Sorry if this is a newby question, but it was something I was tinkering with a bit last night(adsbygoogle = window.adsbygoogle || []).push({});

"As an object increases its speed relative to you, its relative mass increases. Therefore, if a neutron star passes by you at a certain speed, it should turn into a black hole."

The schwartzchild radius is [tex]R = \frac{2MG}{c^2}[/tex] (which can be derived by setting [tex]v=c[/tex] in the escape velocity equation)

So a mass of [tex]M \geq \frac{Rc^2}{2G}[/tex] will be a black hole.

Using special relativity,

[tex]M = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

So we can solve the equation

[tex]\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \geq \frac{Rc^2}{2G}[/tex] for v.

[tex]\therefore v \geq \sqrt{c^2-\left(\frac{2Gm_0}{Rc}\right)^2}[/tex]

If we plug in the data for a neutron star,

[tex]\rho = 4.9 \times 10^{17}\ \mbox{kg/m}^3[/tex]

[tex]r = 12 \times 10^3\ \mbox{m}[/tex]

We get [tex]v > 0.9c[/tex], which is certainly achievable.

In your frame of reference, you would see the star collapse into a black hole. In the neutron star's frame of reference, nothing would happen.

Does that work?

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# Relativity and collapsing stars

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