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Schwarzschild Metric with Planck Length

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Michael R.R. Good, Eric V. Linder

General Relativity and Quantum Cosmology · Submitted 3 Mar 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The black hole has thermal particle production that leads to complete evaporation of the black hole, resulting in non-divergent entanglement entropy, Page curve turn-over, and an asymptotic quantum pure state with no information loss.

how it is stated · asserted 1.00 read the record →

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arXiv ID2003.01333 (version 1)
Pith IDYHSVA6DY, Pith's permanent record of this paper and its review
CitationEric V. Linder, Michael R.R. Good. "Schwarzschild Metric with Planck Length." arXiv:2003.01333 (2020). https://pith.science/paper/YHSVA6DY
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,036 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.30 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present a modified Schwarzschild solution for a model of evaporation of a black hole with information preservation. By drawing a direct analogy to the quantum pure accelerating mirror (dynamical Casimir effect of a 1D horizon), we derive a Schwarzschild metric with not only the usual Schwarzschild radius but an additional length scale related to the Planck length. The black hole has thermal particle production that leads to complete evaporation of the black hole, resulting in non-divergent entanglement entropy, Page curve turn-over, and an asymptotic quantum pure state with no information loss.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a modified Schwarzschild solution for a model of evaporation of a black hole with information preservation. contribution 1.00 0.93 0.23 asserted 0.99
s1 By drawing a direct analogy to the quantum pure accelerating mirror (dynamical Casimir effect of a 1D horizon), we derive a Schwarzschild metric with not only the usual Schwarzschild radius but an additional length scale related to the Planck length. method 0.79 0.94 0.12 asserted 1.00
s2 The black hole has thermal particle production that leads to complete evaporation of the black hole, resulting in non-divergent entanglement entropy, Page curve turn-over, and an asymptotic quantum pure state with no information loss. result 0.97 0.84 0.80 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • figures and tables
  • references and citing sentences
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a modified Schwarzschild solution for a model of evaporation of a black hole with information preservation. By drawing a direct analogy to the quantum pure accelerating mirror (dynamical Casimir effect of a 1D horizon), we derive a Schwarzschild metric with not only the usual Schwarzschild radius but an additional length scale related to the Planck length. The black hole has thermal particle production that leads to complete evaporation of the black hole, resulting in non-divergent entanglement entropy, Page curve turn-over, and an asymptotic quantum pure state with no information loss.

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How the literature uses it

11 arXiv papers cite this in 15 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Compares with it 2 papers
  • The model still produces an infinite total particle count in contrast to asymptotic zero velocity (static) mirrors like that proposed by Walker and Davies [ref] , or the `Schwarzschild mirror with quantum purity' model [ref] , which yield finite total particle count $N$.

    Accelerating boundary analog of a Kerr black hole · Extremal Kerr · 1.00

  • Infinite total particle emission is not a property of asymptotic zero velocity (static) mirrors like the Walker-Davies model [ref] , or the `Schwarzschild mirror with quantum purity' model [ref] , which yield finite total particle count $N$.

    Hawking radiation particle spectrum of a Kerr-Newman black hole · Extremal Kerr-Newman · 1.00

Cites it as background 7 papers
  • The ABC has been explored for several known solutions, including Schwarzschild [ref] , Reissner-Nordström [ref] , and Kerr [ref] , reducing the complexity of particle creation in higher dimensional curved spacetimes to a simple flat (1+1)-dimensional spacetime (e.g. see the remarkable simplicity afforded in the non-relativistic regime [ref] ) of an accelerating mirror slicing through the vacuum, even in the case of unitary evolution [ref] , see also e.g. the Schwarzschild-Planck trajectory [ref] .

    Upon the horizon's verge: Thermal particle creation between and approaching horizons · Introduction · 0.85

  • Recall that in the original Schwarzschild-Planck mirror analysis [ref] , the conjecture was that the new length scale was related to the Planck length, with $g∝1/l_Pl$.

    IR-finite thermal acceleration radiation · Meaning of Large-$g$ · 0.89

  • Traditionally, e.g. [ref] , and recently, e.g. [ref] , moving mirror models in $(1+1)$-dimensions are employed to study properties of Hawking radiation for black holes.

    Electron as a Tiny Mirror: Radiation From a Worldline With Asymptotic Inertia · Elements of Electrodynamics: Energy From Moving Electrons · 0.97

What it cites · 25 sentences without a confident label

Uses the method or tool of 1 paper
  • One of the powerful aspects of the quantum pure black mirror is the analytic expression for the Bogolyubov beta coefficients [ref] , allowing simple computation of the particle production properties (e.g. the spectrum [ref] ).

    Remnant-free Moving Mirror Model for Black Hole Radiation Field · Particle Production · 0.80

Cites as support 5 papers
Cites as background 2 papers

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