Renormalized Energy Momentum Tensor Research Articles

Aspects of the BTZ black hole interacting with fields

We show that there is no superradiance for the Dirac field in the rotating BTZ black hole if the field vanishes at infinity. Then we outline the calculation of the expression for the renormalized energy–momentum tensor, the effective action as well as the heat kernel for the Dirac field for the BTZ black hole. Finally, we point out how to construct the Hartle–Hawking–Israel state for the real scalar field in the non-rotating BTZ black hole in two and three dimensions.

Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime

Recent work in the literature has studied rigid Casimir cavities in a weak gravitational field, or in de Sitter spacetime, or yet other spacetime models. The present review paper studies the difficult problem of direct evaluation of scalar Green functions for a Casimir-type apparatus in de Sitter spacetime. Working to first order in the small parameter of the problem, i.e. twice the gravity acceleration times the plates’ separation divided by the speed of light in vacuum, suitable coordinates are considered for which the differential equations obeyed by the zeroth- and first-order Green functions can be solved in terms of special functions. This result can be used, in turn, to obtain, via the point-split method, the regularized and renormalized energy–momentum tensor both in the scalar case and in the physically more relevant electromagnetic case.

Spontaneously broken conformal symmetry: dealing with the trace anomaly

The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance. At the same time any realistic theory must contain gravity and is thus non-renormalizable. We show that discarding the renormalizability it is possible to construct viable models allowing to preserve the scale invariance at the quantum level. We present explicit one-loop computations for two toy models to demonstrate the main idea of the approach. Constructing the renormalized energy momentum tensor we show that it is traceless, meaning that the conformal invariance is also preserved.

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ ≠ 0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g μ , ν ρ with ρ > 0 , thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p ⩽ 0 .

Scalar Casimir effect on a D-dimensional Einstein static universe

We compute the renormalized energy–momentum tensor of a free scalar field coupled to gravity on an (n + 1)-dimensional Einstein static universe (ESU), , with arbitrary low energy effective operators (up to mass dimension n + 1). A generic class of regulators is used, together with the Abel–Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalized for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalized energy density and a quantity σ which determines if the strong energy condition holds for the ‘quantum fluid’. We briefly discuss the quantum fluid backreaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a ‘Casimir stabilization of Einstein static universes’.

Casimir energy and a cosmological bounce

We review different computation methods for the renormalized energy–momentum tensor of a quantized scalar field in an Einstein static universe. For the extensively studied conformally coupled case, we check their equivalence; for different couplings, we discuss violation of different energy conditions. In particular, there is a family of masses and couplings which violate the weak and strong energy conditions but do not lead to spacelike propagation. Amongst these cases is that of a minimally coupled massless scalar field with no potential. We also point out a particular coupling for which a massless scalar field has vanishing renormalized energy–momentum tensor. We discuss the backreaction problem and in particular the possibility that this Casimir energy could both source a short inflationary epoch and avoid the big bang singularity through a bounce.

A remark on alpha vacua for quantum field theories on de Sitter space

It is shown that the so-called $\alpha$-vacua which have been proposed as candidates for states of free quantum fields on de Sitter space have infinitely strong fluctuations for typical observables as averaged renormalized energy momentum tensor.

Interacting Field Theories in Robertson-Walker Spacetimes: Analytic Approximations

The renormalization of a scalar field theory with a quartic self-coupling via adiabatic regularization in a Robertson-Walker spacetime is discussed. The adiabatic counterterms are presented in a way that is most conducive to numerical computations. A variation of the adiabatic regularization method is presented which leads to analytic approximations for the energy–momentum tensor of the quantum field and the quantum contribution to the effective mass of the mean field. Conservation of the energy–momentum tensor for the field is discussed and it is shown that the part of the energy–momentum tensor which depends only on the mean field is not conserved but the full renormalized energy–momentum tensor is conserved, as expected and required by the semiclassical Einstein's equation. It is also shown that if the analytic approximations are used the resulting approximate energy–momentum tensor is conserved. This allows a self-consistent backreaction calculation to be performed using the analytic approximations. The usefulness of the approximations is discussed.

Vacuum polarization of a complex automorphic scalar field in two-dimensional spacetime with closed null geodesics and the time-machine problem

A quantized automorphic scalar field in two-dimensional spacetime with closed null geodesics (Cauchy horizon) is considered. The renormalized energy—momentum tensor 〈Tμv〉ren is obtained. It is shown that for specific values of the automorphic parameter 〈Tμv〉ren remains regular on the Cauchy horizon.