Thank you for your interesting question.

Many plants like black walnuts and sunflowers and other allelopathic plants exude something into the soil to reduce plant competition.   The chemical is called juglone which reduces or inhibits other plants from growing near it.  The black walnut leaves and roots and other parts exude this chemical.  See this site for more info: Plants That Inhibit Other Plants | Illinois Extension | UIUC

There are, however, many plants that will survive under a black walnut tree.   Here are several.

Groundcovers include:

• sweet woodruff
• Ajuga
• St John's Wort

Perennials include:

• Hostas
• Astilbe
• Iris
• Shasta Daisy
• Coneflower (Echinacea)
• Bee Balm (Monarda sp.)
• Yarrow (Achillea millefolium)
• Calendula (Calendula officinalis)
• Violet (Viola sp.)

Shrubs include:

• Elder (Sambuca sp.)
• Forsythia
• Spice bush
• Cherry (Prunus sp.)
• Rose (Rosa sp.)
• Pears (Pyrus sp.)
• Plum (Prunus sp.)
• Apricots (Prunus, sp)
• Columbie - Rocky Mountain
• Currants (Ribes spp.)
• Hazelnut (Corylus Americana)

See this site for more detailed lists of plants which will survive: Landscaping and Gardening Around Walnuts and Other Juglone Producing Plants (psu.edu)

I hope this helps.  Good luck!  Sincerely,