New Black Hole Solutions of Second and First Order Formulations of Nonlinear Electrodynamics
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2024
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| author | Verbin, Yosef Pulice, Beyhan Övgün, Ali Huang, Hyat |
| author_facet | Verbin, Yosef Pulice, Beyhan Övgün, Ali Huang, Hyat |
| contents | Inspired by the so-called Palatini formulation of General Relativity and of its modifications and extensions, we consider an analogous formulation of the dynamics of a self-interacting gauge field which is determined by non-linear extension of Maxwell's theory, usually known as nonlinear electrodynamics. In this first order formalism the field strength and the gauge potential are treated, a priori as independent, and, as such, varied independently in order to produce the field equations. Accordingly we consider within this formalism alternative and generalized non-linear Lagrangian densities, some of them of a new kind which gives up the restriction of equivalence to second order Lagrangians. Several new spherically-symmetric objects are constructed analytically and their main properties are studied. The solutions are obtained in flat spacetime ignoring gravity and for the self-gravitating case with emphasis on black holes. As a background for comparison between the first and second order formalisms, some of the solutions are obtained by the conventional second order formalism, while for others a first order formalism is applied. Among the self-gravitating solutions we find new families of black holes and study their main characteristics. Some of the flat space solutions can regularize the total energy of a point charge and a subset of them exhibit also finite field strength and energy density, although their black hole counterparts are not regular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Black Hole Solutions of Second and First Order Formulations of Nonlinear Electrodynamics Verbin, Yosef Pulice, Beyhan Övgün, Ali Huang, Hyat General Relativity and Quantum Cosmology High Energy Physics - Theory Inspired by the so-called Palatini formulation of General Relativity and of its modifications and extensions, we consider an analogous formulation of the dynamics of a self-interacting gauge field which is determined by non-linear extension of Maxwell's theory, usually known as nonlinear electrodynamics. In this first order formalism the field strength and the gauge potential are treated, a priori as independent, and, as such, varied independently in order to produce the field equations. Accordingly we consider within this formalism alternative and generalized non-linear Lagrangian densities, some of them of a new kind which gives up the restriction of equivalence to second order Lagrangians. Several new spherically-symmetric objects are constructed analytically and their main properties are studied. The solutions are obtained in flat spacetime ignoring gravity and for the self-gravitating case with emphasis on black holes. As a background for comparison between the first and second order formalisms, some of the solutions are obtained by the conventional second order formalism, while for others a first order formalism is applied. Among the self-gravitating solutions we find new families of black holes and study their main characteristics. Some of the flat space solutions can regularize the total energy of a point charge and a subset of them exhibit also finite field strength and energy density, although their black hole counterparts are not regular. |
| title | New Black Hole Solutions of Second and First Order Formulations of Nonlinear Electrodynamics |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.20989 |