Dust mop
The stone trade specifies one and adds three words that change the product entirely: clean, non-treated and dry.
In detail
A dust mop is a wide flat head that traps loose particulate by fibre contact rather than by suction, and on a hard floor it does the most valuable job in the maintenance cycle: removing grit before anything drags it. The stone institute's specification is worth reading exactly, because it excludes most of what is sold. Interior floors are dust-mopped frequently with a CLEAN, NON-TREATED, DRY dust mop. Non-treated rules out the impregnated or oiled heads sold to make dust cling, because the treatment transfers to the floor and to any sealer on it. Dry rules out damp mopping as a substitute, and clean rules out the commonest failure — a loaded head that redistributes grit rather than holding it. The same guidance names two things people overlook: mats and rugs with slip-resistant backing at entrances keep abrasive grit off the floor in the first place, and a vacuum's attachments and WHEELS may themselves be worn and scratch. That last observation generalises usefully: on a hard floor the tool most likely to cause damage is often the one being wheeled across it.
What works
Sources for this page
Sources
Care & Cleaning of Natural Stone
Natural Stone Institute · Trade or professional body
Relied on for: That interior floors are dust-mopped frequently with a clean, non-treated, dry dust mop, that mats and rugs with slip-resistant backing keep abrasive grit off the floor, and that a vacuum's attachments and wheels may be worn and scratch. (states this directly)
Conserve O Gram 15/2: Dusting Guidelines for Stone Objects and Interior Architectural Features
National Park Service, US Department of the Interior · Government or regulator
Relied on for: That dust with an abrasive component can scratch objects if pressure is applied during removal. (states this directly)