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Erratum: Thin-shell wormholes supported by ordinary matter in Einstein-Gauss-Bonnet gravity[Phys. Rev. D 76, 087502 (2007)]
Martı́n G. Richarte and Claudio Simeone(Received 4 March 2008; published 7 April 2008)
DOI: 10.1103/PhysRevD.77.089903 PACS numbers: 04.20.Gz, 04.40.Nr, 99.10.Cd
In the paper [1] spherically symmetric thin-shell wormholes were studied in Einstein-Gauss-Bonnet gravity, and it waspointed out that for certain values of the parameters, thin-shell wormholes could be supported by matter not violating theenergy conditions. In particular, the result was reported for both null charge Q and null cosmological constant �, and forpositive values of the Gauss-Bonnet parameter �. However, this is not right, and the error comes from the equationnumbered there as (17). Errors in this equation propagate to those numbered there as (19) and (23). Once these equationsare corrected, it turns out that the conclusion about the existence of wormhole configurations supported by matter withpositive energy density still holds, but for Q � 0 and �< 0.
The right form of the equations mentioned above is, respectively,
S�� �1
8�
�6
�
b� 2�
�4
�3
b3 � 12�1� _b2��
b3
��; (17)
�0 � �1
8�
�6
�����������f�b0�
pb0
� 2������������f�b0�
q �4f�b0�
b30
�12
b30
��; (19)
� � �32�b
20
�����������f�b0�
q� 2��
�����������f�b0�
q�f�b0� � 3��; (23)
where b is the wormhole radius, the dot indicates a derivative with respect to the proper time, and b0 is the radius in the
static case in which we are interested; f is the function describing the original metric, and � ����������������������_b2 � f�b�
q.
Once the explicit form of the function f (with � � 0) is introduced, the condition �0 > 0 leads to
� 8�� 2b20 � b
20
�����������������������������������������1�
16M�
�b40
�8Q2�
3b60
vuut > 0; (E1)
which can be valid only for �< 0. If the singularity in the original manifold from which the construction starts is to be‘‘shielded’’ by the event horizon, we must restrict to ��>�M (see Ref. [8] in [1]). The subsequent analysis isconsiderably simplified by considering the critical value of charge given by Q2
c � 3j�M=�� � �j2; then there would beonly one horizon in the original manifold, its radius being independent of the charge: r2
hor � �M=�� � �. The point wouldthen be to achieve the condition above with b0 greater than the horizon radius and with ��>�M.
However, it can be shown that for values of � such that a singularity and a horizon exist, it is not possible to fulfillEq. (E1) for any wormhole radius greater than rhor; the reason is that a horizon exists for �>�M=�3��, which is notcompatible with the condition (E1) if b0 is greater than the corresponding horizon radius. Instead, a simple numericalanalysis shows that for � slightly smaller than �M=�3�� both the singularity at r > 0 and the horizon disappear in theoriginal manifold so the only condition to be imposed is that given by Eq. (E1). And for �< 0 one is always able to chooseb0 such that this is indeed fulfilled. Therefore, the conclusion of [1] (that it is possible to have matter with positive energydensity—and as a consequence, with positive total energy, because � is proportional to �0 —supporting a thin-shellwormhole) still holds, but with a non-null charge and a negative Gauss-Bonnet parameter.
[1] M. G. Richarte and C. Simeone, Phys. Rev. D 76, 087502 (2007).
PHYSICAL REVIEW D 77, 089903(E) (2008)
1550-7998=2008=77(8)=089903(1) 089903-1 © 2008 The American Physical Society