Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes

Katagiri, Takuya; Kimura, Masashi

doi:10.48550/arxiv.2101.03479

Cited by 1 publication

(11 citation statements)

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“…We shall explicitly show that the Aretakis constants and instability correspond to, respectively, constants and blowups of some components of higher-order covariant derivatives of the field at late times in that frame along the horizons. This shows that a similar geometrical interpretation as in the AdS 2 case [30] is possible for our present setup.…”

Section: Aretakis Constants and Instability In The Parallelly Propaga...supporting

confidence: 80%

“…In [19,22,[35][36][37], it has been shown that there exists one-to-one correspondence of the Aretakis constants and the Newman-Penrose constants [38] in four-dimensional extremal Reissner-Nordström black 1 It has been argued that in [19] the Aretakis instability in global AdS 2 is just a coordinate effect, while in [29] the Aretakis instability in the near-horizon geometry of extremal black holes is not the coordinate effect. In [30], contrary to the claim in [19], it has been shown that the late-time divergent behavior in global AdS 2 has a geometrical meaning: blowups of some component of covariant derivatives of fields in the parallelly propagated null geodesic frame.…”

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confidence: 84%

“…According to [30,41], the Aretakis constants in AdS 2 can be derived by using ladder operators, called mass ladder operators [30,41,49], constructed from the spacetime conformal symmetry. Since AdS 2 structure approximately appear in the vicinity of extremal black hole horizons, we expect that the Aretakis constants (2.20) can also be derived similarly as [30,41]. From this point of view, we construct the Aretakis constants in the extremal black holes (2.10) in this section.…”

Section: Aretakis Constants From Ladder Operators Associated With App...mentioning

confidence: 99%

“…The behavior of test fields in the near-horizon geometry can be reduced to scalar fields on AdS 2 . In the pure AdS 2 case, it has been shown that the Aretakis constants of the massive Klein-Gordon field can be derived from ladder operators associated with the spacetime conformal symmetry [30,41]. We expect that the Aretakis constants in the extremal black holes can be derived from the ladder operators associated with the approximate AdS 2 symmetry near the extremal black hole horizons.…”

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confidence: 95%

“…The relation with asymptotic symmetries near degenerate Killing horizons is suggested in [39,40]. For the AdS 2 case, the relation with the spacetime conformal symmetry in AdS 2 is pointed out [30,41]. This paper aims to obtain a deeper understanding of the properties of the Aretakis constants and instability.…”

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confidence: 97%

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The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings

Katagiri,

Kimura

2021

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We study late-time behaviors of massive scalar fields in general static and spherically symmetric extremal black hole spacetimes in arbitrary dimensions. We show the existence of conserved quantities on the extremal black hole horizons for specific mass squared and multipole modes of the scalar fields. Those quantities on the horizon are called the Aretakis constants and are constructed from the higher-order derivatives of the fields. Focusing on the region near the horizon at late times, where is well approximated by the near-horizon geometry, we show that the leading behaviors of the fields are described by power-law tails. The late-time power-law tails lead to the Atetakis instability: blowups of the transverse derivatives of the fields on the horizon. We further argue that the Aretakis constants and instability correspond to respectively constants and blowups of components of covariant derivatives of the fields at the late time in the parallelly propagated null geodesic frame along the horizon. We finally discuss the relation between the Aretakis constants and ladder operators constructed from the approximate spacetime conformal symmetry near the extremal black hole horizons. I. INTRODUCTIONExtremal black holes have long played an important role in various aspects. They have zero Hawking temperature and are expected to bring us valuable insights into the black hole thermodynamics [1-6] and the Hawking radiation [7,8]. In the context of astrophysics, it is suggested that many astrophysical black holes are nearly extremal [9-13], and high energy phenomena around such black holes are discussed, e.g., in [14][15][16]. For understanding the nature of the extremal black holes, it is important to investigate the dynamical properties of test fields and particles around them.Aretakis [17,18] has discussed late-time behaviors of test massless scalar fields in fourdimensional extremal Reissner-Nordström black holes. When generic initial data are given on an initial hypersurface crossing the horizon, he argued that the higher-order transverse derivatives of the fields blow up polynomially in time, not exponential, on the event horizon, while they decay outside the horizon. This blowup on the horizon is called the Aretakis instability. The occurrence of the Aretakis instability is associated with the fact that latetime behaviors of fields are described by power-law tails [19][20][21][22][23][24], not the exponential decay in time. The instability also occurs against vector, tensor, and massive or charged scalar fields [19,25,26], and in other spacetimes such as extremal Kerr(-Newman) [25,27], extremal Bañados-Teitelboim-Zanelli [28], and two-dimensional anti-de Sitter spacetimes (AdS 2 ) [19, 29, 30] 1 , and in higher dimensions [31]. The nonlinear evolution of the Aretakis instability has been investigated in [32][33][34].Related to the Aretakis instability, conserved quantities along the horizons, which are constructed from the higher-order radial derivatives of the fields, are studied [17,18]. These conserved quantitie...

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Section: Aretakis Constants and Instability In The Parallelly Propaga...supporting

confidence: 80%

mentioning

confidence: 84%

Section: Aretakis Constants From Ladder Operators Associated With App...mentioning

confidence: 99%

mentioning

confidence: 95%

mentioning

confidence: 97%

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The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings

Katagiri,

Kimura

2021

Preprint

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Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes

Cited by 1 publication

References 36 publications

The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings

The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings

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