Time-Dependent Conformal Transformations and the Propagator for Quadratic Systems

Zhao, Q.-L.; Zhang, P. M.; Horváthy, P. A.

doi:10.3390/sym13101866

Cited by 6 publications

(3 citation statements)

References 52 publications

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“…See refs. [36,37] for complementary investigations on the symmetries of specific second order ordinary differential equations and [38][39][40] for a discussion on the dynamical symmetry of time-dependent systems.…”

Section: Jhep07(2022)112mentioning

confidence: 99%

Hidden symmetry of the static response of black holes: applications to Love numbers

Achour¹,

Livine

Mukohyama

et al. 2022

J. High Energ. Phys.

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We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra $$ \mathfrak{sh} $$ sh (1) = $$ \mathfrak{sl} $$ sl (2, ℝ) ⋉ $$ \mathcal{H} $$ H . The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al., dubbed the HJPSS symmetry, coincides with one of the $$ \mathfrak{sl} $$ sl (2, ℝ) generators of the Schrödinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schrödinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case.

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Section: Jhep07(2022)112mentioning

confidence: 99%

Hidden symmetry of the static response of black holes: applications to Love numbers

Achour¹,

Livine

Mukohyama

et al. 2022

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The contributions by Inomata et al [6] and Zhao et al [7] reconsider joint transformations of space and time, mapping different physical systems onto each other. In [6], the well-known Newton-Hooke duality and its generalization to arbitrary power-law potentials is reviewed.…”

mentioning

confidence: 99%

“…Here, duality is viewed as a symmetry concept. The contribution [7] reconsiders space-time transformations, mapping a quadradic system onto that of a free particle. The close relation of this transformation with the time-dependent Bargmannconformal transformation is established and illustrated.…”

mentioning

confidence: 99%