[1] The main area of his research was soft matter physics (liquid crystals, biophysics, biomolecular electronics and nanophysics).

Petrov investigated theoretically and experimentally dielectric, elastic, flexoelectric and surface properties of nematic liquid crystals with different types of molecular asymmetry.

In the living matter physics he created the knowledge of bioflexoelectricity, including a new theoretical model for description of the elasticity and flexoelectricity of biological membranes from the general molecular asymmetry point of view.

He discovered gradient flexoelectric effect in nematic liquid crystals under the action of inhomogeneous electric fields (1971–1974); flexoelectric oscillations in nematic liquid crystals (1975–1979); direct flexoeffect in biological membrane with ion channels (1988–1993); helielectricity in chiral lyotropic lipid phases (aqueous and nonaqueous) (1988–1989); inverse flexoeffect of bilayer lipid membranes (1993); photoflexoeffect in photo-active membranes (1992–1994).

[2] Petrov was awarded the Freedericksz Medal for outstanding contributions in the field of liquid crystal physics by the Russian Liquid Crystal Society (2004), the Outstanding Contribution to Science Annual Award of the Ministry of Education and Science of Bulgaria (Scientist of the year 2007) and the Marin Drinov Sign of Honour of Bulgarian Academy of Sciences on a ribbon (2008).