Nonlocal Modification of the Kerr Metric
In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-09-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/9/1771 |
| _version_ | 1797576536895782912 |
|---|---|
| author | Valeri P. Frolov Jose Pinedo Soto |
| author_facet | Valeri P. Frolov Jose Pinedo Soto |
| author_sort | Valeri P. Frolov |
| collection | DOAJ |
| description | In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>g</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>=</mo><msub><mi>η</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>+</mo><mo>Φ</mo><msub><mi>l</mi><mi>μ</mi></msub><msub><mi>l</mi><mi>μ</mi></msub></mrow></semantics></math></inline-formula>. Using Newman’s approach, we identify a shear free null congruence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">l</mi></semantics></math></inline-formula> with the generators of the null cone with apex at a point <i>p</i> in the complex space. The Kerr metric is obtained if the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula> is chosen to be a solution of the flat Laplace equation for a point source at the apex <i>p</i>. To construct the nonlocal modification of the Kerr metric, we modify the Laplace operator <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>▵</mo></mrow></semantics></math> by its nonlocal version <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">exp</mo><mo>(</mo><mo>−</mo><msup><mo>ℓ</mo><mn>2</mn></msup><mo>▵</mo><mo>)</mo><mo>▵</mo></mrow></semantics></math></inline-formula>. We found the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula> in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality. AlbertaThy 5–23. |
| first_indexed | 2024-03-10T21:54:27Z |
| format | Article |
| id | doaj.art-517a8ee195414daa8c06e0b4ab23ea39 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:54:27Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-517a8ee195414daa8c06e0b4ab23ea392023-11-19T13:12:25ZengMDPI AGSymmetry2073-89942023-09-01159177110.3390/sym15091771Nonlocal Modification of the Kerr MetricValeri P. Frolov0Jose Pinedo Soto1Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, CanadaTheoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, CanadaIn the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>g</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>=</mo><msub><mi>η</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>+</mo><mo>Φ</mo><msub><mi>l</mi><mi>μ</mi></msub><msub><mi>l</mi><mi>μ</mi></msub></mrow></semantics></math></inline-formula>. Using Newman’s approach, we identify a shear free null congruence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold-italic">l</mi></semantics></math></inline-formula> with the generators of the null cone with apex at a point <i>p</i> in the complex space. The Kerr metric is obtained if the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula> is chosen to be a solution of the flat Laplace equation for a point source at the apex <i>p</i>. To construct the nonlocal modification of the Kerr metric, we modify the Laplace operator <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>▵</mo></mrow></semantics></math> by its nonlocal version <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">exp</mo><mo>(</mo><mo>−</mo><msup><mo>ℓ</mo><mn>2</mn></msup><mo>▵</mo><mo>)</mo><mo>▵</mo></mrow></semantics></math></inline-formula>. We found the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Φ</mo></semantics></math></inline-formula> in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality. AlbertaThy 5–23.https://www.mdpi.com/2073-8994/15/9/1771nonlocal gravityKerr metricblack holesKerr-Schild |
| spellingShingle | Valeri P. Frolov Jose Pinedo Soto Nonlocal Modification of the Kerr Metric Symmetry nonlocal gravity Kerr metric black holes Kerr-Schild |
| title | Nonlocal Modification of the Kerr Metric |
| title_full | Nonlocal Modification of the Kerr Metric |
| title_fullStr | Nonlocal Modification of the Kerr Metric |
| title_full_unstemmed | Nonlocal Modification of the Kerr Metric |
| title_short | Nonlocal Modification of the Kerr Metric |
| title_sort | nonlocal modification of the kerr metric |
| topic | nonlocal gravity Kerr metric black holes Kerr-Schild |
| url | https://www.mdpi.com/2073-8994/15/9/1771 |
| work_keys_str_mv | AT valeripfrolov nonlocalmodificationofthekerrmetric AT josepinedosoto nonlocalmodificationofthekerrmetric |