Quasinormal frequencies of asymptotically flat two-dimensional black holes

A. Lopez-Ortega; I. Vega-Acevedo

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Quasinormal frequencies of asymptotically flat two-dimensional black holes

A. Lopez-Ortega, I. Vega-Acevedo

General Relativity and Quantum Cosmology · Submitted 13 May 2011

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The authors' main claim Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole.

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We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes.	contribution 0.67	0.39	0.10	unclear 0.77
s1	To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations.	method 1.00	0.96	0.05	asserted 0.99
s2	Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole.	result 0.78	0.97	0.33	asserted 1.00
s3	We compare our results on its quasinormal frequencies with other already published.	contribution 0.67	0.75	0.07	asserted 0.88

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Original abstract

We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.

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10 arXiv papers cite this in 39 sentences

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In a similar way to [ref] , we see that for asymptotically anti-de Sitter two-dimensional black holes the massless Klein-Gordon equation simplifies to a free Schrödinger type equation (see Eqs. (25) and (26) in [ref] ), and since its solutions do not satisfy the boundary conditions of the QNM, we find that the massless Klein-Gordon field does not have well defined QNF in asymptotically anti-de Sitter two-dimensional black holes.

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions · Quasinormal frequencies of the Klein-Gordon field · 0.80

Uses its method or tool 1 paper

Using the tortoise coordinate [equation] we transform the radial equation ([ref]) into the Schrödinger type equation [ref] , [ref] [equation] with the effective potential $V = m^2 e^2 M r_*$.

Quasinormal modes of a two-dimensional black hole · QNF of the Klein-Gordon field · 0.86

Uses its data or values 1 paper

Moreover, the Dirac field with mass $m$ has QNF equal to [ref] [equation] for its component $Ψ_1$ and [equation] for its component $Ψ_2$.

Entropy spectra of single horizon black holes in two dimensions · Single horizon two-dimensional black holes · 0.98

Compares with it 2 papers

Thus to satisfy the boundary condition at infinity we must solve the equations [equation] From these conditions we get that in UAO black hole the QNF of the massive Klein-Gordon field are equal to [equation] Note that the QNF of the Klein-Gordon field in UAO black hole are purely imaginary as those of Refs. [ref] – [ref] for lower dimensional gravitational systems.

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions · Quasinormal frequencies of the Klein-Gordon field · 0.88
We observe that they are different from the real effective potentials given in Ref. [ref] , but in the last reference they used a different dyad and a different representation of the gamma matrices to write the Dirac equation.

Quasinormal frequencies of the dimensionally reduced BTZ black hole · QNFs of the Dirac field · 0.90

Cites it as support 1 paper

For these reasons, in what follows we calculate numerically the QNF of the minimally coupled massive Klein-Gordon field, since we expect that the massless Klein-Gordon field does not have well defined QNF (see Subsection [ref] and Ref. [ref] ).

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions · Quasinormal frequencies of the CAO black hole · 0.97

Cites it as background 5 papers

For two-dimensional black holes we know the exact calculations of the QNF that appear in Refs. [ref] – [ref] .

Quasinormal frequencies of asymptotically anti-de Sitter black holes in two dimensions · Introduction · 0.80
Recently the QNF of several lower dimensional spacetimes have been calculated [ref] – [ref] .

Quasinormal modes of a two-dimensional black hole · Introduction · 0.96
Many studies have also discussed the scattering parameters of the fermionic field, including quasinormal frequencies, in the context of various BH spacetimes [ref] , also for acoustic BH [ref]

Fermionic greybody factors in Schwarzschild acoustic black holes · Introduction · 0.98

What it cites · 44 sentences without a confident label

Builds on 2 papers

The results about the QNF of the Dirac field in Witten black hole extend those obtained for the Klein-Gordon field [ref] , [ref] and the massless Dirac field [ref] .

Quasinormal modes and stability of a five-dimensional dilatonic black hole · Introduction · 0.98
The results about the QNF of the Dirac field in Witten black hole extend those obtained for the Klein-Gordon field [ref] , [ref] and the massless Dirac field [ref] .

Quasinormal Modes and Stability Criterion of Dilatonic Black Hole in 1+1 and 4+1 Dimensions · Introduction · 0.98

Uses the method or tool of 1 paper

Thus [equation] where [equation] Note that under a conformal transformation of metric ([ref]), that is [equation] if we change the two spinor, the Dirac operator, and the mass in the form [equation] then the quantities $Ψ̃$, $Ψ̃$, and $m̃$ satisfy the Dirac equation in spacetime ([ref]) [ref] .

The Dirac equation in D-dimensional spherically symmetric spacetimes · Quasinormal modes of massless fields in two-dimensional black holes · 0.94

Compares with 4 papers

Thus for the components $Ψ̃_1$ and $Ψ̃_2$ we find that their QNF are purely imaginary as those of Refs. [ref] – [ref] .

Quasinormal Modes of Charged Dilaton Black Holes in 2+1 Dimensions · Quasinormal frequencies of the Dirac field in Witten black hole · 0.98
Thus for the components $Ψ̃_1$ and $Ψ̃_2$ we find that their QNF are purely imaginary as those of Refs. [ref] – [ref] .

Non-minimal scalar fields in 2D de Sitter and dilaton black holes · Quasinormal frequencies of the Dirac field in Witten black hole · 0.98
They find well defined asymptotic QNF and their conclusions do not contradict the previous results because in [ref] they calculate the asymptotic QNF of the massless Klein-Gordon field non-minimally coupled to the dilaton field and here we analyze the minimally coupled Klein-Gordon field.

Quasinormal modes for single horizon black holes in generic 2-d dilaton gravity · Quasinormal modes of massless fields in two-dimensional black holes · 0.96

Cites as background 12 papers

A well studied two-dimensional spacetime is the uncharged Witten black hole [ref] , [ref] , [ref] , [ref] , whose metric and dilaton are [equation] where $ϕ_0$ is a constant.[Sometimes this black hole is called CGHS dilaton black hole [ref] .] This black hole is asymptotically flat and it has a horizon at $r_H = 0$ [ref] , [ref] .

Non-minimal scalar fields in 2D de Sitter and dilaton black holes · Quasinormal frequencies of the Dirac field in Witten black hole · 1.00
A well studied two-dimensional spacetime is the uncharged Witten black hole [ref] , [ref] , [ref] , [ref] , whose metric and dilaton are [equation] where $ϕ_0$ is a constant.[Sometimes this black hole is called CGHS dilaton black hole [ref] .] This black hole is asymptotically flat and it has a horizon at $r_H = 0$ [ref] , [ref] .

Dilaton Gravity in Two Dimensions · Quasinormal frequencies of the Dirac field in Witten black hole · 1.00
A well studied two-dimensional spacetime is the uncharged Witten black hole [ref] , [ref] , [ref] , [ref] , whose metric and dilaton are [equation] where $ϕ_0$ is a constant.[Sometimes this black hole is called CGHS dilaton black hole [ref] .] This black hole is asymptotically flat and it has a horizon at $r_H = 0$ [ref] , [ref] .

Charged Black Holes in Two-Dimensional String Theory · Quasinormal frequencies of the Dirac field in Witten black hole · 1.00

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