My new apartment has no 3 prong plugs with ground

Ejs811, Look at your electrical panel. Sometimes it will state the capacity of your electrical service. Or, you can set up your gear and not worry about it. The only thing possibly drawing a lot of current is your amplifier and it depends on the load presented by your speakers and the volume you listen at. I would not count on your landlord rewiring any time soon.

There will be two mains fuses, at the top of your electrical panel. Read the sizes on those, to determine how much amperage is available, per phase. Outlet boxes in older homes ARE NOT USUALLY grounded. Especially if the wiring is knob and tube. Unless the wires were run through metal conduit(EMT), metallic liquid-tite, Bx cabling or have a third ground conductor to the box; it is NOT grounded. Grounding(running a pigtail) to the new outlet to an ungrounded box would be a waste of time/effort. Besides; the ground terminal on grounded outlets, is already grounded to the box through the mounting tabs/screws.

Call an electrician (maybe the owner will split the cost). I live in a 90 year old house and had a dedicated line installed for the HiFi and most of the recepticals replaced.
When the electician found some outlets with pre-war wiring, I said dont bother running new lines as they are not used for high current items. (it would have been expensive). Most of my oulets are now 3-prong and up to code.