Inside a Schwarzschild black hole

Hello and welcome

 schwarzschild.png

Ever wondered what lies beyond the event horizon of a black hole? Current thinking asserts any one of numerous different outcomes, once you cross the horizon; 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 just what to believe. We offer a somewhat unremarkable answer; not nearly so exciting, but needing no undiscovered extensions to existing theory or StatTrekian beliefs, and as such, so much 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, ultimately testable and demonstrated by the otherwise unexplained existence of supermassive black holes, and the substantial gap in the distribution of intermediate masses. This will never be entirely understood without an occasional smidgen of mathematics, but, if you have a basic college-level understanding, then there should be nothing overly daunting for you to follow. So take the plunge. 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 can 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: 
    \[ c^2d\tau ^2=\left(1-\frac {r_s}{r}\right)c^2dt^2 -\left(1-\frac {r_s}{r}\right)^{-1}dr^2-r^2\left(d\theta ^2+\sin ^2\theta \,d\varphi ^2\right) ,\] where \[r_s =\frac{2GM}{c^2}\].
    If this is all a bit daunting, the last two terms are just the same for Newton's law of universal gravitation. It is the first term that changes things. In particular, where \(r\) and \(r_s\) are reduced radii, \(G\) is the gravitational constant, (the same constant used in the gravity equation of Newton) and \(c\) is the speed of light.
    The key fact to notice about this equation is the second term which seems to 'blow up' when \(r=r_s\). This term is what gives rise to the event horizon at \(r_s\), the Schwarzschild radius.
  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 unchanging.

An immediate consequence of Birkhoff’s theorem is that the field inside a symmetric non-rotating spherical 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 for a very simple thought experiment

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 an active life.) For simplicity, let the ball be spherically symmetric and nonrotating. The collapsing ball of matter will, if massive enough, form a black hole with an event horizon having a reduced radius, \(r_s\), given by this simple equation \(r_s=\frac{2Gm}{c^2}\) given above.

In the following argument, all radii will be reduced radii.

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

The new stuff: here it gets interesting->

 

Agree or disagree, or have any questions or observations about this, and I would love to hear from you, so please This email address is being protected from spambots. You need JavaScript enabled to view it., or leave a comment. Your views, whatever they are, are always most welcome.

 

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