E=mc^2

and...

E^2=m^2*c^4

.... are only different if there is a physical meaning to negative mass
and negative energy values, where the second equation allows for both
positive and negative mass-energy solutions.

I'd like to assert that the negative energy solutions more practically
apply to GR using Einstein's own original abandoned version of the
cosmological constant.

http://www.astro.ucla.edu/~wright/cosmo_constant.html

If, as with Einstein's model, the negative pressure component reflects
-rho and gravitational curvature, then negative mass-energy would
necessarily be expressed via negative density, as well.

In order to make a real massive particle from this energy, you must
condense enough of it over a finite region of space to achieve positve
mass, density and curvature.

In Einsteins static model, if you condense vaccum energy, then you
necessarily increase negative energy and pressure, as well, by way of
rarefaction, so the vaccum necessarily expands during pair production.

Dirac's Cosmological Model had a decreasing cosmological constant, but
'Dirac's Sea of Electrons' did not have negative relative density, or
his hole theory would not result in a decreasing cosmological constant,
since an increase in mass energy will necessarily be offset by the
increase in negative energy and pressure.

Dirac successfully unified SR and QM by way of the Dirac Equation, but
it could not be unified with GR, and it projects the absurd idea of
"tachyons", in terms of negative mass particles.

TILT

That's got to be the wrong background, because tachyons won't *appear*
anywhere if the vacuum has -rho, per the above.

Somebody dropped the ball when they leaped to conclude that an expanding
universe will necessarily run-away.