing – not even a beam of light – can escape their clutches.  Today’s astronomers are discovering numerous examples of this counterintuitive effect.  Black holes are one result.

As Figure 3 indicates, an enormous black hole 50 million light years from Earth has been discovered to have a mass equal to 2 billion times the mass of our sun.   It is located in the M87 Galaxy in the constellation Virgo.

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Figure 3:  In 1994 the Hubble Space Telescope discovered a huge black hole approximately 300,000,000,000,000,000,000,000 miles from planet Earth nestled among the stars of the M87 galaxy in the Virgo constellation.  Astronomers estimate that it is 2,000,000,ooo times heavier than our son.  That black hole’s event horizon has a radius of 3,700,000,000 miles or about 40 astronomical units. One astronomical unit being the distance from the earth to our sun.The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons.  Notice that both the horizontal and the vertical axes range over 20 orders of magnitude!  In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles.  The event horizon of a black hole is the maximum radius from which no light can escape.

The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons.  Notice that both the horizontal and the vertical axes range over 20 orders of magnitude!  In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles.  The event horizon of a black hole is the maximum radius from which no light can escape.

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