Is it true that light escaping from white dwarfs will show a gravitational redshift?

Hint: White dwarfs are basically the burned-out cores of stars. The central region of a typical white dwarf star is composed of a mixture of carbon and oxygen surrounded by a thin envelope of helium and an even thinner layer of hydrogen. We shall now analyze the phenomena of gravitational shift in accordance with the white dwarf stars.

Complete step by step answer:
Just as a rocket trying to get away from the gravitational pull of the Earth loses some gravitational potential energy and thus requires some escape velocity, light emitted from stars also loses some gravitational potential energy in order to escape from the gravitational pull of the star. However, light does not slow down as it tries to get away but it still loses some of its energy by overcoming that gravitational potential well and it does that by giving up some of its wavelength or some of its frequency. This is because the energy of a photon, the energy of light is directly proportional to the frequency of its oscillation. So, as light tries to get away from the Earth, it starts to oscillate lower and that is what we know as the gravitational redshift.

White dwarfs contain about the mass of the Sun but have roughly the radius of Earth and that is why they are among the densest objects in space. A teaspoon of matter from the white dwarf would weigh up to a hundred ton according to NASA. This implies that these white dwarf stars enforce a greater gravitational pull on the light emitted from them.
Therefore, due to high density, the light emitted from a white dwarf star will experience a greater gravitational redshift.

Note: When a star like the sun or with an initial mass of up to 3 or 4 solar masses has burned off all of its hydrogen fuel. It expands to become a red giant. After the outward pressure from the fusion reaction stops, the star expels most of its outer material and creates a planetary nebula which remains as the core other star which becomes a very hot white dwarf with a temperature of over 100,000 Kelvin.