Energy continuity equation


by Phrak
Tags: continuity, energy, equation
Phrak
Phrak is offline
#1
Jan19-11, 05:41 AM
P: 4,513
Is there such an animal as an energy continuity equation, or one involving Pmu or the stress energy tensor?

It suddenly stuck me that if we are to be so inclined by theory as we are by empirical evidence that energy is a conserved quantity, then there should be an equation that describes it in four dimensions.

Rather than bring in general relativity all at once where energy is not well defined (I have reservations), the stress energy tensor is still a tensor in special relativity, and so special relativity might be the better place to start.
Phys.Org News Partner Science news on Phys.org
Review: With Galaxy S5, Samsung proves less can be more
Making graphene in your kitchen
Study casts doubt on climate benefit of biofuels from corn residue
DaleSpam
DaleSpam is offline
#2
Jan19-11, 05:48 AM
Mentor
P: 16,481
Yes, the continuity equation:
[tex]\nabla_{\nu}T^{\mu\nu}=0[/tex]

This expresses the conservation of energy and momentum locally in curved spacetime and globally in flat spacetime.
Phrak
Phrak is offline
#3
Jan20-11, 04:09 AM
P: 4,513
Quote Quote by DaleSpam View Post
Yes, the continuity equation:
[tex]\nabla_{\nu}T^{\mu\nu}=0[/tex]

This expresses the conservation of energy and momentum locally in curved spacetime and globally in flat spacetime.
Thanks, I should have done some research sooner. It seems, at this point the validity of \nabla T = 0 in special relativity goes on a case by case basis, until the Einstein equation is invoked where the Bianchi identity is applied to the other side.


Register to reply

Related Discussions
Continuity equation for Schrodinger equation with minimal coupling Quantum Physics 5
Continuity Like Equation Classical Physics 0
continuity equation from Stress-Energy tensor Special & General Relativity 3
Deriving the continuity equation from the Dirac equation (Relativistic Quantum) Advanced Physics Homework 3
Why is the continuity equation called the continuity equation? General Physics 1