Massive white dwarfs in $$f(\mathtt {R,L_m})$$ gravity
Ronaldo V. Lobato, G. A. Carvalho, N. G. Kelkar, M. Nowakowski
Abstract
Abstract In this work, we investigate the equilibrium configurations of massive white dwarfs (MWD) in the context of modified gravity, namely $$f(\mathtt {R,L_m})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity, where $$\mathtt {R}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> stands for the Ricci scalar and $$\mathtt {L_m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> is the Lagrangian matter density. We focused on the specific case $$f(\mathtt {R,L_m})= \mathtt {R}/2 + \mathtt {L_m}+ \sigma \mathtt {R}\mathtt {L_m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>σ</mml:mi> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:mrow> </mml:math> , i.e., we have considered a non-minimal coupling between the gravity field and the matter field, with $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> being the coupling constant. For the first time, the theory is applied to white dwarfs, in particular to study massive white dwarfs, which is a topic of great interest in the last years. The equilibrium configurations predict maximum masses which are above the Chandrasekhar mass limit. The most important effect of the theory is to increase significantly the mass for stars with radius < 2000 km. We found that the theory can accommodate the super-Chandrasekhar white dwarfs for different star compositions. Apart from this, the theory recovers the General Relativity results for stars with radii larger than 3000 km, independent of the value of $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> .