Thread: invariant?

Which of the following are invariant?
1) density
2) the EH of a black hole
3) the measurement of the SR of a particular black hole
4) the density of the universe

Clarify.

My take:
1.) - Density of what?
2.) - Variant
3.) - Define; Measurement of SR in regards to what aspect of a BH?
4.) - Macro: Invariant. Micro: Subtly variant.
5.) - Toms oversexed nature: - Invariant.

Originally Posted by Neverfly

Clarify.

My take:
1.) - Density of what?

basically of anything... a star, a black hole, the universe, a gallon of milk.

Originally Posted by Neverfly

Clarify.
3.) - Define; Measurement of SR in regards to what aspect of a BH?

SR I meant schwarzschild radius ... that caluclation is based on mass of a BH ... but it would need to mean rest mass otherwise it is invariant.

Well, in that case, I'd vote none of the above invariant. The last one MAYBE, but "maybe" isn't always good enough for me.

Originally Posted by Neverfly

Well, in that case, I'd vote none of the above invariant. The last one MAYBE, but "maybe" isn't always good enough for me.

My thought with the last one is that the mass of the universe would be constant ... but I can disagree with you about the distances. So that the density of the universe cant be constant ... but not sure if that argument holds up.

Originally Posted by tom

My thought with the last one is that the mass of the universe would be constant ... but I can disagree with you about the distances. So that the density of the universe cant be constant ... but not sure if that argument holds up.

Thanks. Now you made me sneeze and hiccup at the same exact time and I hate you.

Originally Posted by tom

Which of the following are invariant?

1. density--Density is the ratio of mass to volume. Mass is Lorentz-invariant, but volume is not. Even in Euclidian spacetime, the density depends on several things including temperature and pressure. Therefore the density of nothing is invariant.
2. the EH of a black hole--The event horizon depends only on the mass. It is invariant only if the black hole has fixed mass.
3. the measurement of the SR of a particular black hole--The Schwarzschild radius is a length. Length is not Lorentz-invariant. A distant observer will be visually aware of the black hole. However, an observer under the influence of the black hole's gravitational field [or spacetime distortion] may not be visually aware of it. To such an observer, the Schwarzchild radius may not exist.
4. the density of the universe--The Universe is expanding. Its density can be invariant only if its mass increases in direct proportion to its increase in volume.

You appear to be intrigued by density. The density of ordinary matter is governed by its temperature and pressure. The Universe is inhomogeneous. It has a foam-like structure with the galaxies forming the cell walls of the bubbles. Local density is certainly not invariant. If the average density were invariant, then it would be as much fortuitous accident as fundamental law of the Universe.

2. If I am travelling at the speed of light towards a black hole meanwhile you are at a static distance from the black hole, would we agree on the size of the EH?
3. From my understanding the SR of a black hole ONLY has to do with mass and in merely a calculation of where the EH is for a non-rotating black hole. One question with this is that if I travel towards the BH at near the speed of light the (relativist ) mass of the bh from my perspective increases. However I believe that the SR is based on rest mass not on relativistic mass. So basically from an observer at infinity not moving relative to the BH.

Originally Posted by MisterMe

1. density--Density is the ratio of mass to volume. Mass is Lorentz-invariant, but volume is not. Even in Euclidian spacetime, the density depends on several things including temperature and pressure. Therefore the density of nothing is invariant.
2. the EH of a black hole--The event horizon depends only on the mass. It is invariant only if the black hole has fixed mass.
3. the measurement of the SR of a particular black hole--The Schwarzschild radius is a length. Length is not Lorentz-invariant. A distant observer will be visually aware of the black hole. However, an observer under the influence of the black hole's gravitational field [or spacetime distortion] may not be visually aware of it. To such an observer, the Schwarzchild radius may not exist.
4. the density of the universe--The Universe is expanding. Its density can be invariant only if its mass increases in direct proportion to its increase in volume.

You appear to be intrigued by density. The density of ordinary matter is governed by its temperature and pressure. The Universe is inhomogeneous. It has a foam-like structure with the galaxies forming the cell walls of the bubbles. Local density is certainly not invariant. If the average density were invariant, then it would be as much fortuitous accident as fundamental law of the Universe.

Originally Posted by tom

2. If I am travelling at the speed of light towards a black hole meanwhile you are at a static distance from the black hole, would we agree on the size of the EH?
3. From my understanding the SR of a black hole ONLY has to do with mass and in merely a calculation of where the EH is for a non-rotating black hole. One question with this is that if I travel towards the BH at near the speed of light the (relativist ) mass of the bh from my perspective increases. However I believe that the SR is based on rest mass not on relativistic mass. So basically from an observer at infinity not moving relative to the BH.

You cannot use the term invariant like that. A quantity cannot be invariant under some circumstances. If it is invariant, then it is invariant [under all circumstances]. Relativity is governed by the Lorentz transformation and the Einstein metric. Two obvious quantities that are invariant are the mass and speed of a photon. Relativistic mass and rest mass are terms that are used to explain relativity to school children. Mass is the magnitude of the energy-momentum 4-vector. Momentum gives the three spatial components of this vector. Energy gives the imaginary temporal component.