The New Geometry
Karl Schwarzchild was an astrophysicist who studied Einstein’s 1915 formulation of General Relativity.
He used Einstein’s equations to calculate the space-time curvature inside and outside stars and so developed a fascinating mathematics of space-time curvature we now call Schwarzchild Geometry.
Schwarzchild did not live long to see the world’s appreciation of his genius. In the summer of 1916, he became ill and died on the Russian Front.
Schwarzchild’s geometry is based on the idea that our three-dimensional universe is inside of a higher dimensional hyperspace with features that are alien from the standpoint of traditional Euclidian Geometry.
Try to imagine these:
1)Straight lines which start parallel will cross near the center of a star.
2)The circumference of any circle inside of a star is less than pi times the diameter.
3)On a star’s surface, the sums of the internal angles of triangles are not 180 degrees but greater.
Swarzchild’s geometry also claims that not just space will be warped within the vicinity of a star but time as well.
We now know that on the surface of the sun time is slowed by 64 seconds a year while in the center it is slowed by 5 minutes per year.
We can confirm this with the fact that atoms on a star’s surface emit light at lower frequencies than light from the same kinds of atoms in interstellar space.
Lower frequency means longer wavelength, which is a clue for dilated time.
In 1960 Jim Brault of Princeton University measured the sun’s time dilation, (2 parts per million at the surface), at found that it squared with Einstein’s prediction.
Schwarzchild’s geometry also treats on a subject that we need to learn to understand black holes – critical circumference. This involves the size of a star in relation to the strength of its gravity.
Put simply, the smaller the star, the stronger it can hold on to its light.
To understand critical circumference, we need to use the modern view of what light is. Christian Huygens said that light is made of waves. But its dual nature permits us to say it has particles called photons. As a star’s circumference decreases, its photons manifest themselves in the form of redder an redder light, until a star reaches its critical circumference.
What exactly is a critical circumference?
In the Newtonian mindset, we say it is the point where a star’s gravity is so strong that the light’s “corpuscles” will try to escape but fall back down to the surface of the star.
In the Schwarzchild view, we say loosely speaking, that the photons are infinitely red-shifted out of existence as all their energy is drained out of them.
As for the star, its core will collapse under such tremendous gravity, it becomes a small point called a singularity.
As much faith as Einstein had in his own theories, he was reluctant to accept every one of their implications.
Einstein felt it was just unrealistic that the core of any star could collapse so small that it could hold in light. He was confident that all the thermal pressure would present such an extreme collapse.
But a much different point of view would come from Lahore in what is now Pakistan.