Planets can indeed rob their stars of metals through a process called stellar evolution. As stars age, they fuse heavier elements in their cores through nuclear reactions. This process, known as nucleosynthesis, produces metals that are heavier than hydrogen and helium.

Over time, some of these metals can be transported to the surface of the star through convection currents. If the star has planets, these metals can be further enriched in the circumstellar disk from which the planets formed.

As planets form and grow, they can accrete metals from the disk. This can lead to the depletion of metals in the star's atmosphere, a phenomenon known as "stellar abundance depletion."

The extent of metal depletion depends on several factors, including the number and size of the planets, the metallicity of the star, and the age of the stellar system. In general, more massive stars and stars with multiple planets tend to show greater metal depletion.

Additionally, the depletion of metals can be more pronounced for certain elements. For example, observations have found significant depletions of lithium, beryllium, and iron in stars with planets compared to stars without planets.

Studying the metal abundances of stars and the characteristics of their planetary systems can provide insights into the processes of planet formation and evolution, and the interactions between planets and their host stars.