Lets' say that something is in a universe with a perfect vacuum, where nothing exists but that object. This universe has an infinite amount of space and time. Now that object emits a single photon. Will this photon eventually return to the sender due to the senders own gravity, or will the photon continue to travel straight for the rest of eternity?

Photons are affected by gravity, thats why they bend around black holes. But I've read or heard somewhere (I have no sources for this, so this could be wrong) that the speed of a photon is constant. So if the photon wants to return to the sender it would have to slow down, and eventually start going the oppesit direction, which would defy the rule that the speed of light is constant.

I can't come with a logical conclusion to this problem, so some help would be appreciated.