User:Tohline/Appendix/Ramblings/InsideOut - Revision history

Tohline: /* Enumerated Questions */

2017-10-13T11:47:56Z

Enumerated Questions

← Older revision		Revision as of 11:47, 13 October 2017
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	<ol>		<ol>
	<li>Can we construct a ''Newtonian'' structure out of normal matter that has a mass of, say, <math>~10^9 M_\odot</math> whose equilibrium radius is much less than the radius of the BH horizon associated with that object?</li>		<li>Can we construct a ''Newtonian'' structure out of normal matter that has a mass of, say, <math>~10^9 M_\odot</math> whose equilibrium radius is much less than the radius of the BH horizon associated with that object? Does it necessarily have a mean temperature whose associated sound speed is super-relativistic?</li>
	<li>Who else in the published literature has explored questions along these lines?		<li>Who else in the published literature has explored questions along these lines?
	</ol>		</ol>

Tohline: /* Looking Outward, From Inside a Black Hole */

2017-10-13T11:40:30Z

Looking Outward, From Inside a Black Hole

← Older revision		Revision as of 11:40, 13 October 2017
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	<tr>		<tr>
	<td align="right">		<td align="right">
	<math>~\frac{GM}{c^2 R}</math>		<math>~\frac{2GM}{c^2 R}</math>
	</td>		</td>
	<td align="center">		<td align="center">
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	<math>~		<math>~
	\frac{3M}{4\pi R^3} =		\frac{3M}{4\pi R^3} =
	\frac{3M}{4\pi} \biggl[ \frac{GM}{c^2}\biggr]^{-3} =		\frac{3M}{4\pi} \biggl[ \frac{2GM}{c^2}\biggr]^{-3} =
	\frac{3c^6}{4\pi G^3 M^2}		\frac{3c^6}{2^5\pi G^3 M^2}
	</math>		</math>
	</td>		</td>
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	<td align="left">		<td align="left">
	<math>~		<math>~
	\biggl[\frac{(3 \times 10^{10})^6}{4 (\tfrac{2}{3}\times 10^{-7})^3 (2\times 10^{33})^2 M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}		\biggl[\frac{(3 \times 10^{10})^6}{2^5 (\tfrac{2}{3}\times 10^{-7})^3 (2\times 10^{33})^2 M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}
	</math>		</math>
	</td>		</td>
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	<td align="left">		<td align="left">
	<math>~		<math>~
	\biggl[\frac{3^{6+3} \times 10^{60}}{2^{7} (10^{66-21}) M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}		\biggl[\frac{3^{6+3} \times 10^{60}}{2^{10} (10^{66-21}) M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}
	</math>		</math>
	</td>		</td>
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	<td align="left">		<td align="left">
	<math>~		<math>~
	\biggl[\frac{3^{9} \times 10^{60}}{2^{7} (10^{45}) M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}		\biggl[\frac{3^{9} \times 10^{60}}{2^{10} (10^{45}) M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}
	</math>		</math>
	</td>		</td>
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	<td align="left">		<td align="left">
	<math>~		<math>~
	\biggl[\frac{~~1.5~~ \times 10^{17}}{M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3} \, .		\biggl[\frac{2 \times 10^{16}}{M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3} \, .
	</math>		</math>
	</td>		</td>

Tohline: /* Looking Outward, From Inside a Black Hole */

2017-10-13T11:29:19Z

Looking Outward, From Inside a Black Hole

← Older revision		Revision as of 11:29, 13 October 2017
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	{{LSU_HBook_header}}		{{LSU_HBook_header}}

	The relationship between the mass, <math>~M</math>, and radius, <math>~R</math>, of a black hole is,		[Written by J. E. Tohline, early morning of 13 October 2017]  The relationship between the mass, <math>~M</math>, and radius, <math>~R</math>, of a black hole is,
	<div align="center">		<div align="center">
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">
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	<td align="left">		<td align="left">
	<math>~		<math>~
	\frac{3M}{4\pi R^3}		\frac{3M}{4\pi R^3} =
			\frac{3M}{4\pi} \biggl[ \frac{GM}{c^2}\biggr]^{-3} =
			\frac{3c^6}{4\pi G^3 M^2}
	</math>		</math>
	</td>		</td>
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	</td>		</td>
	<td align="center">		<td align="center">
	<math>~=</math>		<math>~\approx</math>
			</td>
			<td align="left">
			<math>~
			\biggl[\frac{(3 \times 10^{10})^6}{4 (\tfrac{2}{3}\times 10^{-7})^3 (2\times 10^{33})^2 M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}
			</math>
			</td>
			</tr>

			<tr>
			<td align="right">

			</td>
			<td align="center">
			<math>~\approx</math>
			</td>
			<td align="left">
			<math>~
			\biggl[\frac{3^{6+3} \times 10^{60}}{2^{7} (10^{66-21}) M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}
			</math>
			</td>
			</tr>

			<tr>
			<td align="right">

			</td>
			<td align="center">
			<math>~\approx</math>
	</td>		</td>
	<td align="left">		<td align="left">
	<math>~		<math>~
	\frac{3M}{~~4\pi~~} ~~\biggl[ \frac~~{GM}{c^2}\biggr]^{-3}		\biggl[\frac{3^{9} \times 10^{60}}{2^{7} (10^{45}) M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3}
	</math>		</math>
	</td>		</td>
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	</td>		</td>
	<td align="center">		<td align="center">
	<math>~=</math>		<math>~\approx</math>
	</td>		</td>
	<td align="left">		<td align="left">
	<math>~		<math>~
	\frac{3c^6}{4\~~pi G~~^3 ~~M^2~~} \, .		\biggl[\frac{1.5 \times 10^{17}}{M_\odot^2}\biggr] ~\mathrm{g}~\mathrm{cm}^{-3} \, .
	</math>		</math>
	</td>		</td>
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	</table>		</table>
	</div>		</div>
			We are accustomed to imagining that the interior of a black hole (BH) must be an exotic environment because a one solar-mass BH has a mean density that is on the order of, but larger than, the density of nuclear matter. From the above expression, however, we see that a <math>~10^9 M_\odot</math> BH has a mean density that is less than that of water (1 gm/cm<sup>3</sup>). And the mean density of a BH having the mass of the entire universe must be very small indeed. This leads us to the following list of questions.

			==Enumerated Questions==

			<ol>
	~~==Leading Questions==~~		<li>Can we construct a ''Newtonian'' structure out of normal matter that has a mass of, say, <math>~10^9 M_\odot</math> whose equilibrium radius is much less than the radius of the BH horizon associated with that object?</li>
			<li>Who else in the published literature has explored questions along these lines?
			</ol>

	=See Also=		=See Also=

Tohline: Created page with 'FORCETOC =Looking Outward, From Inside a Black Hole= {{LSU_HBook_header}} The…'

2017-10-13T10:48:59Z

Created page with '__FORCETOC__   =Looking Outward, From Inside a Black Hole= {{LSU_HBook_header}} The…'

New page

__FORCETOC__ 

=Looking Outward, From Inside a Black Hole=

{{LSU_HBook_header}}

The relationship between the mass, <math>~M</math>, and radius, <math>~R</math>, of a black hole is,
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
<td align="right">
<math>~\frac{GM}{c^2 R}</math>
</td>
<td align="center">
<math>~=</math>
</td>
<td align="left">
<math>~1 \, .</math>
</td>
</tr>
</table>
</div>
The mean density of matter inside a black hole of mass <math>~M</math> is, therefore,
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
<td align="right">
<math>~\bar\rho</math>
</td>
<td align="center">
<math>~=</math>
</td>
<td align="left">
<math>~
\frac{3M}{4\pi R^3}
</math>
</td>
</tr>

<tr>
<td align="right">
 
</td>
<td align="center">
<math>~=</math>
</td>
<td align="left">
<math>~
\frac{3M}{4\pi} \biggl[ \frac{GM}{c^2}\biggr]^{-3}
</math>
</td>
</tr>

<tr>
<td align="right">
 
</td>
<td align="center">
<math>~=</math>
</td>
<td align="left">
<math>~
\frac{3c^6}{4\pi G^3 M^2} \, .
</math>
</td>
</tr>
</table>
</div>

==Leading Questions==

=See Also=
* [http://adsabs.harvard.edu/abs/1917RSPSA..93..148R Lord Rayleigh (1917, Proc. Royal Society of London. Series A, 93, 148-154)] — ''On the Dynamics of Revolving Fluids''

 <br />
{{LSU_HBook_footer}}

User:Tohline/Appendix/Ramblings/InsideOut - Revision history

Tohline: /* Enumerated Questions */

Tohline: /* Looking Outward, From Inside a Black Hole */

Tohline: /* Looking Outward, From Inside a Black Hole */

Tohline: Created page with '__FORCETOC__ =Looking Outward, From Inside a Black Hole= {{LSU_HBook_header}} The…'

Tohline: Created page with 'FORCETOC =Looking Outward, From Inside a Black Hole= {{LSU_HBook_header}} The…'