Boson stars in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> dimensions: stability, oscillation frequencies, and dynamical evolutions

Abstract We construct spherically symmetric boson star (BS) solutions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>∈</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>6</mml:mn> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> </mml:math> spacetime dimensions, considering the effects of both a quartic self-interaction term and a solitonic potential. We then perform a perturbative analysis, generalizing the pulsation equations to arbitrary dimension and potential and hence demonstrating the existence of radially stable higher-dimensional BS solutions. In particular, we find stable solutions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>∈</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>6</mml:mn> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> </mml:math> with a quartic self-interaction term and for D = 5 with a solitonic potential. We supplement these linear results with perturbed and unperturbed nonlinear dynamical evolutions in spherical symmetry, obtained using a dimensional reduction that allows us to evolve spacetimes with any number of background dimensions using the same numerical framework, while preserving the full gauge freedom of standard approaches to numerical relativity. The results of these evolutions indicate that the solutions we identify as perturbatively stable are indeed generally stable to nonlinear spherical dynamics.