# Darboux covariance: A hidden symmetry of perturbed Schwarzschild black holes

@article{Lenzi2021DarbouxCA, title={Darboux covariance: A hidden symmetry of perturbed Schwarzschild black holes}, author={Michele Lenzi and Carlos F. Sopuerta}, journal={Physical Review D}, year={2021} }

Starting from the infinite set of possible master equations for the perturbations of Schwarzschild black holes, with master functions linear in the metric perturbations and their first-order derivatives, we show that of all them are connected via Darboux transformations. These transformations preserve physical quantities like the quasinormal mode frequencies and the infinite hierarchy of Korteweg-de Vries conserved quantities, revealing a new hidden symmetry in the description of the…

## One Citation

Isospectrality of quasinormal modes in nonrotating loop quantum gravity black holes

- Physics
- 2022

We study the quasinormal frequencies of three effective geometries of nonrotating regular black holes derived from loop quantum gravity. Concretely, we consider the Ashtekar-Olmedo-Singh and two…

## References

SHOWING 1-10 OF 61 REFERENCES

Intertwining of the equations of black-hole perturbations.

- Physics, MedicinePhysical review. D, Particles and fields
- 1991

For both Schwarzschild and Reissner-Nordstrom black holes, equations have been given in which the dynamics of perturbations are governed by effective potentials, and the odd-parity potentials are markedly simpler and are necessary for certain semianalytic approaches to numerical studies.

Darboux transformation in black hole perturbation theory

- Physics
- 2017

The Darboux transformation between ordinary differential equations is a 19th century technique that has seen wide use in quantum theory for producing exactly solvable potentials for the Schrodinger…

The quasi-normal modes of the Schwarzschild black hole

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1975

The quasi-normal modes of a black hole represent solutions of the relevant perturbation equations which satisfy the boundary conditions appropriate for purely outgoing (gravitational) waves at…

On algebraically special perturbations of black holes

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1984

Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the…

On the equations governing the perturbations of the Reissner–Nordström black hole

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1979

By considering suitable combinations of the Weyl scalars and the spin coefficients, the basic equations governing the perturbations of the Reissner–Nordström black hole, in the Newman–Penrose…

TOPICAL REVIEW: Quasinormal modes of black holes and black branes

- Physics
- 2009

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and…

Gravitational perturbations of spherically symmetric systems. I. The exterior problem

- Physics
- 1974

Gravitational perturbations of the Schwarzschild metric are treated from a point of view which is adapted, in a natural way, to the gauge group of the perturbed Einstein equations. The metric…

A look at the generalized Darboux transformations for the quasinormal spectra in Schwarzschild black hole perturbation theory: Just how general should it be?

- PhysicsPhysics Letters A
- 2019

Abstract In this article we take a close look at three types of transformations usable in the Schwarzschild black hole perturbation theory: a standard (DT), a binary (BDT) and a generalized (GDT)…

Resolution of the mystery behind Chandrasekhar's black hole transformations

- Physics
- 1977

Investigating, in normal form, the three differential equations of (i) Zerilli (1970), (ii) Bardeen and Press (1973), (iii) Regge and Wheeler (1957), governing the perturbations of the Schwarzschild…

On the equations governing the perturbations of the Schwarzschild black hole

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1975

A coherent self-contained account of the equations governing the perturbations of the Schwarzschild black hole is given. In particular, the relations between the equations of Bardeen & Press, of…