Unruh State Research Articles

Effective action and Hawking flux from covariant perturbation theory

The computation of the radiation flux related to the Hawking temperature of a Schwarzschild Black Hole or another geometric background is still well-known to be fraught with a number of delicate problems. In spherical reduction, as shown by one of the present authors (W. K.) with D.V. Vassilevich, the correct black body radiation follows when two ``basic components'' (conformal anomaly and a ``dilaton'' anomaly) are used as input in the integrated energy-momentum conservation equation. The main new element in the present work is the use of a quite different method, the covariant perturbation theory of Barvinsky and Vilkovisky, to establish directly the full effective action which determines these basic components. In the derivation of W. K. and D.V. Vassilevich the computation of the dilaton anomaly implied one potentially doubtful intermediate step which can be avoided here. Moreover, the present approach also is sensitive to IR (renormalisation) effects. We realize that the effective action naturally leads to expectation values in the Boulware vacuum which, making use of the conservation equation, suffice for the computation of the Hawking flux in other quantum states, in particular for the relevant Unruh state. Thus, a rather comprehensive discussion of the effects of (UV and IR) renormalisation upon radiation flux and energy density is possible.

Proof of the generalized second law for two-dimensional black holes

We investigate the generalized second law for two-dimensional black holes in equilibrium (Hartle-Hawking) and nonequilibrium (Unruh) with the heat bath surrounding the black holes. We obtain a simple expression for the change of total entropy in terms of covariant thermodynamic variables, which is valid not only for the Hartle-Hawking state but also for the Unruh state up to leading order, without assuming a quasi-stationary evolution of the black holes. Using this expression, it is shown that the rate of local entropy production is non-negative in the two-dimensional black hole systems.

Vacuum polarization in the Schwarzschild spacetime and dimensional reduction

A massless scalar field minimally coupled to gravity and propagating in Schwarzschild spacetime is considered. After dimensional reduction under spherical symmetry the resulting 2D field theory is canonically quantized and the renormalized expectation values 〈Tab〉 of the relevant energy-momentum tensor operator are investigated. Asymptotic behaviors and analytical approximations are given for 〈Tab〉 in the Boulware, Unruh and Hartle-Hawking states. Special attention is devoted to the black-hole horizon region where the WKB approximation breaks down.

Quantum corrections for an (anti)evaporating black hole

In this paper we analyze the quantum correction for a Schwarzschild black hole in the Unruh state in the framework of the spherically symmetric gravity (SSG) model. SSG is a two-dimensional dilaton model that is obtained by spherically symmetric reduction from four-dimensional theory. We find the one-loop geometry of the (anti)evaporating black hole and corrections for mass, entropy, and apparent horizon.

Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions

The characteristic features of 〈 T μν 〉 in the Boulware, Unruh and Hartle-Hawking states for a conformal massless scalar field propagating in the Schwarzschild space-time are obtained by means of effective actions deduced by the trace anomaly. The actions are made local by the introduction of auxiliary fields and boundary conditions are carefully imposed on them in order to select the different quantum states.

Anomaly Induced Effective Actions and Hawking Radiation

The quantum stress tensor in the Unruh state for a conformal scalar propagating in a 4D Schwarzschild black hole spacetime is reconstructed in its leading behaviour at infinity and near the horizon by means of an effective action derived by functionally integrating the trace anomaly.

〈Tνμ〉renof the quantized conformal fields in the Unruh state in Schwarzschild spacetime

The renormalized expectation value of the stress energy tensor of the conformally invariant massless fields in the Unruh state in the Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in conformal space and utilizing the regularity conditions in the physical metric. The relations of obtained results to the existing approximations are analysed.

One-loop quantum gravity in Schwarzschild space-time.

The quantum theory of linearized perturbations of the gravitational field of a Schwarzschild black hole is presented. The fundamental operators are seen to be the perturbed Weyl scalars $\dot\Psi_0$ and $\dot\Psi_4$ associated with the Newman-Penrose description of the classical theory. Formulae are obtained for the expectation values of the modulus squared of these operators in the Boulware, Unruh and Hartle-Hawking quantum states. Differences between the renormalized expectation values of both $\bigl| \dot\Psi_0 \bigr|^2$ and $\bigl| \dot\Psi_4 \bigr|^2$ in the three quantum states are evaluated numerically.

Renormalized electromagnetic stress tensor for an evaporating black hole.

The renormalized quantum stress tensor for an electromagnetic field in the Unruh state in Schwarzschild space-time is calculated.Received 14 August 1990DOI:https://doi.org/10.1103/PhysRevD.43.4142©1991 American Physical Society

Approximate stress-energy tensor for evaporating black holes.

We approximate the Israel-Hartle-Hawking and Unruh stress-energy tensors of quantum fields in the neighborhood of a static Schwarzschild black hole. The approximate tensors are constructed from the conservation equations in the ultrastatic optical metric of the black hole and the expected regularity properties at the horizon, in the respective vacua. Our scheme reproduces the approximation of Page, Brown, and Ottewill for the Israel-Hartle-Hawking vacuum and yields a tensor for the Unruh state. The latter exhibits the correct behavior at infinity and predicts luminosities in good agreement with numerical calculations.

Quantum state for a black hole in a de Sitter universe

The analogous of the Unruh state is discussed for a black hole in a de Sitter universe. The influence of the surrounding universe on the quantum properties of the hole is examined.

The quantum stress tensor and the Unruh state conditions

Four physical requirements are imposed on 〈T ab 〉 and its behaviour investigated in a two-dimensional background space-time of Bardeen’s type.