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Planck energy:

[tex]E_P = m_P c^2 = \sqrt{\frac{\hbar c^5}{G}}[/tex]

Gravitational radius:

[tex]r_G = \frac{r_s}{2} = \frac{G m_P}{c^2}[/tex]

Gravitational radius is equivalent to Compton wavelength:

[tex]r_G = \overline{\lambda}_C[/tex]

[tex]\frac{G m_P}{c^2} = \frac{\hbar}{m_P c}[/tex]

Planck force is a constant in the Einstein field equation:

[tex]F_P = \frac{E_P}{r_G} = m_P c^2 \left( \frac{c^2}{G m_P} \right) = \frac{c^4}{G} = \frac{8 \pi T_{\mu \nu}}{G_{\mu\nu}}[/tex]

The maximum ratio of energy per gravitational length:

[tex]\boxed{\frac{c^4}{G} = \frac{8 \pi T_{\mu \nu}}{G_{\mu\nu}}}[/tex]

Are Planck scale dimensions the maximum limits in the Universe?

Reference:

http://en.wikipedia.org/wiki/Planck_force" [Broken]

http://en.wikipedia.org/wiki/Planck_mass" [Broken]

http://en.wikipedia.org/wiki/Planck_energy" [Broken]

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# Planck scale dimensions

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