Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity
In this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by t...
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MDPI AG
2021-07-01
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| author | G. Alencar V. B. Bezerra C. R. Muniz H. S. Vieira |
| author_facet | G. Alencar V. B. Bezerra C. R. Muniz H. S. Vieira |
| author_sort | G. Alencar |
| collection | DOAJ |
| description | In this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those that are valid in general relativity (GR). We verified that asymptotic safety guarantees that the Ellis–Bronnikov wormhole can satisfy the radial energy conditions at the throat 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>, within an interval of values of the latter, which is quite different from the result found in GR. Following this, we evaluate the effective 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>, at <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>, showing that the quantum gravitational effects modify Einstein’s field equations in such a way that it is necessary to have a very exotic source of matter to generate the wormhole spacetime–phantom or quintessence-like matter. This occurs within some ranges of the throat radii, even though the energy conditions are or are not violated there. Finally, we find that, although at <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> we have a quintessence-like matter, upon growing <i>r</i>, we inevitably came across phantom-like regions. We speculate whether such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios. |
| first_indexed | 2024-03-10T09:20:44Z |
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| id | doaj.art-5171a6ebc7ec46049f537fd3f82966d1 |
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| issn | 2218-1997 |
| language | English |
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| spelling | doaj.art-5171a6ebc7ec46049f537fd3f82966d12023-11-22T05:11:37ZengMDPI AGUniverse2218-19972021-07-017723810.3390/universe7070238Ellis–Bronnikov Wormholes in Asymptotically Safe GravityG. Alencar0V. B. Bezerra1C. R. Muniz2H. S. Vieira3Departamento de Física, Universidade Federal do Ceará, Campus do Pici, Fortaleza 60455-760, CE, BrazilDepartamento de Física, Universidade Federal da Paraíba, João Pessoa 58051-970, PB, BrazilFaculdade de Educação, Universidade Estadual do Ceará, Ciências e Letras de Iguatu, Iguatu 63500-000, CE, BrazilTheoretical Astrophysics, Institute for Astronomy and Astrophysics, University of Tübingen, 72076 Tübingen, GermanyIn this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those that are valid in general relativity (GR). We verified that asymptotic safety guarantees that the Ellis–Bronnikov wormhole can satisfy the radial energy conditions at the throat 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>, within an interval of values of the latter, which is quite different from the result found in GR. Following this, we evaluate the effective 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>, at <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>, showing that the quantum gravitational effects modify Einstein’s field equations in such a way that it is necessary to have a very exotic source of matter to generate the wormhole spacetime–phantom or quintessence-like matter. This occurs within some ranges of the throat radii, even though the energy conditions are or are not violated there. Finally, we find that, although at <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> we have a quintessence-like matter, upon growing <i>r</i>, we inevitably came across phantom-like regions. We speculate whether such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios.https://www.mdpi.com/2218-1997/7/7/238asymptotically safe gravitygeneral relativityEllis–Bronnikov wormhole |
| spellingShingle | G. Alencar V. B. Bezerra C. R. Muniz H. S. Vieira Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity Universe asymptotically safe gravity general relativity Ellis–Bronnikov wormhole |
| title | Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity |
| title_full | Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity |
| title_fullStr | Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity |
| title_full_unstemmed | Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity |
| title_short | Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity |
| title_sort | ellis bronnikov wormholes in asymptotically safe gravity |
| topic | asymptotically safe gravity general relativity Ellis–Bronnikov wormhole |
| url | https://www.mdpi.com/2218-1997/7/7/238 |
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