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When is a Black Hole not a Black Hole?

The recent commotion of capturing, supposedly for the first time, an image of a black hole (through an algorithm!) is truly staggering. The image seen below is supposedly that of the "chaos swirling around the central point."

The first ever photo of a black hole. Image courtesy of Event Horizon Telescope collaboration et al.

The claim is that what we are witnessing is the event horizon, the point of no return, as light crosses over the threshold. The light that is observed is that of a hot gas as it gets heated up and crosses over the event horizon into the pitch black depths of the black hole.

The black hole is in a neighboring galaxy, M87, which is about 53 million light years away from us. Notwithstanding its small size, it supposedly has a mass of 6.5 BILLION suns! According to R K Biggs, in his article "How do you take a picture of a black hole? in, "Nothing is remotely relatable and one has to just appreciate the news abstractly, however fascinating."

Black holes have been reportedly to be ubiquitous, even at the center of our own galaxy, and, yet, without realizing it, the definition of a black hole has been changed! Rather than being an isolated species where no light--and no gravitational field--can escape their event horizons, the stellar mass black hole candidates are really neutron stars located in massive accretion discs which form the central engines of AGNs (Active Galactic Nuclei). Sometimes seen as bars which emit radiation of a non-thermal spectrum.

A bar in the Milky Way

Let us recall that Hawking's association of a temperature of a black hole and its surface gravity stemmed from his analogy with field theory consisting of harmonic oscillators. The spectrum that Hawking claimed that a black hole emitted was purely black body radiation which is thermal radiation. It has nothing whatsoever to do with the radiation of the central engine of an AGN.

Moreover, if light can't escape the tentacles of a black hole, how can its gravitational field be felt beyond the event horizon? The only solution we have of a (non-rotating, neutral) black hole is Schwarzschild's solution of the "vacuum" Einstein equations. By "vacuum" we mean that the solution was obtained from empty space where the gravitational field alone can subsist since it is engraved in the Einstein tensor and not in the energy-stress tensor to which it is equated. As light, or any "test" particle, approaches the event horizon it does so with ZERO velocity and ZERO acceleration.

By test particle we mean an imaginary mass which is used to probe the gravitational field since Einstein's equations can't solve the two body problem. The other body--the central mass--snuck in as an arbitrary constant of integration when the Ricci components are set equal to zero and subsequently integrated. The "central" mass is not part of the problem, but appears as a boundary condition that at infinity, one should regain Newtonian theory. Without a mass, there would be no gravitational attraction in contrast to what general relativity claims that gravity is embedded in the geometry.

Einstein, and his young collaborator Rosen, were particularly upset with singularities, and in his book, "Out of My Later Years", explains how they built "bridges over the singularity." That wasn't at all necessary since Schwarzschild's solution cannot be prolonged beyond the event horizon. Schwarzschild knew this, but subsequent writers found it convenient to forget it, inventing coordinate transforms so that the only non-removable singularity would be at the origin. They should have consulted books on non-Euclidean geometries before tempting such a ridiculous exercise. No, it is not true that time and space swap roles inside the event horizon. Yes, this is material for science fiction movies, but not for physics and mathematics.

If, indeed, Karl Schwarzschild is the father of the black hole, why would he have wasted his time developing an inner solution to his equations? The so-called "exterior" solution to the event horizon is generally what is recognized as the Schwarzschild solution, and his "inner" solution has conveniently been swept under the carpet. The inner solution cannot be extended beyond the event horizon just as the exterior solution cannot be extended within the event horizon. In fact, the inner solution is a hyperbolic metric of constant curvature, analogous to the Poincare' disc metric. As the inhabitants of his disc approach the rim of the disc (the event horizon) they shrink in size along with their measuring sticks and clocks so that it would take an infinite amount of time to reach the periphery. Beyond that there is nothing! The disc defines the hyperbolic plane. So Schwarzschild's inner and outer solutions are complementary---never to meet. The inner solution has a constant mass density, and, surprisingly, NO black hole.

Seemingly "heretical" explanations that have confused central engines of AGN and "orthodox" formulation of black hole "physics" can be found in the books by Wolfgang Kundt, "Astrophysics--A Primer", and my book, "Seeing Gravity."

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