https://doi.org/10.1140/epjc/s10052-023-11341-0
Regular Article - Theoretical Physics
On Einstein–Born–Infeld conformally invariant theory
1
Federal Research Center, Institute of Applied Mathematics, M. V. Keldysh Institute of the Russian Academy of Sciences, Miusskaya sq. 4, 125047, Moscow, Russian Federation
2
Institute of Interdisciplinary and Applied Physics (INFINA), Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Universidad de Buenos Aires, Buenos Aires, Argentina
Received:
8
January
2023
Accepted:
19
February
2023
Published online:
2
March
2023
A new Weyl Born Infeld model is presented. It takes as basis the formalism for the mathematical description of conformal gravity based on the local twistor geometry from Merkulov (Class Quantum Gravity 1:349–354, 1984). As in the pure Maxwell case, the electromagnetic field can be naturally incorporated into this scheme by a modification of the local twistor parallel transport law. The dynamical equations of the linear case, namely the Bach equations for gravity and the Maxwell equations for the electromagnetic field, can not be obtained by varying a single quantity-the modified twistor connection, unless a geometric condition on a particular function of the invariants is imposed. When that condition is met, the Weyl–Maxwel gravity system are contained in the obtained set. The invariance under standard dualities and other generalized maps are briefly discussed.
© The Author(s) 2023
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