Mode-sum regularization of $⟨{\varphi }^2⟩$ in the angular-splitting method

Abstract

The computation of the renormalized stress-energy tensor or ${⟨{\varphi }^2⟩}_{ren}$ in curved spacetime is a challenging task, at both the conceptual and technical levels. Recently we developed a new approach to compute such renormalized quantities in asymptotically-flat curved spacetimes, based on the point-splitting procedure. Our approach requires the spacetime to admit some symmetry. We already implemented this approach to compute ${⟨{\varphi }^2⟩}_{ren}$ in a stationary spacetime using t-splitting, namely splitting in the time-translation direction. Here we present the angular-splitting version of this approach, aimed for computing renormalized quantities in a general (possibly dynamical) spherically-symmetric spacetime. To illustrate how the angular-splitting method works, we use it here to compute ${⟨{\varphi }^2⟩}_{ren}$ for a quantum massless scalar field in Schwarzschild background, in various quantum states (Boulware, Unruh, and Hartle-Hawking states). We find excellent agreement with the results obtained from the t-splitting variant, and also with other methods. Our main goal in pursuing this new mode-sum approach was to enable the computation of the renormalized stress-energy tensor in a dynamical spherically symmetric background, e.g. an evaporating black hole. The angular-splitting variant presented here is most suitable to this purpose.

34 pages, 12 figures. Submitted to Phys. Rev. D

References in corpus (2)

• Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
• The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum

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