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

Lanir, Assaf; Levi, Adam; Ori, Amos; Sela, Orr

doi:10.1103/physrevd.97.024033

Cited by 47 publications

(53 citation statements)

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“…Method of computation of Φ 2 ren We use here the mode-sum expression derived in Ref. [26] for the TPF, to which we apply the θ-splitting variant [19] of the PMR method. In this treatment, we follow the same procedure used in Sec.…”

Section: Supplemental Materialsmentioning

confidence: 99%

“…The required input for the computation of Φ 2 ren inside the BH is the radial function ψ ωl (r) and also ρ up ωl , namely the reflection coefficient for the "up" modes (see e.g. [26]) outside the BH. We compute ψ ωl (r) and ρ up ωl numerically, and use them to construct the mode contributions to the two-point function inside the BH, as prescribed in Ref.…”

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confidence: 99%

“…Trace of the stress tensor: For a minimally coupled massless scalar field, the RSET trace T µ µ ren is uniquely determined [26] by Φ 2 (x) ren via T µ µ ren = − The local term only depends on the background metric, which is perfectly regular at the IH. Therefore the singular piece of T µ µ ren is fully described by the D'Alembertian term.…”

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Analysis of quantum effects inside spherical charged black holes

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We numerically compute the renormalized expectation value Φ 2 ren of a minimally-coupled massless quantum scalar field in the interior of a four-dimensional Reissner-Nordstrom black hole, in both the Hartle-Hawking and Unruh states. To this end we use a recently developed mode-sum renormalization scheme based on covariant point splitting. In both quantum states, Φ 2 ren is found to approach a finite value at the inner horizon (IH). The final approach to the IH asymptotic value is marked by an inverse-power tail r −n * , where r * is the Regge-Wheeler "tortoise coordinate", and with n = 2 for the Hartle-Hawking state and n = 3 for the Unruh state. We also report here the results of an analytical computation of these inverse-power tails of Φ 2 ren near the IH. Our numerical results show very good agreement with this analytical derivation (for both the power index and the tail amplitude), in both quantum states. Finally, from this asymptotic behavior of Φ 2 ren we analytically compute the leading-order asymptotic behavior of the trace T µ µ ren of the renormalized stress-energy tensor at the IH. In both quantum states this quantity is found to diverge like b(r − r−) −1 r −n−2 * (with n specified above, and with a known parameter b). To the best of our knowledge, this is the first fully-quantitative derivation of the asymptotic behavior of these renormalized quantities at the inner horizon of a four-dimensional Reissner-Nordstrom black hole.

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Analysis of quantum effects inside spherical charged black holes

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“…Similar to [75], and analogously to (117), the symmetrized two-point function in the Hartle-Hawking state can be expressed as…”

Section: Comparison With the Btz Black Holementioning

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Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime

Hollands

Wald

Zahn

2020

Class. Quantum Grav.

116

134

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In classical General Relativity, the values of fields on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under consideration extends beyond this domain of dependence, and fields, therefore, are not entirely determined by their initial data. This occurs, for example, in the well-known (maximally) extended Reissner-Nordström or Reissner-Nordström-deSitter (RNdS) spacetimes. The boundary of the region determined by the initial data is called the "Cauchy horizon." It is located inside the black hole in these spacetimes. The strong cosmic censorship conjecture asserts that the Cauchy horizon does not, in fact, exist in practice because the slightest perturbation (of the metric itself or the matter fields) will become singular there in a sufficiently catastrophic way that solutions cannot be extended beyond the Cauchy horizon. Thus, if strong cosmic censorship holds, the Cauchy horizon will be converted into a "final singularity," and determinism will hold. Recently, however, it has been found that, classically this is not the case in RNdS spacetimes in a certain range of mass, charge, and cosmological constant. In this paper, we consider a quantum scalar field in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We find that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up with affine parameter, V , along a radial null geodesic transverse to the Cauchy horizon as T V V ∼ C/V 2 with C independent of the state and C = 0 generically in RNdS spacetimes. This divergence is stronger than in the classical theory and should be sufficient to convert the Cauchy horizon into a singularity through which the spacetime cannot be extended as a (weak) solution of the semiclassical Einstein equation. This behavior is expected to be quite general, although it is possible to have C = 0 in certain special cases, such as the BTZ black hole. arXiv:1912.06047v1 [gr-qc] 12 Dec 2019As we shall show in sec. 3, the behavior of the quantum stress tensor is determined by the trace anomaly and the continuity equation alone. We find that eq. (5) holds, with C ∼ κ 2 c − κ 2 − . Our arguments are technically rather 3 Our arguments rest on the assumption of regularity across the cosmological horizon, or the weaker condition that Tvv vanishes on the cosmological horizon, with v the "Killing parameter". This condition has a natural limit in RN, that of absence of radiation infalling from spatial infinity. It seems natural to discuss the behavior at the Cauchy horizon in terms of such asymptotic conditions, as without asymptotic conditions also the classical consideration of strong cosmic censorship becomes meaningless, as discussed for example in the Introduction to [12]: The domain of dependence of a compact achronal set in any globally hyperbolic spacetime has a Cauchy horizon, across which it is of course smoothly ex...

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“…Upon this background we introduce an (uncharged) minimally-coupled massless scalar quantum field Φ (x), obeying the (covariant) d'Alembertian equation, Φ = 0. We decompose the field into modes, which, owing to the symmetries of the metric, may be separated into e −iωt , spherical harmonics Y lm (θ, ϕ), and a function of r [42]. The latter is encoded in the radial function ψ ωl (r), satisfying:…”

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Quantum Fluxes at the Inner Horizon of a Spherical Charged Black Hole

2020

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In an ongoing effort to explore quantum effects on the interior geometry of black holes, we explicitly compute the semiclassical flux components Tuu ren and Tvv ren (u and v being the standard Eddington coordinates) of the renormalized stress-energy tensor for a minimally-coupled massless quantum scalar field, in the vicinity of the inner horizon (IH) of a Reissner-Nordström black hole. These two flux components turn out to dominate the effect of backreaction in the vicinity of the IH; and furthermore, their regularization procedure reveals remarkable simplicity. We consider the Hartle-Hawking and Unruh quantum states, the latter corresponding to an evaporating black hole. In both quantum states, we compute Tuu ren and Tvv ren in the vicinity of the IH for a wide range of Q/M values. We find that both Tuu ren and Tvv ren attain finite asymptotic values at the IH. These asymptotic values are found to be either positive or negative (or vanishing in-between), depending on the Q/M parameter. Note that having a nonvanishing Tvv ren at the IH implies the formation of a curvature singularity on its ingoing section, the Cauchy horizon. Motivated by these findings, we also take initial steps in the exploration of the backreaction effect of these semiclassical fluxes on the near-IH geometry.

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

Cited by 47 publications

References 30 publications

Analysis of quantum effects inside spherical charged black holes

Analysis of quantum effects inside spherical charged black holes

Quantum instability of the Cauchy horizon in Reissner–Nordström–deSitter spacetime

Quantum Fluxes at the Inner Horizon of a Spherical Charged Black Hole

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