How could Enterprise remain at warp after ejecting its cores in Star Trek (2009)

In the 2009 film,

The Enterprise ejects and detonates its warp cores in an attempt to close a massive singularity. They maintain warp speed in order to attempt to escape the gravitational pull of the singularity.

How did the Enterprise maintain warp despite having ejected its cores?

Answer

Just as a photon torpedo is able to maintain warp flight using a warp sustainer engine (even though it has no warp core itself), so too should a ship be able to sustain a warp field on auxiliary power for some time after a warp core is no longer present/active. Here is the relevant excerpt from the photon torpedo entry on Memory Alpha, taken from the Star Trek: The Next Generation Technical Manual:

The propulsion system of the torpedoes is a warp sustainer engine. The engine coils of the torpedo grab and hold a hand-off field from the launcher tube's sequential field induction coils. A miniature matter/antimatter fuel cell adds power to the hand-off field. When launched in warp flight, torpedo will continue to travel at warp, when launched at sublight, torpedo will travel at a high sublight speed, but will not cross the warp threshold. (pg. 129)

As Kalamane points out in a comment, the ability to maintain a warp field without a warp core has been referenced before in the TNG episode "Brothers". The excerpt from the script:

PICARD: Mister La Forge, prepare for saucer separation.

WESLEY: Sir, we're at Warp nine three.

PICARD: I am aware of the risks, Ensign. When the umbilical splits, we should regain primary control, do you agree?

LAFORGE: Yes, sir.

PICARD: The saucer module should fall out of warp in two minutes. Be prepared to sweep back. Pull it in with a tractor beam.

If the warp-core-less saucer section has enough power to maintain a hand-off warp field from the secondary hull for a couple of minutes, then a whole ship that has lost its warp core should be able to do the same.