1) First we shall define(adsbygoogle = window.adsbygoogle || []).push({}); to exist, relative to an observer, to mean that "the object in question lies in the observer's past light cone"

2) We define ablack holeto be an "area of sufficiently compressed mass such that an event horizon of non-zero radius exists"

3) Next we make the presumption that black holes exist today (for observers on Earth)

4) We recognize that all existing mass approaching this black hole currently will cross the event horizon at [tex]t_{crossing} = +\infty[/tex]

5) We claim that the black hole was created at [tex]t_{creation}[/tex] where [tex]-\infty < t_{creation} < t_{now}[/tex] (i.e. some point in the finite past)

6) We recognize that an event horizon of non-zero radius requires mass to exist within it, by definition

Therefore, in order for #3 to hold, at some point in time called [tex]t_{dubious}[/tex] where [tex]t_{creation} <= t_{dubious} < t_{now}[/tex], the Earth observers must be able to claim that mass crossed the event horizon of the black hole in question (in order to satisfy #6 and #1). However, for those same observers at and prior to [tex]t_{creation}[/tex], [tex]t_{dubious}[/tex] now resides in their future light cone, and will eventually reside in their past light cone, which contradicts #4. A contradiction indicates that one of our presumptions is incorrect.

The conclusion is that either all black holes are eternal (which is the only way [tex]t_{creation}[/tex] can reside in Earth observers' past light cones), or theycannot be said to existfor Earth observers.

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# Are ALL black holes eternal?

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