Black holes and regular black holes in coincident $$f({\mathbb {Q}},{\mathbb {B}}_Q)$$ gravity coupled to nonlinear electrodynamics

Abstract

Abstract In this work, we consider an extension of the symmetric teleparallel equivalent of General Relativity (STEGR), namely, $$f({\mathbb {Q}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, by including a boundary term $${\mathbb {B}}_Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> </mml:math> , where $${\mathbb {Q}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Q</mml:mi> </mml:math> is the non-metricity scalar. More specifically, we explore static and spherically symmetric black hole and regular black hole solutions in $$f({\mathbb {Q}},{\mathbb {B}}_Q)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity coupled to nonlinear electrodynamics (NLED). In particular, to obtain black hole solutions, and in order to ensure that our solutions preserve Lorentz symmetry, we assume the following relation $$f_Q = -f_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:mrow> </mml:math> , where $$f_{Q}=\partial f/\partial {\mathbb {Q}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>∂</mml:mi> <mml:mi>f</mml:mi> <mml:mo>/</mml:mo> <mml:mi>∂</mml:mi> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> and $$f_{B}= \partial f/\partial {\mathbb {B}}_Q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>B</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>∂</mml:mi> <mml:mi>f</mml:mi> <mml:mo>/</mml:mo> <mml:mi>∂</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> </mml:mrow> </mml:math> . We develop three models of black holes, and as the starting point for each case we consider the non-metricity scalar or the boundary term in such a way to obtain the metric functions A ( r ). Additionally, we are able to express matter through analytical solutions for specific NLED Lagrangians $${{\mathcal {L}}}_{\textrm{NLED}}(F)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mtext>NLED</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . Furthermore, we also obtain generalized solutions of the Bardeen and Culetu types of regular black holes, by imposing specific metric functions.

Topics & Concepts