Spacetime Diagram of a Black Hole
This spacetime diagram has been developed to describe the collapse of a spherical star to form a spherical black hole. The trajectories of outgoing light rays are plotted as; P-P', Q-Q', R-R', S-S'.
Events P and S send photons along paths P-P' and S-S'. Events Q and R cannot signals out to the distant universe, they are trapped within the event horizon of the black hole heading towards the singularity. The apparent horizon is created at the stars centre e, it then expands to emerge through the star's surface.
Definition of Terms
Event Horizon :
Black Holes have a boundary the point at which light just fails to escape, this is called the Event Horizon or Schwarzschild
radius
Singularity :
Shortened definition,
a singularity is timelike but cannot be embedded in a larger spacetime.
The a more technical definition would be:
"A spacetime is singular if it is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime."
Singularity in relation to a black hole can be seen as a consquence of the gravity inside a black hole producing an "apparent
horizon" pulling outgoing light rays back in, the gravity becoming so strong a null point in time is created.
Vacuum fluctuations : are random and unpredictable oscillations in small regions of space. Where vacuum fluctions give rise to
an instantainously high value, energy being momentarily stolen from adjacent space and then returned, virtual particles and
virtual antiparticles, are formed. As energy cannot be created out of nothing one is positive and one is negative. Normally as
the field fluctuates the positive and negative particles seek out and annihilate each other. Electromagnetic vacuum fluctions give
rise to virtual photons and gravitional vacuum fluctuations give rise to virtual gravitons.
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