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In [1], we examined the effects of dark energy on the gravitational energy for the quintessential charged-Kerr black holes by approximate Lie symmetry approach. It was shown that the gravitational energy of the charged-Kerr black hole spacetime surrounded by dark energy decreased due to the presence of the cosmological constant (
$ {\omega}_{c}=-1 $ ) and quintessence dark energy ($ {\omega}_{q}=-\dfrac{2}{3} $ ) [1]. Whereas, for the case of frustrated network of cosmic strings ($ {\omega}_{n}=-\dfrac{1}{3} $ ) the contribution in energy of the charged-Kerr black hole due to the presence of dark energy term$ E_{n} $ was observed to be positive for different values of dark energy parameterα(as shown in FIG. 7.) while FIG. 8. shows the effect of dark energy with different values of spina. We observed there, that if the dark energy parameterαis initially small, then the value of$ E_{n} $ will increase primarily and then it showed a gradual decline for the larger values ofα[1]. This result needs correction.Therefore in this corrigendum, we present the effects of dark energy on the energy content of the charged-Kerr black hole surrounded by the dark energy for
$ {\omega}_{n}=-\frac{1}{3} $ . It is observed that at this value of the equation of state parameter, the presence of the dark energy first decreases the energy content of the charged-Kerr black hole surrounded by the dark energy and then increases the energy. This is shown by the graphical results. -
As shown in [1], in the case of
$ {\omega}_{n}=-\frac{1}{3} $ , we get the following re-scaling factor of energy for the charged-Kerr spacetime surrounded by dark energy$ M_{C-K-n}=\frac{M}{2{r}}\Bigg[1-\frac{{Q}^2}{2{M}^2}\Bigg]+\frac{3Ma}{4r^{2}}+\frac{M\alpha}{2r}\Bigg[\frac{1}{1-\alpha}-\frac{a}{2r}\Bigg] $
(1) It was observed, for
$ {\omega}_{n}=-\frac{1}{3} $ , the total energy in the charged-Kerr spacetime surrounded by dark energy varies from the energy in the charged-Kerr spacetime by the following expression [1]$ {E}_{n}=\frac{M\alpha}{2r}\Bigg[\frac{1}{1-\alpha}-\frac{a}{2r}\Bigg] $
(2) In order to analyze the significant features of dark energy, we sketch the expression
$ (2) $ versusαand radial distancer.FromFIG. 1, it is observed that for some values ofαand for smaller values ofrthe value of
$ E_{n} $ is negative which shows that it decreases the energy content of the underlying spacetime, and for some values ofαand relatively bigger values ofr, the value of$ E_{n} $ is positive and hence increases the energy content of the CK spacetime (as evident from (1)). Hence, we observe that the contribution of dark energy term for$ {\omega}_{n}=-\dfrac{1}{3} $ , first decreases the total energy of the underlying spacetime for smaller values of radial coordinaterand then increases for comparatively larger values ofr.FIG. 2depicts the increasing behavior of$ E_{n} $ for different values of spin parametera.
Figure 1.(color online) plots showing the behavior of
$ {E}_n $ for the quintessential charged-Kerr black hole for$ {\omega}_{n}=-\dfrac{1}{3} $ with different values ofαand a fixed value of$ M=1 $ ,$ a=0.4 $ .
Figure 2.(color online) plots showing the behavior of
$ {E}_n $ for the quintessential charged-Kerr black hole for$ {\omega}_{n}=-\dfrac{1}{3} $ with different values ofa,$ 0<\alpha<1/2 $ and a fixed value of$ M=1 $ and$ r=0.4 $ .Therefore, in view of the above discussion it is concluded that the result given in [1] must be stated as
Remark:The effect of cosmological constant and quintessence decreases the energy of the charged-Kerr black hole surrounded by dark energy, whereas the effect of a frustrated network of cosmic strings decreases the energy of the charged-Kerr black hole surrounded by dark energy for some values ofαand for smaller values ofrand increases the energy for some values ofαand relatively bigger values ofras evident from
$ (1) $ .
Erratum: Corrigendum to "Effect of dark energy models on the energy content of charged and rotating black holes" [Chinese Phys. C, 46 (2022) 015101]
- Received Date:2023-08-18
- Available Online:2023-12-15
Abstract:In Liaqat and Hussain (2022) it was proved that the effect of dark energy with
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