Schwarzschild-like Wormholes in Asymptotically Safe Gravity
In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathM...
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MDPI AG
2021-09-01
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| Online Access: | https://www.mdpi.com/2218-1997/7/9/332 |
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| author | Geová Alencar Matheus Nilton |
| author_facet | Geová Alencar Matheus Nilton |
| author_sort | Geová Alencar |
| collection | DOAJ |
| description | In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>X</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub></semantics></math></inline-formula> as a source to improved field equations, and promotes the Newton’s constant into a running coupling constant. In particular, we check whether the radial energy conditions are satisfied and compare with the results obtained from the usual theory. We show that only in the particular case of the wormhole being asymptotically flat(Schwarzschild Wormholes) that the radial energy conditions are satisfied at the throat, depending on the chosen values for its radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula>. In contrast, in the general Schwarzschild-like case, there is no possibility of the energy conditions being satisfied nearby the throat, as in the usual case. After that, we calculate the radial state parameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></semantics></math></inline-formula>, in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula>, in order to verify what type of cosmologic matter is allowed at the wormhole throat, and we show that in both cases there is the possibility of the presence of exotic matter, phantom or quintessence-like matter. Finally, we give the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions for all regions of space. Interestingly, we find that Schwarzschild-like Wormholes with excess of solid angle of the sphere in the asymptotic limit have the possibility of having non-exotic matter as source for certain values of the radial coordinate <i>r</i>. Furthermore, it was observed that quantum gravity corrections due the ASG necessarily imply regions with phantom-like matter, both for Schwarzschild and for Schwarzschild-like wormholes. This reinforces the supposition that a phantom fluid is always present for wormholes in this context. |
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| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T07:09:38Z |
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| spelling | doaj.art-63fb72b887d6406299377cffc04927662023-11-22T15:33:00ZengMDPI AGUniverse2218-19972021-09-017933210.3390/universe7090332Schwarzschild-like Wormholes in Asymptotically Safe GravityGeová Alencar0Matheus Nilton1Departamento de Física, Campus do Pici, Universidade Federal do Ceará, Fortaleza 60455-760, Ceará, BrazilDepartamento de Física, Campus do Pici, Universidade Federal do Ceará, Fortaleza 60455-760, Ceará, BrazilIn this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>X</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub></semantics></math></inline-formula> as a source to improved field equations, and promotes the Newton’s constant into a running coupling constant. In particular, we check whether the radial energy conditions are satisfied and compare with the results obtained from the usual theory. We show that only in the particular case of the wormhole being asymptotically flat(Schwarzschild Wormholes) that the radial energy conditions are satisfied at the throat, depending on the chosen values for its radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula>. In contrast, in the general Schwarzschild-like case, there is no possibility of the energy conditions being satisfied nearby the throat, as in the usual case. After that, we calculate the radial state parameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></semantics></math></inline-formula>, in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula>, in order to verify what type of cosmologic matter is allowed at the wormhole throat, and we show that in both cases there is the possibility of the presence of exotic matter, phantom or quintessence-like matter. Finally, we give the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions for all regions of space. Interestingly, we find that Schwarzschild-like Wormholes with excess of solid angle of the sphere in the asymptotic limit have the possibility of having non-exotic matter as source for certain values of the radial coordinate <i>r</i>. Furthermore, it was observed that quantum gravity corrections due the ASG necessarily imply regions with phantom-like matter, both for Schwarzschild and for Schwarzschild-like wormholes. This reinforces the supposition that a phantom fluid is always present for wormholes in this context.https://www.mdpi.com/2218-1997/7/9/332asymptotically safe gravitygeneral relativitySchwarzschild-like wormhole |
| spellingShingle | Geová Alencar Matheus Nilton Schwarzschild-like Wormholes in Asymptotically Safe Gravity Universe asymptotically safe gravity general relativity Schwarzschild-like wormhole |
| title | Schwarzschild-like Wormholes in Asymptotically Safe Gravity |
| title_full | Schwarzschild-like Wormholes in Asymptotically Safe Gravity |
| title_fullStr | Schwarzschild-like Wormholes in Asymptotically Safe Gravity |
| title_full_unstemmed | Schwarzschild-like Wormholes in Asymptotically Safe Gravity |
| title_short | Schwarzschild-like Wormholes in Asymptotically Safe Gravity |
| title_sort | schwarzschild like wormholes in asymptotically safe gravity |
| topic | asymptotically safe gravity general relativity Schwarzschild-like wormhole |
| url | https://www.mdpi.com/2218-1997/7/9/332 |
| work_keys_str_mv | AT geovaalencar schwarzschildlikewormholesinasymptoticallysafegravity AT matheusnilton schwarzschildlikewormholesinasymptoticallysafegravity |