Renormalized vacuum polarization on rotating warped AdS3 black holes
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Citations
Vacuum polarization throughout general subtracted black hole spacetimes
References
Quantum Fields in Curved Space
General Relativity; an Einstein Centenary Survey
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
Black hole physics : basic concepts and new developments
Black Hole Physics: Basic Concepts and New Developments
Related Papers (5)
Frequently Asked Questions (9)
Q2. What are the future works mentioned in the paper "Renormalized vacuum polarization on rotating warped ads3 black holes" ?
In the future, the authors intend to extend this method to compute the expectation value of the stress-energy tensor. The authors anticipate that this method can be extended to wider classes of rotating black hole spacetimes, and in particular in four dimensions to the Kerr spacetime.
Q3. What is the advantage of using the Minkowski spacetime?
The advantage of using the Minkowski spacetime is that its symmetries allow us to compute the Green’s function in both closed form and as a mode sum.
Q4. What is the function for x ?
After this matching is performed, the vacuum polarization is just given by〈Φ2(x)〉 = lim θ̃→0 GBHren(x, x ′) , (3.28)which is a well-defined smooth function for x ∈ Ĩ.
Q5. What is the definition of a spacetime with a Killing field?
In the context of quantum field theory, as it is detailed below, the nonexistence of an everywhere timelike Killing vector field in the exterior region of the spacetime is directly related to the nonexistence of a well defined quantum vacuum state which is regular at the horizon and is invariant under the isometries of the spacetime.
Q6. What is the metric of the spacelike stretched black hole?
The dimensionless coupling ν ∈ (1,∞) is the warp factor, and in the limit ν → 1 the above metric reduces to the metric of the BTZ black hole in a rotating frame.
Q7. What is the renormalization procedure for the Feynman propagator?
This is followed by a detailed account of the Hadamard renormalization procedure, in which the authors subtract the divergences in the mode sum by a sum over Minkowski modes with the same singularity structure.
Q8. What is the renormalized vacuum polarization in other Hadamard states of interest?
To find the renormalized vacuum polarization in other Hadamard states of interest, such as the Boulware vacuum state, it would suffice to use the Hartle-Hawking state as a reference and just to calculate the difference, which is finite without further renormalization.
Q9. what is the singular part of the Feynman propagator?
the singular, state-independent part of the Feynman propagator isGHad(x, x ′) :=i 4 √ 2π U(x, x′)√ σ(x, x′) + i . (2.21)This is known as the “Hadamard singular part” and it is singular at x′ → x.