- #1
rjbeery
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Discussions involving Hawking radiation in the study of black holes usually require their preexistence; however, if we apply the Hawking radiation process to the initial stages of a birthing black hole I'm confused about how the theory claims the event horizon would form in the first place.
In a simple non-rotating non-charged neutron star of, say, 4M the neutron degeneracy pressure would not be exceeded throughout the structure simultaneously; rather, it would occur at the center of the sphere where pressure is greatest. More specifically, it would occur between two neutrons at the center of the sphere, which would then allow further compacting of the surrounding matter, cascading into a traditional black hole. However, the Hawking black hole time-to-dissipate is given by:
[tex]t_{\operatorname{ev}} = \frac{5120 \pi G^2 M_0^{3}}{\hbar c^4} \;[/tex]
which is directly related to the mass of the BH as:
[tex]8.410 \times 10^{-17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s} \;[/tex]
Our theoretical "minimalist" black hole would have a mass of two neutrons, or:
[tex]M_0 = 2*1.6749*10^{-27}{\mathrm{kg}} = 3.3498*10^{-27}{\mathrm{kg}} [/tex]
Which gives a time-to-dissipate as:
[tex]8.410 \times 10^{-17} \left[\frac{3.3498*10^{-27}{\mathrm{kg}}}{\mathrm{kg}}\right]^3 \mathrm{s} \; = 3.1612 \times 10^{-96} seconds[/tex]
In other words, much, much shorter than Planck time! The original formation of the EH would theoretically dissipate more quickly than the cascading compaction could possibly propagate. The result would quickly become a similar structure of reduced mass...with no event horizon
Has this concept been explored?
In a simple non-rotating non-charged neutron star of, say, 4M the neutron degeneracy pressure would not be exceeded throughout the structure simultaneously; rather, it would occur at the center of the sphere where pressure is greatest. More specifically, it would occur between two neutrons at the center of the sphere, which would then allow further compacting of the surrounding matter, cascading into a traditional black hole. However, the Hawking black hole time-to-dissipate is given by:
[tex]t_{\operatorname{ev}} = \frac{5120 \pi G^2 M_0^{3}}{\hbar c^4} \;[/tex]
which is directly related to the mass of the BH as:
[tex]8.410 \times 10^{-17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s} \;[/tex]
Our theoretical "minimalist" black hole would have a mass of two neutrons, or:
[tex]M_0 = 2*1.6749*10^{-27}{\mathrm{kg}} = 3.3498*10^{-27}{\mathrm{kg}} [/tex]
Which gives a time-to-dissipate as:
[tex]8.410 \times 10^{-17} \left[\frac{3.3498*10^{-27}{\mathrm{kg}}}{\mathrm{kg}}\right]^3 \mathrm{s} \; = 3.1612 \times 10^{-96} seconds[/tex]
In other words, much, much shorter than Planck time! The original formation of the EH would theoretically dissipate more quickly than the cascading compaction could possibly propagate. The result would quickly become a similar structure of reduced mass...with no event horizon
Has this concept been explored?
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