Now, there is a large literature from such mathematical luminaries as Lars Ahlfors on getting around these difficulties, but all authors agree that the best definitions are far from clear and that most attempts to make a viable theory of "quaternionic analysis" lead to failure.
As others have already pointed out, to someone who knows something about either quaternions or gtr it is quickly apparent that you have little knowledge of the relevant math or physics.
Do you see now why you are already in trouble here?
I'd say it's a good example of a statement which is "not even wrong".
But if anyone cares: when you compare the optical experience of different families of inertial observers in such standard models as the Schwarzschild vacuum, an exact vacuum solution to the Einstein field equation which lies at the heart of general relativity,. you find that in fact different observers have very different physical and/or optical experiences, depending upon the details of their kinematic (motion) history.
(Here, by "physical experience" I mean such things as tidal forces, while by "optical experience" I mean such things as strong-field light bending and gravitational lensing. For example, close to the event horizon of a black hole, light rays can very easily wind around several times before "escaping to infinity", and for this reason, an observer hovering just over the event horizon of a Schwarzschild hole sees a picture of "the night sky" which is very different from that seen by a distant observer!)
In fact, nothing Heger has said here has anything to do with general relativity, or even with physics. He has merely alluded to some ideas in pure mathematics, but his references are so muddled that it seems clear to me that he doesn't understand what he is trying to talk about.
It seems to me that he is trying to hide behind his own private language (his own private meaning of "black hole", "quaternion", "spacetime", and so on) to hide the fact that he really has nothing meaningful to say.