TY - JOUR

T1 - Defrosting frozen stars

T2 - Spectrum of internal fluid modes

AU - Brustein, Ram

AU - Medved, A. J.M.

AU - Shindelman, Tom

N1 - Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/8/15

Y1 - 2023/8/15

N2 - The frozen star model provides a classical description of a regularized black hole and is based upon the idea that regularizing the singularity requires deviations from the Schwarzschild geometry which extend over horizon-sized scales, as well as maximally negative radial pressure as an equation of state. The frozen star has also been shown to be ultrastable against perturbations, a feature that can be attributed to the equation of state and corresponds to this model mimicking a black hole in the limit ℏ→0 or, equivalently, the limit of an infinite Newton's constant. Here, we "defrost"the frozen star by allowing its radial pressure to be perturbatively less negative than maximal. This modification to the equation of state is implemented by appropriately deforming the background metric so as to allow the frozen star to mimic a quantum black hole at finite ℏ and Newton's constant. As a consequence, the defrosted star acquires a nontrivial spectrum of oscillatory perturbations. To show this, we first use the Cowling approximation to obtain generic equations for the energy density and pressure perturbations of a static, spherically symmetric background with an anisotropic fluid. The particular setting of a deformed frozen star is then considered, for which the dispersion relation is obtained to leading order in terms of the deviation from maximal pressure. The current results compare favorably with those obtained earlier for the collapsed polymer model, whose strongly nonclassical interior is argued to provide a microscopic description of the frozen and defrosted star geometries.

AB - The frozen star model provides a classical description of a regularized black hole and is based upon the idea that regularizing the singularity requires deviations from the Schwarzschild geometry which extend over horizon-sized scales, as well as maximally negative radial pressure as an equation of state. The frozen star has also been shown to be ultrastable against perturbations, a feature that can be attributed to the equation of state and corresponds to this model mimicking a black hole in the limit ℏ→0 or, equivalently, the limit of an infinite Newton's constant. Here, we "defrost"the frozen star by allowing its radial pressure to be perturbatively less negative than maximal. This modification to the equation of state is implemented by appropriately deforming the background metric so as to allow the frozen star to mimic a quantum black hole at finite ℏ and Newton's constant. As a consequence, the defrosted star acquires a nontrivial spectrum of oscillatory perturbations. To show this, we first use the Cowling approximation to obtain generic equations for the energy density and pressure perturbations of a static, spherically symmetric background with an anisotropic fluid. The particular setting of a deformed frozen star is then considered, for which the dispersion relation is obtained to leading order in terms of the deviation from maximal pressure. The current results compare favorably with those obtained earlier for the collapsed polymer model, whose strongly nonclassical interior is argued to provide a microscopic description of the frozen and defrosted star geometries.

UR - http://www.scopus.com/inward/record.url?scp=85172813557&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.108.044058

DO - 10.1103/PhysRevD.108.044058

M3 - Article

AN - SCOPUS:85172813557

SN - 2470-0010

VL - 108

JO - Physical Review D

JF - Physical Review D

IS - 4

M1 - 044058

ER -