Quasi-Topological Lifshitz Black Holes

M.H. Dehghani; R.B. Mann; W.G. Brenna

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Quasi-Topological Lifshitz Black Holes

W.G. Brenna, M.H. Dehghani, R.B. Mann

High Energy Physics - Theory · Submitted 18 Jan 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.86 · mentions code or data availability 0.02.

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We investigate the effects of including a quasi-topological cubic curvature term to the Gauss-Bonnet action to five dimensional Lifshitz gravity. We find that a new set of Lifshitz black hole solutions exist that are analogous to those obtained in third-order Lovelock gravity in higher dimensions. No additional matter fields are required to obtain solutions with asymptotic Lifshitz behaviour, though we also investigate solutions with matter. Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the effects of including a quasi-topological cubic curvature term to the Gauss-Bonnet action to five dimensional Lifshitz gravity.	contribution 0.98	0.92	0.07	asserted 0.79
s1	We find that a new set of Lifshitz black hole solutions exist that are analogous to those obtained in third-order Lovelock gravity in higher dimensions.	result 1.00	0.96	0.40	asserted 1.00
s2	No additional matter fields are required to obtain solutions with asymptotic Lifshitz behaviour, though we also investigate solutions with matter.	result 0.97	0.88	0.10	asserted 1.00
s3	Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.	result 0.99	0.95	0.47	asserted 1.00

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The paper

Original abstract

We investigate the effects of including a quasi-topological cubic curvature term to the Gauss-Bonnet action to five dimensional Lifshitz gravity. We find that a new set of Lifshitz black hole solutions exist that are analogous to those obtained in third-order Lovelock gravity in higher dimensions. No additional matter fields are required to obtain solutions with asymptotic Lifshitz behaviour, though we also investigate solutions with matter. Furthermore, we examine black hole solutions and their thermodynamics in this situation and find that a negative quasi-topological term, just like a positive Gauss-Bonnet term, prevents instabilities in what are ordinarily unstable Einsteinian black holes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quintic quasi-topological gravity
hep-th 2017-02 conditional novelty 6.0 of 10

A 24-term quintic curvature Lagrangian in five dimensions is exhibited whose spherically symmetric field equations reduce to a single quintic polynomial, yielding ghost-free AdS black holes obeying the first law.
Black holes and black branes in Lifshitz spacetimes
hep-th 2011-05 accept novelty 6.0 of 10

Exact analytic Lifshitz black hole and black brane solutions are constructed for arbitrary z and dimension, and their phase diagrams are shown to change qualitatively at z = 2.
Lifshitz holography
hep-th 2015-12 conditional novelty 3.0 of 10

A structured review of the holographic dictionary for Lifshitz backgrounds, arguing that the bulk matter supporting the geometry sources the non-relativistic energy-momentum complex plus scalar operators rather than a...

How the literature uses it

21 arXiv papers cite this in 27 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 10 sentences without a confident label

Builds on it 1 paper

After the work of [ref] , the generalization to Lifshitz solution has been done in [ref] .

Hyperscaling-violating Lifshitz Solutions in Cubic Gravity · Black Hole Solution · 0.83

Compares with it 1 paper

Similar to the effect of the quasi-topological term in numerical black hole solutions [ref] , the thermodynamic behaviour of the quasi-topological term closely follows Gauss-Bonnet thermodynamics for black holes beyond a certain radius (on the order of $r_h ∼1$).

Quasi-topological Reissner-Nordstr\"om Black Holes · RN Thermodynamics · 0.93

Cites it as background 14 papers

Quasitopological gravity is one the most important modified gravities that has been studied in Refs. [ref] .

Thermodynamics of Rotating Lifshitz Dilaton Black Brane in Quartic Quasitopological gravity · Introduction · 0.94
Attempts have been made to find analytic and numeric black hole/brane solutions which asymptotically admit Lifshitz geometry [ref] .

Asymptotically Lifshitz Brane-World Black Holes · Introduction · 0.88
Until now, some investigations of the quasitopological black hole solutions have been done [ref] .

Yang-Mills black holes in Quasitopological gravity · Introduction · 0.97

What it cites · 21 sentences without a confident label

Uses the method or tool of 3 papers

We are then able to write the equations of motion in the same manner as [ref] , obtaining the conserved quantity [equation] This derivation was performed using the form of the quasi-topological Lagrangian for $D$ dimensions, given by ([ref]), and the form of the conserved quantity was checked explicitly for $D$ from $7$ through $11$ to determine the dimensionally independent form given.

Thermodynamics of Lovelock-Lifshitz Black Branes · The conserved quantity along the radial coordinate $r$ · 0.94
With these ODEs, initial conditions are chosen from the series solution (evaluated just beyond the horizon), and then the shooting method (explained in [ref] ) is used to obtain solutions.

Black holes in asymptotically Lifshitz spacetime · Numerical Solutions · 0.95
With these ODEs, initial conditions are chosen from the series solution (evaluated just beyond the horizon), and then the shooting method (explained in [ref] ) is used to obtain solutions.

Lifshitz Topological Black Holes · Numerical Solutions · 0.95

Compares with 3 papers

Although the asymptotic behaviour of our solution is different from Ref. [ref] and $f(r) ≠g(r)$, we obtain the same result: [equation] where $D$ is the number of dimensions and $A$ is the surface area of the black hole (since our metric is spherically symmetric, the surface area will be proportional to $r^D-2_0$).

Black Holes in Quasi-topological Gravity · Thermodynamics · 0.99
This solution matches the form of one obtained in 3rd order Lovelock gravity for $D>6$ [ref] , as our field equations are of the same form.

Thermodynamic Instability of Black Holes of Third Order Lovelock Gravity · Matter-free Solutions · 0.99
Due to the equivalence of our field equations, they match the values obtained in third order Lovelock gravity [ref] , once the substitutions $μL^4 =-α̂_3$ and $λL^2 =α̂_2$ are made.

Lovelock-Lifshitz Black Holes · Large $r$ Series Solutions · 1.00

Cites as background 11 papers

Some new exact black hole solutions were obtained as well as a broad class of numerical solutions, and asymptotic Lifshitz solutions with curvature-squared terms in the action have also been investigated [ref] .

Analytic Lifshitz black holes in higher dimensions · Introduction · 0.80
Some new exact black hole solutions were obtained as well as a broad class of numerical solutions, and asymptotic Lifshitz solutions with curvature-squared terms in the action have also been investigated [ref] .

A Lifshitz Black Hole in Four Dimensional R^2 Gravity · Introduction · 0.80
Some new exact black hole solutions were obtained as well as a broad class of numerical solutions, and asymptotic Lifshitz solutions with curvature-squared terms in the action have also been investigated [ref] .

Lifshitz Black Hole in Three Dimensions · Introduction · 0.80

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