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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.

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

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Because it's convenient for the plot. –  Kevin Nov 17 '11 at 15:20
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If they can get a 'bone lock' with the transporter in Voyager to beam people through interference without just beaming their skeleton to the ship, then they can go warp speed without a Warp Core for a few minutes. –  Kalamane Nov 17 '11 at 15:29
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I don't know. It seems to me they could have simply modulated shield harmonics while reversing the polarity of the quantum flux capacitor, all the while channeling power away from life support through the plasma conduits (which lack fuses and run behind consoles next to crewmen's heads) into the deflector array, emitting a neutrino-enhanced tacheon beam that's modulated at 1.12 ghz. –  Paperjam Nov 17 '11 at 19:29
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@Kalamane Ah yes, that's right. Good catch. My mistake would have opened up a temporal rift sending the ship back in time, to our time, in Hollywood, where movies and TV shows are made... –  Paperjam Nov 17 '11 at 21:36
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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.

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Supporting this answer, the TNG Episode Brothers has Picard say that if they separate the saucer section while at warp it will drop out of warp in two minutes. –  Kalamane Nov 19 '11 at 15:36
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A "Warp Core" is just the label given to the matter-antimatter reactor on most starships. A starship can technically be warp-capable without a warp core so long as it has some other energy source to power the warp coils, which are the mechanisms which actually generate the warp bubble and allow the ship to travel at warp speeds.

So a simple in-universe explanation would be that the warp core was ejected, but the ship still had enough reserve energy (either in batteries/energy banks/residual drive plasma that remained in the EPS) to maintain a warp bubble for however long it was.

Also, a warp bubble could be a self-sustaining phenomenon.

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I don't know that warp bubbles would be self-sustained. I recall starships being capable of maximum warp for only relatively short (hours/days) periods of time, suggesting that maintaining the field took a lot of energy. –  Paperjam Nov 20 '11 at 7:23
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@Paperjam: Well, probably not perpetually self-sustaining. But it's still possible that at lower warp, the bubble could be sustained for a non-trivial length of time. It could be similar to subluminal travel. Planes can glide at their optimal cruising speeds for some time without losing too much speed. However, to maintain top speed, they would need to have their engines running at full throttle and continually pump energy into the system. That's because at higher speeds, there's a lot more drag to slow you down. –  Lèse majesté Nov 20 '11 at 7:33
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Newton's 1st law of motion states that a body in motion will stay in motion until an outside force act upon it. I would assume that they were traveling that fast and nothing was causing it to stop being at warp immediately, so the ship would keep it's velocity constant until an outside force (gravity from another mass, the ship stopping itself, etc) caused it to stop.

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Forces like a black hole? –  Kalamane Nov 17 '11 at 18:44
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And does that law apply to faster-than-light speeds? The only way they can travel that fast is in a warp bubble. Once that bubble is no longer maintainable they "drop out of warp". While they may continue to have momentum, that momentum is far less than the speed of light. –  Paperjam Nov 17 '11 at 19:23
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It seems highly unlikely that Newton's laws would apply to warp travel - for one thing, if they did, every time a starship jumped into warp it would need to scatter a tremendous amount of matter in the opposite direction. –  David Z Nov 20 '11 at 21:24
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Like everyone said above, the warp bubble is separated due to the remaining energy left from the warp core loss in the power conduits.

Think about it like a real life bubble, you have two bubbles after one splits until they both eventually pop or fly away. Yet in VOY: Day of honor, whenvoyager lost its warp core it immediately dropped out of warp a few seconds after.

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This answer doesn't really add to any of the previous answers, and actually raises a new question. –  Monty129 Aug 22 '13 at 21:12
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Warp fields, warp bubbles and spatial distortions are used to accelerate to warp speeds. The warp field and bubble allows the ship to "surf" the distortions to FTL (faster than light) speeds. To maintain warp speed, all you have to do is maintain a warp field and bubble, plus the spatial distortions with a warp sustainer engine. Same way a photon torpedo warps out of the tubes. Warp bubbles can hold their shape longer on its on WITHOUT any external energy.

http://en.memory-alpha.org/wiki/warp_field

http://en.memory-alpha.org/wiki/warp_bubble

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No, warp fields cannot hold their shape on their own. Photon torpedoes have warp sustainer engines. –  Izkata Mar 27 at 0:01
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