Covariant Evolution of Gravitoelectromagnetism
The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of...
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MDPI AG
2022-06-01
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| Online Access: | https://www.mdpi.com/2218-1997/8/6/318 |
| _version_ | 1797481677746864128 |
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| author | Ashkbiz Danehkar |
| author_facet | Ashkbiz Danehkar |
| author_sort | Ashkbiz Danehkar |
| collection | DOAJ |
| description | The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of dynamical and kinematic equations governing the matter coupling and evolution of the electric and magnetic parts of the Weyl tensor, so-called gravitoelectric and gravitomagnetic fields. A detailed analysis of the Weyl gravitoelectromagnetic fields can be conducted using a number of algebraic and differential identities prescribed by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mn>3</mn></mrow></semantics></math></inline-formula> covariant formalism. In this review, we consider the dynamical constraints and propagation equations of the gravitoelectric/-magnetic fields and covariantly debate their analytic properties. We discuss the special conditions under which gravitational waves can propagate, the inconsistency of a Newtonian-like model without gravitomagnetism, the nonlinear generalization to multi-fluid models with different matter species, as well as observational effects caused by the Weyl fields via the kinematic quantities. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mn>3</mn></mrow></semantics></math></inline-formula> tetrad and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>2</mn></mrow></semantics></math></inline-formula> semi-covariant methods, which can equally be used for gravitoelectromagnetism, are briefly explained, along with their correspondence with the covariant formulations. |
| first_indexed | 2024-03-09T22:17:58Z |
| format | Article |
| id | doaj.art-250ce073e59141d8993113c18c9779c4 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T22:17:58Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-250ce073e59141d8993113c18c9779c42023-11-23T19:19:12ZengMDPI AGUniverse2218-19972022-06-018631810.3390/universe8060318Covariant Evolution of GravitoelectromagnetismAshkbiz Danehkar0Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USAThe long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of dynamical and kinematic equations governing the matter coupling and evolution of the electric and magnetic parts of the Weyl tensor, so-called gravitoelectric and gravitomagnetic fields. A detailed analysis of the Weyl gravitoelectromagnetic fields can be conducted using a number of algebraic and differential identities prescribed by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mn>3</mn></mrow></semantics></math></inline-formula> covariant formalism. In this review, we consider the dynamical constraints and propagation equations of the gravitoelectric/-magnetic fields and covariantly debate their analytic properties. We discuss the special conditions under which gravitational waves can propagate, the inconsistency of a Newtonian-like model without gravitomagnetism, the nonlinear generalization to multi-fluid models with different matter species, as well as observational effects caused by the Weyl fields via the kinematic quantities. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mn>3</mn></mrow></semantics></math></inline-formula> tetrad and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>2</mn></mrow></semantics></math></inline-formula> semi-covariant methods, which can equally be used for gravitoelectromagnetism, are briefly explained, along with their correspondence with the covariant formulations.https://www.mdpi.com/2218-1997/8/6/318Weyl tensorcovariant formalismgravitomagnetismgravitational waves |
| spellingShingle | Ashkbiz Danehkar Covariant Evolution of Gravitoelectromagnetism Universe Weyl tensor covariant formalism gravitomagnetism gravitational waves |
| title | Covariant Evolution of Gravitoelectromagnetism |
| title_full | Covariant Evolution of Gravitoelectromagnetism |
| title_fullStr | Covariant Evolution of Gravitoelectromagnetism |
| title_full_unstemmed | Covariant Evolution of Gravitoelectromagnetism |
| title_short | Covariant Evolution of Gravitoelectromagnetism |
| title_sort | covariant evolution of gravitoelectromagnetism |
| topic | Weyl tensor covariant formalism gravitomagnetism gravitational waves |
| url | https://www.mdpi.com/2218-1997/8/6/318 |
| work_keys_str_mv | AT ashkbizdanehkar covariantevolutionofgravitoelectromagnetism |