In fact, one can go further in criticizing the whole notion of "relativistic mass" – and therefore the presumption that it is reasonable to expect identical effects to those associated with mass proper. I think no one said it better than D.B. Larson:

"Conclusions outside the scope of the observations are not knowledge.

"Somewhat analogous to the practice of extrapolation, but of a more questionable character, is the practice of exaggeration; that is, claiming more than what the observations or measurements actually substantiate. A classic example is Einstein’s theory that mass is a function of velocity. Throughout scientific literature this theory is described as having been 'proved' by the results of experiment and by the successful use of the predictions of the theory in the design of the particle accelerators. Yet at the same time that a host of scientific authorities are proclaiming this theory as firmly established and incontestable experimental fact, practically every elementary physics textbook admits that it is actually nothing more than an arbitrary selection from among several possible alternative explanations of the observed facts. The experiments simply show that if a particle is subjected to an unchanged electric or magnetic force, the resulting acceleration decreases at high velocities and approaches a limit of zero at the velocity of light. The further conclusion that the decrease in acceleration is due to an increase in mass is a pure assumption that has no factual foundation whatever.

"As one textbook author explains the situation: "There seems to be no reason to believe that there is any change in the charge, and we therefore conclude that the mass increases." Another says: "This decrease is interpreted as in increase of mass with speed, charge being constant." Obviously an interpretation of the observed facts is not a fact in itself, and it is rather strange that the theorists have been so eager to accept this particular interpretation that they have not even taken the time to examine the full range of possible alternative interpretations. As these quotations from the textbooks indicate, it has been taken for granted that either the charge or the mass must be variable, but actually it is the acceleration that has been measured, and the acceleration is a relation of force to mass, not of charge to mass. The accepted interpretations of the observed facts therefore contain the additional assumption that the effective force exerted by a charge is constant irrespective of the velocity of the object to which it is applied. The possibility that this assumption is invalid cannot logically be excluded from consideration; on the contrary, there are some distinct advantages in maintaining both charge and mass as constant magnitudes. When we get down to bedrock it is clear that the theory of an increase in mass is not something that has been proved by experiment, as is so widely claimed; it is a pure assumption that goes beyond the scope of the experiment, and is only one of several possible alternatives. Any theory which leads to the observed decrease in acceleration at high velocities is equally as consistent with the observed facts as Einstein’s theory that the mass increases."

From D.B. Larson, "Just How Much Do We Really Know?," 1961:
http://library.rstheory.org/articles/Larson/JustHowMuch.html

Point is – black hole is simply a region of space that (even) light cannot escape from.
A singularity is completely different, essentially a point in space with infinite gravity.

So all singularities must be black holes, but not all black holes are singularities.

Will nearby objects like planets and stars get sucked into it, like they get sucked into a "normal" black hole?

I suspect not, for the following reasons:

(a) If this object came flying through our solar system (for example), then it would come and go *so quickly* that the gravitational force would not have time to suck the planets and our sun into it. This is because the gravitational force can’t travel faster than the speed of light. So the object would be out of effective range before the planets had time to do more than a brief wobble, I suspect.

(b) In the case that other objects were travelling alongside the flying object at a similar speed in the same direction, then these other objects would also gain relativistic mass. So *all* these objects would be exerting enormous gravitational forces on each other. Again this is very different to the situation of a “normal” black hole, which is surrounded by much less massive objects that it can easily suck in.

What about photons of light travelling in the same direction at the same speed as the flying 1kg mass? Would these photons be sucked into the flying mass due to its huge relativistic mass? Perhaps. I don’t know enough about photons. They seem to be very mysterious to me, travelling at the speed of light yet not appearing to possess much in the way of mass themselves. I don’t really understand photons at all.