Why you don't divide by 0.
Here’s an excellent article from The Electric Universe:
The Black Hole at the Heart of Astronomy
The thoughtless followers of Einstein have fashioned God in their own image as a mathematician but “He” is much smarter and avoids high school howlers like the gravitational “black hole.” Yes, a theoretical “black hole” exists—and it sucks the very heart out of astronomy and astrophysics. The astronomer Halton Arp articulated the math howler of dividing by zero to give a near infinite concentration of mass in a hypothetical black hole:“Since the force of gravity varies as the square of the inverse distance between objects why not make the ultimate extrapolation and let the distance go to zero? You get a LOT of density. Maybe it goes BOOM! But wait a minute, maybe it goes in the opposite direction and goes MOOB! Whatever. Most astronomers decided anyway that this was the only source that could explain the observed jets and explosions in galaxies.”
Precisely! And when the gravitational force is as close to zero as doesn’t matter, in comparison to the electric force, you must be very careful (as any high school student knows) to not divide by zero, otherwise you introduce infinities. What does it mean for the radius of a physical object to tend to zero?
In the face of discordant data, a scientist is required to check the original works and assumptions that lead to the theory under test. But there are very few such scientists in this modern age. As Sir Fred Hoyle put it, today the pressure is on to “do what aging gurus tell them to do, which is nothing”and simply build on the consensus those gurus have established. A fellow Australian, Stephen Crothers, has shown mathematical theorists to be remarkably unintelligent and sloppy in the application of their talent to physical problems. It seems that most of them don’t really follow the mathematical arguments anyway (which is not surprising) but are happy to extol the results of others, based on reputation, regardless of the principles of physics or commonsense. Crothers has done his historical and mathematical homework and delivered a paper, The Schwarzschild solution and its implications for gravitational waves, at the Conference of the German Physical Society, Munich, March 9-13, 2009. He concludes, inter alia, that:
• “Schwarzschild’s solution” is not Schwarzschild’s solution. Schwarzschild’s actual solution does not predict black holes. The quantity ‘r’ appearing in the so-called “Schwarzschild solution” is not a distance of any kind. This simple fact completely subverts all claims for black holes.
• Despite claims for discovery of black holes, nobody has ever found a black hole; no infinitely dense point-mass singularity and no event horizon have ever been found. There is no physical evidence for the existence of infinitely dense point-masses.
• It takes an infinite amount of observer time to verify the presence of an event horizon, but nobody has been and nobody will be around for an infinite amount of time. No observer, no observing instruments, no photons, no matter can be present in a spacetime that by construction contains no matter.
• The black hole is fictitious and so there are no black hole generated gravitational waves. The international search for black holes and their gravitational waves is ill-fated.
• The Michell-Laplace dark body is not a black hole. Newton’s theory of gravitation does not predict black holes. General Relativity does not predict black holes. Black holes were spawned by (incorrect) theory, not by observation. The search for black holes is destined to find none.
• No celestial body has ever been observed to undergo irresistible gravitational collapse. There is no laboratory evidence for irresistible gravitational collapse. Infinitely dense point-mass singularities howsoever formed cannot be reconciled with Special Relativity, i.e. they violate Special Relativity, and therefore violate General Relativity.
• General Relativity cannot account for the simple experimental fact that two fixed bodies will approach one another upon release. There are no known solutions to Einstein’s field equations for two or more masses and there is no existence theorem by which it can even be asserted that his field equations contain latent solutions for such configurations of matter. All claims for black hole interactions are invalid.
• Einstein’s gravitational waves are fictitious; Einstein’s gravitational energy cannot be localised; so the international search for Einstein’s gravitational waves is destined to detect nothing. No gravitational waves have been detected.
• Einstein’s field equations violate the experimentally well-established usual conservation of energy and momentum, and therefore violate the experimental evidence.
In an audience of theoretical physicists there was stunned silence—and not a single question.
A final official word on black holes from the Astronomer Royal who follows an unenviable tradition of holders of that office being completely wrong and retarding progress:
“Black holes, the most remarkable consequences of Einstein’s theory, are not just theoretical constructs. There are huge numbers of them in our Galaxy and in every other galaxy, each being the remnant of a star and weighing several times as much as the Sun. There are much larger ones, too, in the centers of galaxies. Near our own galactic center, stars are orbiting ten times faster than their normal speeds within a galaxy.” —Martin Rees, Our Cosmic Habitat(2001).