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Thermodynamics of Lovelock-Lifshitz Black Branes
High Energy Physics - Theory · Submitted 17 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity.
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The abstract, sentence by sentence
We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity. Using the first law of thermodynamics to obtain the relationship between entropy and temperature, we find that it too is the same as the Einsteinian case, apart from a constant of integration that depends on the Lovelock coefficients.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the thermodynamics of Lovelock-Lifshitz black branes. | contribution 0.93 | 0.92 | 0.04 | asserted 0.71 |
| s1 | We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. | method 0.81 | 0.94 | 0.04 | asserted 0.99 |
| s2 | Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. | result 0.57 | 0.96 | 0.05 | asserted 1.00 |
| s3 | Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity. | result 0.99 | 0.96 | 0.68 | asserted 1.00 |
| s4 | Using the first law of thermodynamics to obtain the relationship between entropy and temperature, we find that it too is the same as the Einsteinian case, apart from a constant of integration that depends on the Lovelock coefficients. | result 1.00 | 0.96 | 0.22 | asserted 1.00 |
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The paper
Original abstract
We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity. Using the first law of thermodynamics to obtain the relationship between entropy and temperature, we find that it too is the same as the Einsteinian case, apart from a constant of integration that depends on the Lovelock coefficients.
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References
How the literature uses it
21 arXiv papers cite this in 30 sentences
Papers citing it · 8 sentences without a confident label
Builds on it 1 paper
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We also found that we can extend the thermodynamics of Lifshitz black branes [ref] to the charged case, provided the parameter $z<n-1$.
Charged Lifshitz Black Holes · Concluding Remarks · 0.99
Uses its method or tool 3 papers
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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.
Quasi-Topological Lifshitz Black Holes · The conserved quantity along the radial coordinate $r$ · 0.94
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However, we can specify a stress tensor complex for the asymptotically Lifshitz spacetimes [ref] that consists of energy density $ℰ$, energy flux $ℰ_i$, momentum density $𝒫_i$, and spatial stress tensor $𝒫_ij$ by the bellow formula [equation] and [equation] The above conserved quantities obey the bellow conservation equations [ref] [equation] Using Eqs. [ref]-[ref], we calculate the energy density of the quasitopological Lifshitz dilaton black brane as this [equation] If we replace the large $r$ expansions [ref] in Eq. [ref], so we can attain the mass of this black brane as the following [equation] where $C_tot$ is the total constant at the infinity that has been defined in Eq. [ref].
Quasitopological Lifshitz dilaton black brane · Thermodynamics and conserved quantities · 0.89
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Applying the same method described in [ref] reveals that [equation] is conserved along the radial coordinate $r$ and [equation] where $D$ is an integration constant, which is chosen such that $κ(r)$ vanishes at the horizon, that is [equation] We shall evaluate $𝒞$ both at the horizon radius and infinity.
Charged Lifshitz Black Holes · Conserved Charge · 1.00
Cites it as background 13 papers
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We will restrict our attention to electrically charged black brane solutions to ([ref]), whose thermodynamics has been investigated recently in a number of studies [ref] , aimed at applying holographic methods to strongly coupled condensed matter systems.[See also [ref] for a discussion on the thermodynamics of Lifshitz geometries including higher derivatives.] The finite temperature solution to ([ref]) which is perhaps best known is the uncharged AdS black brane, [equation] in which the gauge field and the dilatonic scalar field are both constant.
Generating Temperature Flow for eta/s with Higher Derivatives: From Lifshitz to AdS · The Setup · 0.98
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Lifshitz solutions in the presence of higher curvature terms were previously investigated in [ref] .
Higher derivative corrections to Lifshitz backgrounds · Lifshitz solutions in higher derivative gravity · 0.99
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Lifshitz black holes with higher curvature gravities are in Refs. [ref] .
Thermodynamics of Rotating Lifshitz Dilaton Black Brane in Quartic Quasitopological gravity · Introduction · 0.95
What it cites · 1 sentence without a confident label
Cites as background 1 paper
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The holography of gravity theories including higher powers of the curvature, particularly curvature-cubed interactions, have attracted increased attention [ref] .
Holographic studies of quasi-topological gravity · Introduction · 0.98
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