- #1
touqra
- 287
- 0
Can the energy density of an empty but expanding spacetime decrease with expansion?
Does a black hole have a stress-energy tensor?
Does a black hole have a stress-energy tensor?
Classically? Not really. If the cosmological constant of the universe is zero then the energy density is zero in empty spacetime.touqra said:Can the energy density of an empty but expanding spacetime decrease with expansion?
Does a black hole have a stress-energy tensor?
pmb_phy said:Classically? Not really. If the cosmological constant of the universe is zero then the energy density is zero in empty spacetime.
Pete
If the cosmological constant is non-zero then spacetime may still be either expanding or contracting.touqra said:What about a non-zero cosmological constant?
Without a non-zero cosmological constant, an empty spacetime wouldn't expand, isn't it?
pmb_phy said:If the cosmological constant is non-zero then spacetime may still be either expanding or contracting.
And yes - A Black hole does have a stress-energy-momentum-tensor.
Pete
That is incorrect. That expression holds everywhere except at the origin, i.e. where the black hole is. The mass distriution is describribed by a delta function.touqra said:I found out that the energy density of a Schwarzschild black hole, [tex] T_{00} = 0[/tex].
pmb_phy said:That is incorrect. That expression holds everywhere except at the origin, i.e. where the black hole is. The mass distriution is describribed by a delta function.
Of course it is.Stingray said:That's not true.
So what? We're not talking about those tensors regarding a black hole, we're talkikng about a 2nd rank tensor (1+#). Otherwise please site proof.It's possible to show rigorously that there are no solutions to Einstein's equations for 0+1 or 1+1 dimensional stress-energy tensors (within the context of standard distribution theory).
Not from what I've seen.Commonly discussed black holes do not have stress-energy tensors (other than charged ones of course).
pmb_phy said:So what? We're not talking about those tensors regarding a black hole, we're talkikng about a 2nd rank tensor (1+#). Otherwise please site proof.
pervect said:While this answer is sloppy and Stingray's answer is more correct, I think the sloppy answer will probably serve tougra better.
Chronos said:Even black holes are now believed [at least by many theorists] to have a finite volume, hence are integrable.
Why not? That's how it is actually defined. E.g. T^00 is energy density and that means its a point function. T^0i is ith component of momontum density which is also a point function. Same thing with all the other components.Chronos said:It's not meaningful to talk about stress energy tensors at points, AFAIK.
pmb_phy said:Why not? That's how it is actually defined. E.g. T^00 is energy density and that means its a point function. T^0i is ith component of momontum density which is also a point function. Same thing with all the other components.
It's pointless to talk about a point particle with a non-vanishing stress-energy tensor since this means there is a singularity.Stingray said:From what I gathered, he meant that it's not meaningful to talk about stress-energy tensors of points rather than at points. Maybe not, though.
That's true. However in real life one considers the situation and determines how small the particle must be and how low the mass must be so as to let the geodesic approach that of a ideal test particle. In any case there is nothing wrong with a singularity. A micro black hole has a miniscule mass compared with the Earth (its on the order of mass of Mt. Everest). But there's nothing wrong with thinking of such a micro black hole as a test particle so long as one limits its mass to be so small as to not contribute significantly to the stress-energy-momentum tensor of the spacetime its moving in for regions of several Schwarzschild radii.MeJennifer said:It's pointless to talk about a point particle with a non-vanishing stress-energy tensor since this means there is a singularity.
touqra said:Can the energy density of an empty but expanding spacetime decrease with expansion?
touqra said:Does a black hole have a stress-energy tensor?
touqra said:What about a non-zero cosmological constant?
touqra said:Without a non-zero cosmological constant, an empty spacetime wouldn't expand, isn't it?
touqra said:How is that possible if the mass of the BH contributes to a non-zero total energy
touqra said:and the volume of the BH can be taken as a spherical volume with a total area equals to that of its event horizon?
Stingray said:That's not true.
The stress-energy tensor is a mathematical concept used in Einstein's theory of general relativity to describe the energy and momentum of a given region of space. It is a 4x4 tensor that represents the distribution of energy and momentum within a given space-time.
Black holes are predicted by Einstein's theory of general relativity, which uses the stress-energy tensor to describe the curvature of space-time. As black holes have a strong gravitational pull, they warp the fabric of space-time and therefore have a stress-energy tensor associated with them.
The stress-energy tensor helps scientists understand the properties of black holes, such as their mass, spin, and electric charge. It also describes the intense gravitational field of a black hole and how it affects the surrounding space-time.
No, the stress-energy tensor cannot be used to study the interior of a black hole as it breaks down at the central singularity where the laws of physics as we know them do not apply. However, it can still provide valuable insights into the behavior of black holes in their surrounding space-time.
Yes, the stress-energy tensor is a fundamental tool in understanding the behavior of gravity in astrophysical systems, such as neutron stars and supernovae. It is also used in cosmology to study the evolution of the universe and the distribution of matter and energy within it.