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

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 $⟨{\hat{T}}_{\mu \nu }{⟩}_{ren}$ and of $⟨{\hat{\Phi }}^2{⟩}_{ren}$ 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 $⟨{\hat{T}}_{\mu \nu }{⟩}_{ren}$ and of $⟨{\hat{\Phi }}^2{⟩}_{ren}$ in the Boulware state near the outer (event) horizon, and we obtain analytical expressions that correspond to previous numerical results.

23 pages, 1 figure; references and appendix added

References in corpus (8)

• Versatile method for renormalized stress-energy computation in black-hole spacetimes
• Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
• Stress Tensor from the Trace Anomaly in Reissner-Nordstrom Spacetimes
• Mode-sum regularization of $⟨{\varphi }^2⟩$ in the angular-splitting method
• Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole
• Renormalized stress-energy tensor for stationary black holes
• Numerical study of the gravitational shock wave inside a spherical charged black hole
• Inside an evaporating two-dimensional charged black hole

Cited by in corpus (16)

• Quantum Instability of the Cauchy Horizon in Reissner-Nordström-deSitter Spacetime
• Quantum fluxes at the inner horizon of a spherical charged black hole
• Analysis of quantum effects inside spherical charged black holes
• Semiclassical instability of inner-extremal regular black holes
• Holographic Probes of Inner Horizons
• Quantum Singularities
• Remarks on the thermofield double state in 4D black hole background
• Quantum (dis)charge of black hole interiors
• Hadamard renormalization for a charged scalar field
• Mode-sum renormalization of $⟨{\Phi }^2⟩$ for a quantum scalar field inside a Schwarzschild black hole
• Quantization of a charged scalar field on a charged black hole background
• A simple quantum test for smooth horizons
• The renormalized charged scalar current in the Reissner-Nordström-de Sitter spacetime
• Construction of the Unruh State for a Real Scalar Field on the Kerr-de Sitter Spacetime
• Regular Quantum States on the Cauchy Horizon of a Charged Black Hole
• Computation of $⟨{\Phi }^2⟩$ and quantum fluxes at the polar interior of a spinning black hole