Eikonal quasinormal modes and photon orbits of deformed Schwarzschild black holes

Chen, Che-Yu; Chiang, Hsu-Wen; Tsao, Jie-Shiun

doi:10.1103/physrevd.106.044068

Cited by 16 publications

(9 citation statements)

References 99 publications

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“…For this reason, we adopt the analysis of Ref. [115] where a general formalism has been developed. The deformed Schwarzschild black hole metric is parameterized as…”

Section: Quasinormal Modes In Noncommutative Black Hole Spacetimementioning

confidence: 99%

“…while the first order operator, i.e., D 2 (1)m,ω , is presented in (A1) of Appendix A [115]. In addition, the Fourier modes of the wavefunction, i.e., ψ m,ω , can be expanded as…”

Section: Quasinormal Modes In Noncommutative Black Hole Spacetimementioning

confidence: 99%

“…Our aim now is to extract the master equation in a Schrödinger-like form, where the latter includes the effective potential. First, we introduce the tortoise radius r * [115]…”

Section: Quasinormal Modes In Noncommutative Black Hole Spacetimementioning

confidence: 99%

“…At this point, one may think of adopting the analysis of Ref. [115] and, thus, utilize (5.17) in [115] which is an approximated expression of the effective potential for the case of m = 0. A couple of comments are in order here.…”

Section: Adding Up the Terms For The Effective Potentialmentioning

confidence: 99%

“…Appendix B: The coefficients of the effective potential (35) The coefficients a j lm , ...., h j lm of the effective potential (35) are given as [115] a…”

mentioning

confidence: 99%

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Quasinormal Modes in Noncommutative Schwarzschild black holes

Zhao¹,

Cai²,

Das³

et al. 2023

Preprint

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We investigate the quasinormal modes of a massless scalar field in a Schwarzschild black hole, which is deformed due to noncommutative corrections. We present the deformed Schwarzschild black hole solution, which depends on the noncommutative parameter Θ, and we extract the master equation as a Schrödinger-like equation, giving the explicit expression of the effective potential which is modified due to the noncommutative corrections. We solve the master equation numerically and we find that the noncommutative gravitational corrections "break" the stability of the scalar perturbations in the long time evolution of the massless scalar field. The significance of these results is twofold. Firstly, our results can be related to the detection of gravitational waves by the near future gravitational wave detectors, such as LISA, which will have a significantly increased accuracy. In particular, these observed gravitational waves produced by binary strong gravitational systems have oscillating modes which can provide valuable information. Secondly, our results can serve as an additional tool to test the predictions of general relativity, as well as to examine the possible detection of this kind of gravitational corrections.

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“…For this reason, we adopt the analysis of Ref. [115] where a general formalism has been developed. The deformed Schwarzschild black hole metric is parameterized as…”

Section: Quasinormal Modes In Noncommutative Black Hole Spacetimementioning

confidence: 99%

“…while the first order operator, i.e., D 2 (1)m,ω , is presented in (A1) of Appendix A [115]. In addition, the Fourier modes of the wavefunction, i.e., ψ m,ω , can be expanded as…”

Section: Quasinormal Modes In Noncommutative Black Hole Spacetimementioning

confidence: 99%

“…Our aim now is to extract the master equation in a Schrödinger-like form, where the latter includes the effective potential. First, we introduce the tortoise radius r * [115]…”

Section: Quasinormal Modes In Noncommutative Black Hole Spacetimementioning

confidence: 99%

Section: Adding Up the Terms For The Effective Potentialmentioning

confidence: 99%

“…Appendix B: The coefficients of the effective potential (35) The coefficients a j lm , ...., h j lm of the effective potential (35) are given as [115] a…”

mentioning

confidence: 99%

See 3 more Smart Citations

Quasinormal Modes in Noncommutative Schwarzschild black holes

Zhao¹,

Cai²,

Das³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Testing General Relativity with Black Hole Quasi-normal Modes

Franchini,

Völkel

2024

Springer Series in Astrophysics and Cosmology

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Quasinormal modes and universality of the Penrose limit of black hole photon rings

Giataganas,

Kehagias,

Riotto

2024

J. High Energ. Phys.

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We study the physics of photon rings in a wide range of axisymmetric black holes admitting a separable Hamilton-Jacobi equation for the geodesics. Utilizing the Killing-Yano tensor, we derive the Penrose limit of the black holes, which describes the physics near the photon ring. The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation, as well as the instabilities and Lyapunov exponents of the null geodesics. Consequently, the Lyapunov exponents and frequencies of the photon geodesics, along with the quasinormal modes, can be all extracted from a Hamiltonian in the Penrose limit plane wave metric. Additionally, we explore potential bounds on the Lyapunov exponent, the orbital and precession frequencies, in connection with the corresponding inverted harmonic oscillators and we discuss the possibility of photon rings serving as effective holographic horizons in a holographic duality framework for astrophysical black holes. Our formalism is applicable to spacetimes encompassing various types of black holes, including stationary ones like Kerr, Kerr-Newman, as well as static black holes such as Schwarzschild, Reissner-Nordström, among others.

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Eikonal quasinormal modes and photon orbits of deformed Schwarzschild black holes

Cited by 16 publications

References 99 publications

Quasinormal Modes in Noncommutative Schwarzschild black holes

Quasinormal Modes in Noncommutative Schwarzschild black holes

Testing General Relativity with Black Hole Quasi-normal Modes

Quasinormal modes and universality of the Penrose limit of black hole photon rings

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