Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime
Year: 2025
Type: article
Abstract: We obtain semiclassical gravity solutions in the Poincaré fundamental domain of ( 3 + 1 ) -dimensional Anti-de Sitter spacetime, PAdS4, with a (massive or massless) Klein–Gordon field (with possibly non-trivial curvature coupling) with Dirichlet or Neumann boundary. Some results are explicitly and graphically presented for special values of the mass and curvature coupling (e.g. minimal or conformal coupling). In order to achieve this, we study in some generality how to perform the Hadamard renormalisation procedure for non-linear observables in maximally symmetric spacetimes in arbitrary dimensions, with emphasis on the stress-energy tensor. We show that, in this maximally symmetric setting, the Hadamard bi-distribution is invariant under the isometries of the spacetime, and can be seen as a ‘single-argument’ distribution depending only on the geodesic distance, which significantly simplifies the Hadamard recursion relations and renormalisation computations.
Source: Classical and Quantum Gravity
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4408833471