The regularized stress-energy tensor of the quantized massive scalar, spinor and vector fields inside the degenerate horizon of the regular charged black hole in the (anti-)de Sitter universe is constructed and examined. It is shown that although the components of the stress-energy tensor are small in the vicinity of the black hole degenerate horizon and near the regular center, they are quite big in the intermediate region. The oscillatory character of the stress-energy tensor can be ascribed to various responses of the higher curvature terms to the changes of the metric inside the (degenerate) event horizon, especially in the region adjacent to the region described by the nearly flat metric potentials. Special emphasis is put on the stress-energy tensor in the geometries being the product of the constant curvature two-dimensional subspaces.Comment: Title modified to match published version. References adde

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The first-order semiclassical Einstein field equations are solved in the interior of the Schwarzschild-Tangherlini black holes. The source term is taken to be the stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling calculated within the framework of the Schwinger-DeWitt approximation. It is shown that for the minimal coupling the quantum effects tend to isotropize the interior of the black hole (which can be interpreted as an anisotropic collapsing universe) for D = 4 and 5, whereas for D = 6 and 7 the spacetime becomes more anisotropic. Similar behavior is observed for the conformal coupling with the reservation that for D = 5 isotropization of the spacetime occurs during (approximately) the first 1/3 of the lifetime of the interior universe. On the other hand, we find that regardless of the dimension, the quantum perturbations initially strengthen the grow of curvature and its later behavior depends on the dimension and the coupling. It is shown that the Karlhede's scalar can still be used as a useful device for locating the horizon of the quantum-corrected black hole, as expected.

The approximate stress-energy tensor of the quantized massive scalar, spinor and vector fields in the spatially flat Friedman-Robertson-Walker universe is constructed. It is shown that for the scalar fields with arbitrary curvature coupling, ξ, the stress-energy tensor calculated within the framework of the Schwinger-DeWitt approach is identical to the analogous tensor constructed in the adiabatic vacuum. Similarly, the Schwinger-DeWitt stress-energy tensor for the fields of spin 1/2 and 1 coincides with the analogous result calculated by the Zeldovich-Starobinsky method. The stress-energy tensor thus obtained are subsequently used in the back reaction problem. It is shown that for pure semiclassical Einstein field equations with the vanishing cosmological constant and the source term consisting exclusively of its quantum part there are no self-consistent exponential solutions driven by the spinor and vector fields. A similar situation takes place for the scalar field if the coupling constant belongs to the interval ξ > ∼ 0.1. For a positive cosmological constant the expansion slows down for all considered types of massive fields except for minimally coupled scalar field. The perturbative approach to the problem is briefly discussed and possible generalizations of the stress-energy tensor are indicated.

We investigate the vacuum polarization, φ 2 , of the quantized massive scalar field with a general curvature coupling parameter in the spatially-flat N -dimensional Friedman-Robertson-Walker spacetime with 4 ≤ N ≤ 12. The vacuum polarization is constructed using both adiabatic and Schwinger-DeWitt approaches and the full final results up to N = 7 are explicitly demonstrated. The behavior of φ 2 for 4 ≤ N ≤ 12 is examined in the exponentially expanding universe, in the power-law and inflationary powerlaw models. In the case of exponential expansion, φ 2 is constant and for a given mass it depends solely on the Hubble constant and the curvature coupling parameter. In the power-law models its behavior is more complicated and, generally, decays in time as t −n , where n/2 is the integer part of N/2. The 2 + 1-dimensional case is also briefly analyzed. The relevance of the present results to the stress-energy tensor is examined.