Inside a Schwarzschild black hole

Hello and welcome

 

 Ever wondered what lies beyond the horizon of a black hole? Current thinking asserts any one of numerous outcomes; time travel, wormholes, being crushed to a point, or instead, perhaps a fiery end in a wall of flame, making it very hard to know what to believe. We offer a somewhat more prosaic answer; not nearly so exciting, but needing no extensions to existing theory, and as such, so more believable.

This is a new vision of what lies beyond the event horizon of a black hole. New, and as we will show later, testable and demonstrated by the otherwise unexplained presence of supermassive black holes. This will never be entirely understood without a smidgen of mathematics, but, if you have a basic college-level understanding, there should be nothing overly hard for you to follow. So let us just jump right in. 

Introduction

To begin with, here are a couple of basic facts about Einstein's theory of general relativity for any visitors who are new to this field. There is no dispute about these facts so I hope you will just accept them for now:

150px-Schwarzschild.jpg

Karl Schwarzschild (1873–1916)  

  1. The gravitational field around a non-rotating symmetrical body (such as a star, or a planet) is given by the Schwarzschild solution, originally developed by Karl Schwarzschild in 1916, just a year after Einstein announced his general theory of relativity: 
    \[ c^2d\tau ^2=\left(1-\frac {r_s}{r}\right)c^2dt^2 -\left(1-\frac {r_s}{r}\right)^{-1}dr^2-r^2\left(d\theta ^2+\sin ^2\theta \,d\varphi ^2\right) \]The key fact to notice about this equation is the first term which seems to 'blow up' when \(r=r_s\). This term is what gives rise to the event horizon.
  2. Birkhoff's theorem added that for any non-rotating spherically symmetric body, the exterior gravitational field in space must be static, with a metric given by a piece of the Schwarzschild metric. This sounds difficult but all this is saying is that there is only one solution, the Schwarzschild solution and that it is static - or unchanging.

An immediate consequence of Birkhoff’s theorem is that the field inside a symmetric non-rotating spherically shell of matter must be flat, or Minkowski space (the only piece of the Schwarzschild metric possible in this circumstance as there is no enclosed mass).

Knowing just these two undisputed facts, we could, for instance, calculate the precise field at the bottom of a mine shaft -- just calculate the field due to the mass beneath our feet whilst ignoring all of the mass above our heads, and neglecting the effect of the relatively slow rotation of the earth. This much is standard stuff and fully confirmed by experiments, here on earth. 

Now, keeping these same two undisputed facts in mind, consider a large ball of matter, collapsing due to the force of gravity, where the forces involved have already exceeded those needed to halt the collapse at the size of a neutron star. (Such as during the final stage of collapse after a sufficiently large star goes supernova at the end of it's active life.) For simplicity, let the ball be spherically symmetric and nonrotating. The collapsing ball of matter, if of sufficient mass, will eventually form a black hole with an event horizon having a reduced radius, \(r_{e}\), given by this simple equation

\[r_{e}=\frac{2Gm}{c^2}\]

where the \(r_e\) is the reduced radius of the event horizon, \(G\) is the gravitational constant, the same constant used in the gravity equation of Newton, \(m\) is the total mass enclosed by the event horizon, and \(c\) is the speed of light. In the following argument, all radii will be reduced radii.

Inside this event horizon the ball of particles will continue to collapse, heading relentlessly towards the origin. So far, we have not deviated in any way from established theories. 

The new stuff: here it gets interesting->

 

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