Scalarization of holonomy-corrected Schwarzschild black holes in Einstein–scalar–Gauss–Bonnet theory

Abstract In Einstein–scalar–Gauss–Bonnet theory, spontaneous scalarization with a negative Gauss–Bonnet coupling, denoted as $$ \text {GB}^- $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>GB</mml:mtext> <mml:mo>-</mml:mo> </mml:msup> </mml:math> scalarization, is absent for the classical Schwarzschild background and is usually associated with sufficiently rapid rotation. In this work, we study scalar perturbations on a holonomy-corrected Schwarzschild black hole background inspired by loop quantum gravity. We show that the correction to the background curvature can make the effective scalar mass squared negative outside the horizon when the LQG parameter satisfies $$\alpha /M&gt;(\alpha /M)_\text {crit}\simeq 1.62772$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext>crit</mml:mtext> </mml:msub> <mml:mo>≃</mml:mo> <mml:mn>1.62772</mml:mn> </mml:mrow> </mml:math> . This provides a new realization of curvature-induced scalarization in the $$ \text {GB}^- $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>GB</mml:mtext> <mml:mo>-</mml:mo> </mml:msup> </mml:math> sector, enabled by the holonomy-corrected Schwarzschild background. We derive the analytical necessary condition for the onset of the tachyonic instability and confirm it by time-domain evolutions of scalar perturbations. The instability region in the $$|\lambda |/M^2-\alpha /M$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>-</mml:mo> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> parameter space expands as the coupling strength $$-\lambda /M^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> increases, and its lower boundary approaches the analytical threshold in the large-coupling limit. Since the holonomy parameter represents an effective quantum-gravity correction, the effect is expected to be relevant mainly for microscopic or primordial black holes.