  Extremely luminous, red eruptive variables like RV in M31 are being suggested
as exemplars of a new class of astrophysical object. Our greatly extended
series of nova simulations shows that classical nova models can produce very
red, luminous eruptions. In a poorly studied corner of 3-D nova parameter space
(very cold, low-mass white dwarfs, accreting at very low rates) we find bona
fide classical novae that are very luminous and red because they eject very
slowly moving, massive envelopes. A crucial prediction of these nova models -
in contrast to the predictions of merging star ("mergeburst") models - is that
a hot remnant, the underlying white dwarf, will emerge after the massive
ejected envelope has expanded enough to become optically thin. This blue
remnant must fade on a timescale of decades - much faster than a "mergeburst",
which must fade on timescales of millennia or longer. Furthermore, the cooling
nova white dwarf and its expanding ejecta must become redder in the years after
eruption, while a contracting mergeburst must become hotter and bluer. We
predict that red novae will always brighten to L~1000 Lsun for about 1 year
before rising to maximum luminosity at L~10^6 - 10^7 Lsun. The maximum
luminosity attainable by a nova is likely to be L~10^7 Lsun, corresponding to
M-12. In an accompanying paper we describe a fading, luminous blue candidate
for the remnant of M31-RV; it is observed with HST to be compatible only with
the nova model.
