Thanks for the hints in the replies. After some investigation this seems to work. For the case if it is of use to someone:
QStyleOptionSlider opt;
slider->initStyleOption(&opt);
QStyle *styl=style();
Rect rectHandle=styl->subControlRect(QStyle::CC_Slider, &opt, QStyle::SC_SliderHandle, NULL);
Rect rectGroove=styl->subControlRect(QStyle::CC_Slider, &opt, QStyle::SC_SliderGroove, NULL);
int avl=styl->pixelMetric(QStyle::PM_SliderSpaceAvailable, &opt, this); // width in an horizontal slider of the groove (width of widget - margins)