Q:

what is the effective mass of a hole, how do you define a hole.

- Meenakshi

India

- Meenakshi

India

A:

I guess that you are referring to a so-called 'Black Hole', a massive, extremely dense stellar object. A defining feature is that its gravity is so strong that light cannot escape from the surface, hence the name black hole. In principle you can determine its mass if there is an

object with known mass orbiting it at a known distance. Using Newton's laws, along with a few corrections from general relativity, the period of the orbit is related to the black hole mass.

Astronomers are pretty sure there is a black hole at the center of our own galaxy, the milky way. NASA has a web site that might interest you.

http://imagine.gsfc.nasa.gov/docs/science/know_l1/black_holes.html

LeeH

This is an example of how the cultures of different branches of physics don’t always overlap as much as we’d like. My guess is that the question is about holes which conduct electricity in solids. (and maybe you had still a third meaning in mind) These holes are typically empty states in nearly filled bands of states in semiconductors. Under the influence of an applied electric field, the pattern of which states are occupied shifts. The momentum of the state that is unoccupied shifts. That’s just like how the momentum of an electron shifts in an electric field. There’s still a ratio of the momentum of the state to its velocity, and that ratio is the effective mass. (If you want to be technical, the velocity we mean here is the group velocity.) The ratio can depend on what direction the field is applied, so the effective mass can be a tensor and not always just a plain scalar number. I guess formally it’s the inverse of the tensor which gives the second derivative of the energy with respect to the wavevector, converted to standard units by multiplying by hbar^{2}.

Mike W.

If further explanation is needed, let us know.

Mike W.

object with known mass orbiting it at a known distance. Using Newton's laws, along with a few corrections from general relativity, the period of the orbit is related to the black hole mass.

Astronomers are pretty sure there is a black hole at the center of our own galaxy, the milky way. NASA has a web site that might interest you.

http://imagine.gsfc.nasa.gov/docs/science/know_l1/black_holes.html

LeeH

This is an example of how the cultures of different branches of physics don’t always overlap as much as we’d like. My guess is that the question is about holes which conduct electricity in solids. (and maybe you had still a third meaning in mind) These holes are typically empty states in nearly filled bands of states in semiconductors. Under the influence of an applied electric field, the pattern of which states are occupied shifts. The momentum of the state that is unoccupied shifts. That’s just like how the momentum of an electron shifts in an electric field. There’s still a ratio of the momentum of the state to its velocity, and that ratio is the effective mass. (If you want to be technical, the velocity we mean here is the group velocity.) The ratio can depend on what direction the field is applied, so the effective mass can be a tensor and not always just a plain scalar number. I guess formally it’s the inverse of the tensor which gives the second derivative of the energy with respect to the wavevector, converted to standard units by multiplying by hbar

Mike W.

If further explanation is needed, let us know.

Mike W.

*(published on 10/22/2007)*