arXiv:gr-qc/9804032v5 30 Apr 1998 〈φ 2 〉 in the Spacetime of a Cylindrical Black Hole Andrew DeBenedictis ∗ Department of Physics Simon Fraser University, Burnaby, B.C., Canada V5A 1S6 March 23, 1998 Abstract The renormalised value of 〈φ 2 〉 is calculated for a massless, confor- mally coupled scalar field in the Hartle-Hawking vacuum state. This calculation is a first step towards the calculation of the gravitational back reaction of the field in a black cosmic string spacetime which is asymptotically anti-DeSitter and possesses a non constant dilaton field. It is found that the field is divergence free throughout the space- time and attains its maximum value near the horizon. 1 Introduction A useful question to ask when one studies quantum fields in General Relativity is the following: Given that all matter is inherently quantum in nature, will quantum effects remove the singularity at the centre of a black hole spacetime? To answer this question using a scalar field and semi-classical perturbation theory, one must first calculate the expectation value 〈T µν 〉 where T µν is the stress-energy tensor operator of the scalar field φ. In this paper 〈φ 2 〉 is computed in preparation for the computation of 〈T µν 〉 which is used as the source term for the Einstein field equations: * e-mail:adebened@sfu.ca 1