Semiclassical Gravity - Stress-energy Tensor

Stress-energy Tensor

There is some ambiguity in regulating the stress-energy tensor, and this depends upon the curvature. This ambiguity can be absorbed into the cosmological constant, Newton's constant, and the quadratic couplings

and .

There's also the other quadratic term

,

but (in 4-dimensions) this term is a linear combination of the other two terms and a surface term. See Gauss-Bonnet gravity for more details.

Since the theory of quantum gravity is not yet known, it is difficult to say what is the regime of validity of semiclassical gravity. However, one can formally show that semiclassical gravity could be deduced from quantum gravity by considering N copies of the quantum matter fields, and taking the limit of N going to infinity while keeping the product GN constant. At diagrammatic level, semiclassical gravity corresponds to summing all Feynman diagrams which do not have loops of gravitons (but have an arbitrary number of matter loops). Semiclassical gravity can also be deduced from an axiomatic approach.