Quantum effects near the Cauchy horizon of a Reissner-Nordstrom black hole

TL;DR

This paper analyzes quantum scalar fields near the horizons of Reissner-Nordstrom black holes, revealing weaker-than-expected divergences in quantum stress-energy and scalar expectation values, with implications for black hole interior stability.

Contribution

It provides analytical insights into the asymptotic behavior of quantum fields near black hole horizons, showing vanishing leading divergences in certain states and confirming previous numerical findings.

Findings

Leading divergences of quantum expectation values vanish near the inner horizon.

Analytical expressions for quantum effects near the outer horizon match previous numerical results.

Quantum vacuum effects may have a weaker impact on the black hole geometry than previously thought.

Abstract

We consider a massless, minimally-coupled quantum scalar field on a Reissner-Nordstrom black hole background, and we study the leading asymptotic behavior of the expectation value of the stress energy tensor operator $\langle\hat{T}_{\mu\nu}\rangle_{ren}$ and of $\langle\hat{\Phi}^{2}\rangle_{ren}$ near the inner horizon, in both the Unruh and the Hartle-Hawking quantum states. We find that the coefficients of the expected leading-order divergences of these expectation values vanish, indicating that the modifications of the classical geometry due to quantum vacuum effects might be weaker than expected. In addition, we calculate the leading-order divergences of $\langle\hat{T}_{\mu\nu}\rangle_{ren}$ and of $\langle\hat{\Phi}^{2}\rangle_{ren}$ in the Boulware state near the outer (event) horizon, and we obtain analytical expressions that correspond to previous numerical results.