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Dynamical Black Holes in 2+1 Dimensions
High Energy Physics - Theory · Submitted 26 Apr 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum.
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The abstract, sentence by sentence
We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ black hole. We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum. The dynamical trapping and event horizons are determined and we investigate the evolution of the outer horizon showing that it may increase or decrease with time, depending on the value of the mass parameter. Finally, we test two proposals for dynamical entropy on this solution, one of them depending on the Kodama vector. In addition we show that the Kodama vector leads to the correct entropy for all stationary black holes in 2+1 dimensions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ black hole. | contribution 0.97 | 0.74 | 0.08 | asserted 0.83 |
| s1 | We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum. | result 1.00 | 0.94 | 0.23 | asserted 1.00 |
| s2 | The dynamical trapping and event horizons are determined and we investigate the evolution of the outer horizon showing that it may increase or decrease with time, depending on the value of the mass parameter. | result 0.87 | 0.96 | 0.22 | hedged possibility 0.53 |
| s3 | Finally, we test two proposals for dynamical entropy on this solution, one of them depending on the Kodama vector. | contribution 0.92 | 0.94 | 0.10 | asserted 0.92 |
| s4 | In addition we show that the Kodama vector leads to the correct entropy for all stationary black holes in 2+1 dimensions. | result 0.95 | 0.91 | 0.19 | asserted 1.00 |
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The paper
Original abstract
We investigate the global structure of a recently discovered simple exact, non-stationary solution of topologically massive and new massive gravity with the asymptotic charges of an undeformed BTZ black hole. We establish the existence of a timelike singularity in the causal structure of the spacetime even in the absence of angular momentum. The dynamical trapping and event horizons are determined and we investigate the evolution of the outer horizon showing that it may increase or decrease with time, depending on the value of the mass parameter. Finally, we test two proposals for dynamical entropy on this solution, one of them depending on the Kodama vector. In addition we show that the Kodama vector leads to the correct entropy for all stationary black holes in 2+1 dimensions.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as support 1 paper
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We can see an example of such spacetimes in Ref. [ref] , which is a solution of a three dimensional higher derivative gravity. ] Thus, $G^μνK_ν$ is not always a locally conserved current unless the axisymmetric spacetime becomes a warped product such as nonrotating spacetimes.
Extension of Kodama vector and quasilocal quantities in three-dimensional axisymmetric spacetimes · Extension of Kodama vector · 0.98
Cites it as background 1 paper
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New Massive Gravity (NMG), proposed in 2009 by Bergshoeff, Hohm and Townsend [ref] (also called BHT massive gravity), has received a great deal of attention due to its remarkable properties, particularly in the context of the AdS/CFT correspondence conjecture and because a variety of exact solutions have been found (see for example [ref] ).
Circular geodesics stability in a static black hole in new massive gravity · Introduction · 1.00
What it cites · 90 sentences without a confident label
Builds on 6 papers
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We will now present a generalization of this approach to dimensions $d≥3$[While the sources used in this work [ref] restrict their discussion to four dimensional spacetimes, a generalization of the Kodama vector to $d$ dimensions has been discussed in [ref] .
Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity · The Kodama vector and dynamical entropy · 0.94
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We will now present a generalization of this approach to dimensions $d≥3$[While the sources used in this work [ref] restrict their discussion to four dimensional spacetimes, a generalization of the Kodama vector to $d$ dimensions has been discussed in [ref] .
Gauss-Bonnet black holes with non-constant curvature horizons · The Kodama vector and dynamical entropy · 0.94
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We will now present a generalization of this approach to dimensions $d≥3$[While the sources used in this work [ref] restrict their discussion to four dimensional spacetimes, a generalization of the Kodama vector to $d$ dimensions has been discussed in [ref] .
Gravitational Energy in Spherical Symmetry · The Kodama vector and dynamical entropy · 0.94
Uses the method or tool of 6 papers
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In this section, we will make use of the prescription for defining dynamical black hole entropy that was put forward by Vivek Iyer and Robert Wald in [ref] , and which we will call the Iyer-Wald approach.
Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy · Idea · 1.00
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We can calculate the dynamic surface gravity $κ$ using the definition ([ref]) proposed in [ref] or alternatively using the definition $±κk_μ=k^β∇_[μk_β]$, $κ≥0$ proposed in [ref] .
Unified first law of black-hole dynamics and relativistic thermodynamics · $μ<1$, $μ≠-1$ · 0.99
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We can calculate the dynamic surface gravity $κ$ using the definition ([ref]) proposed in [ref] or alternatively using the definition $±κk_μ=k^β∇_[μk_β]$, $κ≥0$ proposed in [ref] .
Boundary Terms and Noether Current of Sphereical Black Holes · $μ<1$, $μ≠-1$ · 0.99
Uses data or values from 1 paper
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The Riemann- and Einstein-tensor of ([ref]) were already calculated in [ref] and read [equation] where we made use of the Ricci-scalar $R=R̅=-6$ which for vacuum solutions is fixed by the trace of the equations of motion of TMG as a function of the AdS-radius.
Formation of Black Holes in Topologically Massive Gravity · The Metric · 0.83
Compares with 5 papers
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By comparing the linearized equations of motion for massive modes of TMG and NMG (see [ref] for TMG and [ref] for NMG), it can be seen that a linear solution of TMG will also be a linear solution of NMG if we set $m^2=μ^2-1/2$[This is also what was found in [ref] for a solution of TMG of Petrov type N to be a solution of NMG.].
Chiral Gravity in Three Dimensions · Dynamical black holes in NMG · 0.91
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By comparing the linearized equations of motion for massive modes of TMG and NMG (see [ref] for TMG and [ref] for NMG), it can be seen that a linear solution of TMG will also be a linear solution of NMG if we set $m^2=μ^2-1/2$[This is also what was found in [ref] for a solution of TMG of Petrov type N to be a solution of NMG.].
Note on New Massive Gravity in $AdS_3$ · Dynamical black holes in NMG · 0.91
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By comparing the linearized equations of motion for massive modes of TMG and NMG (see [ref] for TMG and [ref] for NMG), it can be seen that a linear solution of TMG will also be a linear solution of NMG if we set $m^2=μ^2-1/2$[This is also what was found in [ref] for a solution of TMG of Petrov type N to be a solution of NMG.].
AdS_3/LCFT_2 - Correlators in New Massive Gravity · Dynamical black holes in NMG · 0.91
Cites as background 23 papers
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To fix the notation let us first recall the line-element of the non-rotating BTZ-black hole with $M=1$ and $l=1$ (i.e. $Λ=-1$) [ref] which reads: [equation] Both in TMG and NMG the linearized gravitational perturbations are given by the solutions of an equation $𝒟^μ_λ h_μν=0$ [ref] , subject to suitable boundary conditions [ref] .
AdS_3/LCFT_2 - Correlators in New Massive Gravity · Dynamical Black Holes in three Dimensions · 0.92
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To fix the notation let us first recall the line-element of the non-rotating BTZ-black hole with $M=1$ and $l=1$ (i.e. $Λ=-1$) [ref] which reads: [equation] Both in TMG and NMG the linearized gravitational perturbations are given by the solutions of an equation $𝒟^μ_λ h_μν=0$ [ref] , subject to suitable boundary conditions [ref] .
Note on New Massive Gravity in $AdS_3$ · Dynamical Black Holes in three Dimensions · 0.92
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To fix the notation let us first recall the line-element of the non-rotating BTZ-black hole with $M=1$ and $l=1$ (i.e. $Λ=-1$) [ref] which reads: [equation] Both in TMG and NMG the linearized gravitational perturbations are given by the solutions of an equation $𝒟^μ_λ h_μν=0$ [ref] , subject to suitable boundary conditions [ref] .
Chiral Gravity in Three Dimensions · Dynamical Black Holes in three Dimensions · 0.92
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