English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive explicit expressions for the two-point function of a masslessscalar field in the interior region of a Reissner-Nordstrom black hole, in boththe Unruh and Hartle-Hawking quantum states. The two-point function isexpressed in terms of the standard $lm\omega$ modes of the scalar field (thoseassociated with a spherical harmonic $Y_{lm}$ and a temporal mode $e^{-i\omegat}$), which can be conveniently obtained by solving an ordinary differentialequation, the radial equation. These explicit expressions are the internalanalogs of the well known results in the external region (originally derived byChristensen and Fulling), in which the two-point function outside the blackhole is written in terms of the external $lm\omega$ modes of the field. Theyallow the computation of $<\Phi^{2}>_{ren}$ and the renormalized stress-energytensor inside the black hole, after the radial equation has been solved(usually numerically). In the second part of the paper, we provide an explicitexpression for the trace of the renormalized stress-energy tensor of aminimally-coupled massless scalar field (which is non-conformal), relating itto the d'Alembertian of $<\Phi^{2}>_{ren}$. This expression proves itselfuseful in various calculations of the renormalized stress-energy tensor.

Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole