What are the effects of increased mass on persons traveling at near light speed?

It's been a long time since I studied physics (and then only very superficially), so please bear with my gross naivete. This question's been running around in my head for about two weeks now, and I need a real physicist to set me straight.

Provided that the following are all valid:

• Mass increases with velocity.
• Mass generates a gravitational force.
• As mass increases, so does its gravitational force.
• As an object accelerates, so does its gravitational force, due to the increase in its mass.
• Time passes faster as the gravitational force increases.

Wouldn’t time for a person traveling near the speed of light seem to pass faster, rather than slower than that of a person on Earth? Edit: No. Time passes slower in a larger gravity well. (Thanks, Jim.)

Also, wouldn’t such an individual exert a gravitational pull on objects he or she passed, dragging them along behind him or her to their destination (provided they achieved sufficient mass)?

I'm assuming, at this point, that one or more of my assumptions are wildly inaccurate. Please, feel free to correct me.

• Time passes slower in a larger gravity well. – Jim Feb 6 '15 at 18:23
• This set of question is one of the best reasons to stop teaching "relativistic mass", already. They are also several times duplicated, thought I don't recall what search will turn up the links and I have to go teach class soon. – dmckee --- ex-moderator kitten Feb 6 '15 at 18:27
• @dmckee, I saw (on Wikipedia, of all places) that Einstein, himself, didn't agree with the notion of "relativistic mass." When I was in High School (about 25 years ago), relativistic mass was what they taught. Most of the stuff I see around still teaches it. Has the thinking changed on the matter? – Mike Hofer Feb 6 '15 at 18:37
• @MikeHofer $E^2=m_0^2c^4+p^2c^2$ The relativistic mass is what you get when you let all of that be expressed as $E=mc^2$. The rest mass doesn't change, but the momentum does. However, this is only a simplification used to allow you to express momentum in terms of velocity. It does not mean the mass of the object actually increases, just that the mass in its mass-energy equivalency does. Gravitational mass is not the same as relativistic mass. Gravity depends more on the rest mass – Jim Feb 6 '15 at 18:58
• Professional physics mostly moved away from that phrasing in the 70s and 80s. You still see treatments like that in pop-sci sources and for primary/secondary school. Much to the annoyance of many pros. – dmckee --- ex-moderator kitten Feb 6 '15 at 19:38