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Volumn 53, Issue 4, 1996, Pages 1988-2000

Averaged energy conditions and evaporating black holes

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EID: 0001213221     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.53.1988     Document Type: Article
Times cited : (53)

References (47)
  • 10
    • 85035238361 scopus 로고    scopus 로고
    • Note that in a general spacetime, unlike the relation between the local null and weak energy conditions, ANEC does not simply follow by continuity from AWEC. An example of this is illustrated in Sec. refsec:2DEVAP for the Unruh vacuum state
    • Note that in a general spacetime, unlike the relation between the local null and weak energy conditions, ANEC does not simply follow by continuity from AWEC. An example of this is illustrated in Sec. refsec:2DEVAP for the Unruh vacuum state.
  • 22
    • 85035206455 scopus 로고    scopus 로고
    • This particular choice was initially made in Ref. citeF91 purely for mathematical convenience. Presumably, one could prove analogous inequalities with other choices of sampling functions
    • This particular choice was initially made in Ref. citeF91 purely for mathematical convenience. Presumably, one could prove analogous inequalities with other choices of sampling functions.
  • 32
    • 85035225052 scopus 로고    scopus 로고
    • Note that this expression differs somewhat in form from Eq. (refeq:TLQI2DUNCP). However, the latter is an inequality valid for all quantum states in 2D Minkowski spacetime, whereas the integral in Eq. (refeq:intT) is evaluated for a restricted class of geodesics in a specific quantum state in Schwarzschild spacetime. Note also that the right hand side of Eq. (refeq:intT) is more negative than the right hand side of Eq. (refeq:TLQI2DUNCP). This is presumably due to the integration over a half complete geodesic in Eq. (refeq:intT); even in Minkowski spacetime, there exist states for which Eq. (refeq:TLQI2DUNCP) would not be true if the integration were taken only over a half geodesic
    • Note that this expression differs somewhat in form from Eq. (refeq:TLQI2DUNCP). However, the latter is an inequality valid for all quantum states in 2D Minkowski spacetime, whereas the integral in Eq. (refeq:intT) is evaluated for a restricted class of geodesics in a specific quantum state in Schwarzschild spacetime. Note also that the right hand side of Eq. (refeq:intT) is more negative than the right hand side of Eq. (refeq:TLQI2DUNCP). This is presumably due to the integration over a half complete geodesic in Eq. (refeq:intT); even in Minkowski spacetime, there exist states for which Eq. (refeq:TLQI2DUNCP) would not be true if the integration were taken only over a half geodesic.
  • 34
    • 0004057466 scopus 로고
    • University of Chicago Press, Chicago
    • R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
    • (1984) General Relativity
    • Wald, R.M.1
  • 36
    • 85035225009 scopus 로고    scopus 로고
    • private communication
    • U. Yurtsever (private communication).
    • Yurtsever, U.1
  • 40
    • 85035235683 scopus 로고    scopus 로고
    • The form of Eq. (refeq:awec/qi 4D) is motivated by the following considerations: If we imagine a sequence of observers shot outward with increasing values of k, then (formula presented) propto (formula presented) and δ τ propto (formula presented), so (formula presented) dτ propto ((formula presented))(formula presented) propto (δ τ)(formula presented). The factor of (formula presented) is required in order for the dimensions to be correct. This form is also suggested by the form of the inequality found for orbiting null geodesics, Eq. (refeq:ANECINQ 1norbit)
    • The form of Eq. (refeq:awec/qi 4D) is motivated by the following considerations: If we imagine a sequence of observers shot outward with increasing values of k, then (formula presented) propto (formula presented) and δ τ propto (formula presented), so (formula presented) dτ propto ((formula presented))(formula presented) propto (δ τ)(formula presented). The factor of (formula presented) is required in order for the dimensions to be correct. This form is also suggested by the form of the inequality found for orbiting null geodesics, Eq. (refeq:ANECINQ 1norbit).
  • 42
    • 85035212106 scopus 로고    scopus 로고
    • private communication
    • A. Borde (private communication).
    • Borde, A.1
  • 43
    • 0009400718 scopus 로고
    • See, footnote 2 of, Society for Industrial and Applied Mathematics, Philadelphia, for an interesting example with timelike geodesics
    • See p. 56, footnote 2 of R. Penrose, Techniques of Differential Topology in Relativity (Society for Industrial and Applied Mathematics, Philadelphia, 1972), for an interesting example with timelike geodesics.
    • (1972) Techniques of Differential Topology in Relativity , pp. 56
    • Penrose, R.1
  • 46
    • 85035243569 scopus 로고    scopus 로고
    • The authors are grateful to A. Borde for this remark
    • The authors are grateful to A. Borde for this remark.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.