Dirac-boson stars

Abstract

A bstract In this paper, we construct Dirac-boson stars (DBSs) model composed of a scalar field and two Dirac fields. The scalar field and both Dirac fields are in the ground state. We consider the solution families of the DBSs for the synchronized frequency $$ \overset{\sim }{\omega } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> and the nonsynchronized frequency $$ {\overset{\sim }{\omega}}_D $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>D</mml:mi> </mml:msub> </mml:math> cases, respectively. We find several different solutions when the Dirac field mass $$ {\overset{\sim }{\mu}}_D $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>μ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>D</mml:mi> </mml:msub> </mml:math> and scalar field frequency $$ {\overset{\sim }{\omega}}_s $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>s</mml:mi> </mml:msub> </mml:math> are taken in some particular ranges. In contrast, no similar case has been found in previous studies of multistate boson stars. Moreover, we discuss the characteristics of each type of solution family of the DBSs and present the relationship between the ADM mass M of the DBSs and the synchronized frequency $$ \overset{\sim }{\omega } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> or the nonsynchronized frequency $$ {\overset{\sim }{\omega}}_D $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>D</mml:mi> </mml:msub> </mml:math> . Finally, we calculate the binding energy E B of the DBSs and investigate the relationship of E B with the synchronized frequency $$ \overset{\sim }{\omega } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> or the nonsynchronized frequency $$ {\overset{\sim }{\omega}}_D $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>D</mml:mi> </mml:msub> </mml:math> .