-
10
-
-
85035238361
-
-
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
-
-
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
-
-
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
-
-
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
-
-
private communication
-
U. Yurtsever (private communication).
-
-
-
Yurtsever, U.1
-
40
-
-
85035235683
-
-
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
-
-
private communication
-
A. Borde (private communication).
-
-
-
Borde, A.1
-
43
-
-
0009400718
-
-
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
-
-
The authors are grateful to A. Borde for this remark
-
The authors are grateful to A. Borde for this remark.
-
-
-
|