Black Holes with a Cloud of Strings and Quintessence in a Non-Linear Electrodynamics Scenario
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The paper is fine, I have just two comments,
1, Tsolution that the author calls cloud of strings wasalso studied in
The Gravitational field of a hedgehog and the evolution of vacuum bubbles , E.I. Guendelman( A. Rabinowitz, Phys.Rev.D 44 (1991) 3152-3158, #4
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- there it was named string hedhehog, a more appropriate name for the solution as the configuration of radially oriented consists of a bunch of strings emanating from the origin , not a cloud at all..
2. the non linear gauge theory can produce the effects of the hedgehog or cloud of trings, a pure gauge theory, without other additions can account for these solutions, see
Black hole with confining electric potential in scalar-tensor description of regularized 4-dimensional Einstein-Gauss-Bonnet gravity, A. Övgün,
Physics Letters B
Volume 820, 10 September 2021, 136517
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- and references there
- After the authors take into account and add the information Iam providing, the paper can be published
Author Response
Comments 1: [
Tsolution that the author calls cloud of strings wasalso studied in
The Gravitational field of a hedgehog and the evolution of vacuum bubbles , E.I. Guendelman( A. Rabinowitz, Phys.Rev.D 44 (1991) 3152-3158, #4 there it was named string hedhehog, a more appropriate name for the solution as the configuration of radially oriented consists of a bunch of strings emanating from the origin , not a cloud at all.]
Response 1: [
In the late 1970s, Letelier obtained the solutions corresponding to a cloud of fundamental strings with cylindrical and spherical symmetry (Letelier, P. S. (1979). Clouds of strings in general relativity. Physical Review D, 20(6), 1294). In the case with spherical symmetry, Letelier obtained a metric corresponding to a black hole surrounded by a cloud of strings.
On the other hand, in the early 1990s, Guendelman and Rabinowitz obtained, through a different method, a mathematically identical solution which they called hedgehog black hole (Guendelman, E. I., & Rabinowitz, A. (1991). Gravitational field of a hedgehog and the evolution of vacuum bubbles. Physical Review D, 44(10), 3152).
We mentioned in the introduction of our paper the work of Guendelman and Rabinowitz, but maintained the nomenclature used by Letelier, since it is the way the theme was introduced in literature.]
Comments 2 : [
comment 2
- the non linear gauge theory can produce the effects of the hedgehog or cloud of trings, a pure gauge theory, without other additions can account for these solutions, see
Black hole with confining electric potential in scalar-tensor description of regularized 4-dimensional Einstein-Gauss-Bonnet gravity, A. Övgün,]
Response 2: [The gravitational effect of a cloud of strings (or hedgehog) can be obtained from different methods, like considering a nonlinear gauge theory or simply considering a topological defect in the solid angle. Although these methods induce the same metric, the physical principles behind them are different. We mentioned these alternatives in the introduction of our paper.]
Reviewer 2 Report
Comments and Suggestions for Authors
The manuscript finds exact black hole solutions to Einstein gravity coupled with a nonlinear electrodynamics field, in the presence of a cloud of strings and quintessence. They then discuss some aspects of these black holes, such as the energy conditions and the black hole thermodynamics. While the solutions seem correct, I have some comments and questions given as follows.
1) The authors claim that their black holes are asymptotically flat. As far as I can see, in the presence of a cloud of strings and quintessence, the spacetime is not asymptotically flat.
2) When spacetime is not asymptotically flat, how to define the mass in the present work? Is the mass in Eq.(52) the ADM mass?
3) For thermodynamic stability, the black holes have other thermodynamic variables, such as charge density. I suggest the authors give the first law of thermodynamics for their solutions.
4) Moreover, to check the local thermodynamic stability, one should consider the full Hessian matrix of the system. The heat capacity in Eq.(58) is only one element of the Hessian matrix.
Author Response
Comment 1: [1) The authors claim that their black holes are asymptotically flat. As far as I can see, in the presence of a cloud of strings and quintessence, the spacetime is not asymptotically flat.]
Response 1: [The referee is right. The metric is not asymptotically flat. We corrected this in the manuscript.]
Comment 2: [2) When spacetime is not asymptotically flat, how to define the mass in the present work? Is the mass in Eq.(52) the ADM mass?]
Response 2: [The ADM mass is obtained by integrating The total energy density. In The present case, this integration does not correspond to the mass that appears in Eq. (52). Thus, m is not The ADM mass. The mass appearing in Eq.(52) is simply a mass function, which couples with the nonlinear electromagnetic field, as we can see from the metric .]
Comment 3: [3) For thermodynamic stability, the black holes have other thermodynamic variables, such as charge density. I suggest the authors give the first law of thermodynamics for their solutions.]
Response 3: [In the revised version, we calculate other thermodynamic variables and write the first law of thermodynamics]
Comment 4: [4) Moreover, to check the local thermodynamic stability, one should consider the full Hessian matrix of the system. The heat capacity in Eq.(58) is only one element of the Hessian matrix.]
Response 4: [In the revised version, we calculate the Hessian matrix and use it for analyzing the thermodynamic stability]
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors
In my opinion, there are still some points that need to be understood further, for example, the definition of the mass. They are commom issues in related studies. Nevertheless, I recommend the manniscript for publication in Universe.
