Particle Creation by Black Holes

• p. 22 Reference 23

  Eardley, D., Sachs, R. K.: J. Math. Phys. 14 (1973)

Only the authors can say what is right here.

Judge's note: The page 22 image shows no page number in this entry, unlike the other journal references. Minor bibliographic omission; the page cannot be supplied from the files.

Second check: another model agreed

• p. 22 Reference 18

  Bjorken,T.D., Drell,S.D.: Relativistic quantum mechanics

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the author of "Relativistic Quantum Mechanics" (McGraw Hill) is J. D. Bjorken. The page 22 image does print "Bjorken, T. D.", but nothing in the files establishes the correct initials.

Second check: another model agreed

• p. 1 Abstract

  ≈10^-6 (M☉/M) °K

• p. 3 Section 1, last paragraph

  the order of 10^26 M^-1 °K, where M is the mass, in grams of the black hole. For a black hole of solar mass (10^33 g)

• p. 3 Section 1, last paragraph

  the order of 10^26 M^-1 °K, where M is the mass, in grams of the black hole

• p. 3 Section 1, last paragraph

  a black hole of solar mass (10^33 g)

Only the authors can say what is right here.

Judge's note: Read the abstract on p1 and the last paragraph of p3 on the page images; both are printed as quoted. With the paper's own solar mass of 10^33 g the abstract's form is 10^27/M °K against 10^26/M °K in the introduction. Page 4 ("about 10^12 °K ... mass got down to about 10^14 g") follows the 10^26 form. Both are order-of-magnitude statements ("≈", "of the order of") and no text reconciles them, so this is a real but loose inconsistency that only the author can settle.

Second check: another model agreed

• p. 5 Section 1, unnumbered equation after the black-hole first law

  dU = TdS + pdV

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: the standard first law, with p the pressure and V the volume, is dU = TdS − pdV. The p5 image prints a plus sign. The paper does not define p or V or state a sign convention, and the equation serves only as an analogy to dM = (κ/8π)dA + ΩdJ, so the argument is unaffected.

Second check: another model agreed

• p. 17 Section 4, first paragraph

  since all the time dependence of the metric in Fig. 4 is in the collapsing phase

• p. 10 Fig. 4 caption

  The solution pω of the wave equation has an infinite number of cycles near the event horizon

• p. 7 Fig. 3 caption

  The Penrose diagram of a spherically symmetric collapsing body producing a black hole.

• p. 17 Section 4, first paragraph

  all the time dependence of the metric in Fig. 4 is in the collapsing phase

Judge's note: Viewed Fig. 4 (page 10) and Fig. 3 (page 7). Fig. 3 is the captioned Penrose diagram of the collapsing body. Fig. 4 redraws the same collapse spacetime (collapsing body, event horizon, scri±) with constant-phase surfaces added, so a reference to "the metric in Fig. 4" is defensible. Either figure could be intended; not a demonstrable pointer error.

Second check: another model agreed

• p. 9 Eq. (2.9) and Eq. (2.10)

  a_i|0> = 0 for all i.

• p. 9 Eq. (2.10)

  <0_-|b_i† b_i|0_-> = Σ_j |β_ij|^2

• p. 20 Eq. (4.5)

  <0_-|T_ab|0_->

Judge's note: The p9 image shows |0> in the sentence and in Eq. (2.9), and |0_-> in Eq. (2.10) immediately below. The p20 image shows |0_-> in Eq. (4.5). A text search found no definition of |0_->. The meaning (vacuum on past null infinity) is evident, so this is a notational inconsistency only.

Second check: another model agreed

• p. 14 Eq. (2.30)

  − (iω/κ)(log(v0−v) − logH)

• p. 11 Eq. (2.17)

  − (ω/κ)(log(v0−v) − logD − logC)

Only the authors can say what is right here.

Judge's note: The p14 image shows the factor i in (2.30). Eq. (2.31) then writes L exp{−(iω/κ)[log(v0−v) − log H]}, so (2.30) as printed is the exponent, not the phase. The p11 image shows (2.17) real, with the i appearing only in the exponential (2.18). A notational slip; the results (2.31) to (2.33) are unaffected.

Second check: another model agreed

• p. 2 Section 1, last paragraph

  Let B be the least upper bound |R_abcd| in any orthonormal tetrad

Judge's note: The p2 image prints "Let B be the least upper bound |R_abcd| in any orthonormal tetrad" with no "of" after "bound". Cosmetic omission.

Second check: none (judge only)

• p. 5 First paragraph

  it can have a diverging effection a null surface

• p. 5

  Thus it can have a diverging effection a null surface

Judge's note: The p5 image prints "diverging effection a null surface like the event horizon". It is in the print, not an extraction artefact.

Second check: none (judge only)

• p. 5 Last paragraph

  Beckenstein [19] suggested

• p. 22 References 19, 20

  Beckenstein, J. D.: Phys. Rev. D. 7, 2333—2346 (1973)

• p. 5 Section 1

  Beckenstein [19] suggested that A and κ

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: the author of Phys. Rev. D 7, 2333 (1973) spells his name Bekenstein. The page images (p5 text, p22 references 19 and 20) print "Beckenstein" in all four places, consistently, so nothing inside the paper contradicts it.

Second check: none (judge only)

• p. 6 Fig. 1

  r = 2m

• p. 6 Text describing Fig. 1

  the two diagonal lines r=2M

Judge's note: Fig. 1 is on PDF p7 (journal p205); its label reads "r = 2m" with a lower-case m in the image. The text and Eq. (2.1) on p6 use 2M. The crop C006-a shows only the p6 text, not the figure. Lettering inconsistency in the figure; the meaning is clear.

Second check: none (judge only)

• p. 6 Section 2, last line of page

  the metric is that of the Schwarzchild solution

• p. 6 Section 2, before Eq. (2.1)

  Schwarzschild solution with metric

• p. 21 Section 4

  the Schwarzchild radius

• p. 21 Section 4

  time for light to cross the Schwarzchild radius

Judge's note: The p6 image shows "Schwarzschild" twice in the body and "Schwarzchild" in the last line. The figure captions on p7 use "Schwarzschild"; pp. 7, 9, 10, 11, 14 images and the text layer for later pages show "Schwarzchild". Internal spelling inconsistency.

Second check: none (judge only)

• p. 6 Section 2, first paragraph

  The Kerr-Newman solution represent one such family

Judge's note: The p6 image prints "The Kerr-Newman solution represent one such family of black hole equilibrium states". Grammatical slip; "solutions represent" is likely intended, given "one of these solutions" in the following sentence.

Second check: none (judge only)

• p. 10 Text before Eq. (2.16)

  transport the pair (l^a, n^a) back along to the point where

Only the authors can say what is right here.

Judge's note: The p10 image prints "back along to the point". The preceding text introduces the generator γ, so "back along γ" is probably intended. It could be read as loose English, so this is put as a query.

Second check: none (judge only)

• p. 16 Section 3, second paragraph

  consider first the case of an unchanged, rotating black hole

• p. 16

  consider first the case of an unchanged,

Judge's note: The p16 image prints "unchanged, rotating black hole". The next paragraph begins "One can treat a charged non-rotating black hole", and the section covers angular momentum and charge, so "uncharged" is evidently intended.

Second check: none (judge only)

• p. 16 Section 3, last paragraph

  the charge on the black will reduce the surface gravity

• p. 16 Section 3, paragraph before Eq. (3.5)

  the charge on the black will reduce the surface gravity k

• p. 16

  except that the charge on the black will reduce the surface gravity

Judge's note: The p16 image prints "the charge on the black will reduce the surface gravity k and hence the temperature of the black hole". "hole" is missing after the first "black", and the surface gravity is set as an italic k, not the κ used in Eq. (3.4) on the same page.

Second check: none (judge only)

• p. 16 Section 3, after Eq. (3.4)

  the only particle emission occurs is

• p. 16 Section 3, paragraph after Eq. (3.4)

  the only particle emission occurs is an amount

Judge's note: The p16 image prints "the only particle emission occurs is an amount ∓Γ_jnlm in the modes for which ω<mΩ". A word is missing ("that occurs") or surplus.

Second check: none (judge only)

• p. 16 Section 3, after Eq. (3.4)

  Starobinski [16]

• p. 22 Reference 16

  Starobinsky, A. A.: Zh. E.T.F. 64, 48 (1973)

• p. 16 Section 3, paragraph after Eq. (3.4)

  Starobinski [16] and Unruh [29]

Judge's note: The p16 image prints "Starobinski [16] and Unruh [29]". The p22 image prints "Starobinsky" in references 16, 17 and 30. Both are transliteration variants; the inconsistency is internal to the paper.

Second check: none (judge only)

• p. 17 Section 3, after Eq. (3.6)

  "guage invariant" phase

• p. 17 Section 3, first line of page

  is not gauge-invariant

• p. 17 Section 3, after Eq. (3.6)

  An infinitessimal vector z^a will connect points with a "guage invariant" phase

Judge's note: Read the page 17 image: I count eight occurrences of "guage" and one correct "gauge-invariant" in the first line. Plain misspelling.

Second check: none (judge only)

• p. 17 Section 3, after Eq. (3.6)

  An infinitessimal vector

Judge's note: Printed with a double s on the page 17 image, after Eq. (3.6). A separate misspelling from "guage" (C018), so kept as its own item.

Second check: none (judge only)

• p. 18 Section 4, paragraph after Eq. (4.1)

  particles in each mode. pω by producing an (ω')^-1 tail

• p. 18 Section 4, paragraph after Eq. (4.1)

  particles in each mode. pω by producing an (ω′)^-1 tail

Judge's note: The page 18 image shows a full stop after "mode" at the line end, and the next line begins with "p_ω by producing", which is a fragment unless joined to the preceding sentence.

Second check: none (judge only)

• p. 20 After Eq. (4.10)

  is the fraction of wave-packet of frequency that would be

• p. 20 Section 4, after Eq. (4.10)

  is the fraction of wave-packet of frequency that would be absorbed

Judge's note: On the page 20 image nothing is printed between "frequency" and "that". The sentence defines Γ_ω, so the omitted symbol is ω.

Second check: none (judge only)

• p. 21 Section 4, last paragraph

  is of the order the Planck length

Judge's note: Printed as quoted in the last paragraph of the page 21 image.

Second check: none (judge only)

• p. 22 Reference 9

  Mon, Not. Roy. astr. Soc. 152

• p. 22 Reference 10

  Monthly Notices Roy. Astron. Soc. 168

Judge's note: The page 22 image prints the comma in "Mon, Not.". The differing abbreviation in reference 10 is a style inconsistency; the comma is a plain typo.

Second check: none (judge only)

• p. 22 Reference 15

  Press,W.M., Teukolsky,S.A.: Nature 238, 211 (1972)

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the first author of the Nature 238, 211 (1972) paper is William H. Press (initials W.H., not W.M.). The crop of page 22 clearly shows "Press, W. M." as printed, so the quote is accurate and not an extraction artefact. A search of the article text finds no other mention of Press to compare the initials against, so the files alone cannot establish the correct initials.

Second check: none (judge only)