Quasitopological Lifshitz dilaton black brane

A. Bazrafshan; Gh. Forozani; M. Ghanaatian; S. Rezaei

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Quasitopological Lifshitz dilaton black brane

A. Bazrafshan, M. Ghanaatian, S. Rezaei, Gh. Forozani

High Energy Physics - Theory · Submitted 25 Aug 2024

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

The authors' main claim Our results show that the quasitopological Lifshitz dilaton black brane solutions are thermally stable for each positive values of the dynamical critiacl exponent, $z$.

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We construct a new class of $(n+1)$-dimensional Lifshitz dilaton black brane solutions in the presence of the cubic quasitopological gravity for a flat boundary. The related action supports asymptotically Lifshitz solutions by applying some conditions which are used throughout the paper. We have to add a new boundary term and some new counterterms to the bulk action to have finite solutions. Then we define a finite stress tensor complex by which we can calculate the energy density of the quasitopological Lifshitz dilaton black brane. It is not possible to obtain analytical solutions, and so we use some expantions to probe the functions behaviors near the horizon and at the infinity. Combining the equations, we can attain a total constant along the coordinate $r$. At the horizon, this constant is proportional to the product of the temperature and the entropy and at the infinity, the total constant shows the energ density of the quasitopological Lifshitz dilaton black brane. Therefore, we can reach to a relation between the conserved quantities temperature, entropy and the energy density and get a smarr-type formula. Using the first law of thermodynamics, we can find a relation between the entropy and the temperature and then ontain the heat capacity. Our results show that the quasitopological Lifshitz dilaton black brane solutions are thermally stable for each positive values of the dynamical critiacl exponent, $z$.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct a new class of $(n+1)$-dimensional Lifshitz dilaton black brane solutions in the presence of the cubic quasitopological gravity for a flat boundary.	contribution 1.00	0.96	0.10	asserted 1.00
s1	The related action supports asymptotically Lifshitz solutions by applying some conditions which are used throughout the paper.	method 0.53	0.38	0.04	asserted 0.98
s2	We have to add a new boundary term and some new counterterms to the bulk action to have finite solutions.	method 0.86	0.89	0.03	asserted 1.00
s3	Then we define a finite stress tensor complex by which we can calculate the energy density of the quasitopological Lifshitz dilaton black brane.	method 0.81	0.94	0.04	asserted 0.95
s4	It is not possible to obtain analytical solutions, and so we use some expantions to probe the functions behaviors near the horizon and at the infinity.	method 0.64	0.87	0.02	asserted 1.00
s5	Combining the equations, we can attain a total constant along the coordinate $r$.	result 0.48	0.92	0.03	asserted 0.77
s6	At the horizon, this constant is proportional to the product of the temperature and the entropy and at the infinity, the total constant shows the energ density of the quasitopological Lifshitz dilaton black brane.	result 0.56	0.89	0.08	asserted 1.00
s7	Therefore, we can reach to a relation between the conserved quantities temperature, entropy and the energy density and get a smarr-type formula.	result 0.89	0.95	0.21	asserted 0.90
s8	Using the first law of thermodynamics, we can find a relation between the entropy and the temperature and then ontain the heat capacity.	method 0.83	0.94	0.06	asserted 0.89
s9	Our results show that the quasitopological Lifshitz dilaton black brane solutions are thermally stable for each positive values of the dynamical critiacl exponent, $z$.	result 0.99	0.95	0.74	asserted 1.00

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Original abstract

We construct a new class of $(n+1)$-dimensional Lifshitz dilaton black brane solutions in the presence of the cubic quasitopological gravity for a flat boundary. The related action supports asymptotically Lifshitz solutions by applying some conditions which are used throughout the paper. We have to add a new boundary term and some new counterterms to the bulk action to have finite solutions. Then we define a finite stress tensor complex by which we can calculate the energy density of the quasitopological Lifshitz dilaton black brane. It is not possible to obtain analytical solutions, and so we use some expantions to probe the functions behaviors near the horizon and at the infinity. Combining the equations, we can attain a total constant along the coordinate $r$. At the horizon, this constant is proportional to the product of the temperature and the entropy and at the infinity, the total constant shows the energ density of the quasitopological Lifshitz dilaton black brane. Therefore, we can reach to a relation between the conserved quantities temperature, entropy and the energy density and get a smarr-type formula. Using the first law of thermodynamics, we can find a relation between the entropy and the temperature and then ontain the heat capacity. Our results show that the quasitopological Lifshitz dilaton black brane solutions are thermally stable for each positive values of the dynamical critiacl exponent, $z$.

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What it cites · 30 sentences without a confident label

Uses the method or tool of 6 papers

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].

Thermodynamics of Lovelock-Lifshitz Black Branes · Thermodynamics and conserved quantities · 0.89
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].

Holographic stress tensor for non-relativistic theories · Thermodynamics and conserved quantities · 0.89
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].

Thermodynamics of Rotating Lovelock-Lifshitz Black Branes · Thermodynamics and conserved quantities · 0.89

Compares with 1 paper

For $z=1$ (where $f(r)=g(r)$) and in the absence of the dilaton field, $Φ(r)=0$, the total constant reduces to [equation] where it is proportional to the mass of the quasitopological black brane with $s=1$ in Ref. [ref] .

Third order quasi-topological black hole with power-law Maxwell nonlinear source · constants along the radial coordinate · 0.86

Cites as background 11 papers

Recently, a study of the Gauss-Bonnet Lifshitz dilaton black brane has been done in Ref. [ref] .

Thermodynamics of Gauss-Bonnet-Dilaton Lifshitz Black Branes · Introduction · 0.80
Quasitopological gravity black hole solutions have been investigated in Refs. [ref] .

Quasi-Topological Lifshitz Black Holes · Introduction · 0.99
Quasitopological gravity black hole solutions have been investigated in Refs. [ref] .

Holographic studies of quasi-topological gravity · Introduction · 0.99

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