<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> </mml:math> -Proca stars
C. Lazarte, Miguel Alcubierre
Abstract
Abstract Initially applied to the scalar case, we extend the applicability of the multi-field generalization with angular momentum of bosonic stars to the vector case, in order to obtain new configurations that generalize the one-field spherical Proca stars. These new objects, which we call <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> </mml:math> -Proca stars, arise as stationary and spherically symmetric bosonic stars solutions of the Einstein-(multi)Proca system, whose matter content is formed by an arbitrary odd number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> of complex Proca fields with the same mass, time-frequency, radial profile and angular momentum number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> </mml:math> . We analyze the system of constraint and evolution radial equations for the matter content to show the consistency of our proposal, and obtain numerically the ground states of these new solutions for the first few values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ℓ</mml:mi> </mml:mrow> </mml:math> using spectral methods.