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Relativistic Hydrodynamics a brief review of classical and quantum fluids in relativistic astrophysics
General Relativity and Quantum Cosmology · Submitted 13 Oct 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this study, we conclude that superfluidity is one of the possible ways to quantize gravity.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
The objective of this work is to revisit fundamental aspects of relativistic hydrodynamics, aiming at the construction of a first course in relativistic hydrodynamics and its applications to astrophysics at the level of end of undergraduate course and beginning of graduate course. We aim to introduce more basic concepts of basic hydrodynamics, going through models analogous to gravity to the theory of superfluids, applying mainly to astrophysics and the cosmology of the dark universe. We review the classical hydrodynamics, Galileo symmetry and its extension to Lorentz Symmetry applied to fluids, enabling the analogy of fluids with space-time. We study the conservation of the momentum-energy tensor and the energy conditions of Hawking-Ellis. In the next sections we investigate quantum effects, in particular linked to superfluids, and we also sketch an application to dark matter. In this study, we conclude that superfluidity is one of the possible ways to quantize gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The objective of this work is to revisit fundamental aspects of relativistic hydrodynamics, aiming at the construction of a first course in relativistic hydrodynamics and its applications to astrophysics at the level of end of undergraduate course and beginning of graduate course. | contribution 0.95 | 0.35 | 0.03 | asserted 0.87 |
| s1 | We aim to introduce more basic concepts of basic hydrodynamics, going through models analogous to gravity to the theory of superfluids, applying mainly to astrophysics and the cosmology of the dark universe. | contribution 0.93 | 0.48 | 0.02 | asserted 0.73 |
| s2 | We review the classical hydrodynamics, Galileo symmetry and its extension to Lorentz Symmetry applied to fluids, enabling the analogy of fluids with space-time. | contribution 0.70 | 0.34 | 0.02 | asserted 0.98 |
| s3 | We study the conservation of the momentum-energy tensor and the energy conditions of Hawking-Ellis. | contribution 0.79 | 0.38 | 0.02 | asserted 0.86 |
| s4 | In the next sections we investigate quantum effects, in particular linked to superfluids, and we also sketch an application to dark matter. | contribution 0.82 | 0.62 | 0.03 | asserted 0.56 |
| s5 | In this study, we conclude that superfluidity is one of the possible ways to quantize gravity. | interpretation 0.52 | 0.64 | 0.82 | hedged possibility 0.84 |
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The paper
Original abstract
The objective of this work is to revisit fundamental aspects of relativistic hydrodynamics, aiming at the construction of a first course in relativistic hydrodynamics and its applications to astrophysics at the level of end of undergraduate course and beginning of graduate course. We aim to introduce more basic concepts of basic hydrodynamics, going through models analogous to gravity to the theory of superfluids, applying mainly to astrophysics and the cosmology of the dark universe. We review the classical hydrodynamics, Galileo symmetry and its extension to Lorentz Symmetry applied to fluids, enabling the analogy of fluids with space-time. We study the conservation of the momentum-energy tensor and the energy conditions of Hawking-Ellis. In the next sections we investigate quantum effects, in particular linked to superfluids, and we also sketch an application to dark matter. In this study, we conclude that superfluidity is one of the possible ways to quantize gravity.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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Another important work [ref] has considered the relation of the minimum speed with superfluids and acoustic geometries and the latter is a review published in AIP Advanced, which makes a review about Relativistic Hydrodynamics [ref] .
Deformed Special Relativity with a minimum speed as explanation of the tiny value of the cosmological constant based on the Boomerang experiment in the ${\Lambda}CDM$ scenario · Conclusions and prospects · 0.84
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Other topics, applications and viewpoints on relativistic hydrodynamics can be found in countless review articles such as, for example, [ref] .
Effective Field Theories for Material Media · Further Readings · 1.00
What it cites · 54 sentences without a confident label
Uses the method or tool of 2 papers
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Building then the normalization condition [ref] [equation] where $ℳ$ is the total mass and $ν$ is the volume of a fluid, so we write the mass density of the fluid $ρ=|ψ|^2$.
Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences · Mandelung formalism applied to dark matter · 0.91
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Let us now study our system in terms of the collective variables $n(p)$ which is the density of quasi-particles and $v⃗$ the velocity of the fluid [ref] , we define, according to Volovik citevolo , the distribution of quasiparticles in thermal equilibrium at a temperature $T$ [equation] where $+$ represents fermion and $-$ represents Boson.
Superfluid analogies of cosmological phenomena · Building collective variables for the components $j⃗_s$ and $j⃗_n$ · 0.82
Compares with 3 papers
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The cosmological constant is written by [ref] in terms of the matter fields $ψ_m$ and the scalar field $V_qu$, [equation] this is yet another point of similarity between the works of [ref] and [ref] , since the scalar field equation in [ref] has a functional form very similar to the form of [ref], and we have already demonstrated in [ref] that the field $ϕ$ associated with the Symmetric Special Relativity (SSR) kinematics has inflationary properties.
Variation of the speed of light and a minimum speed in the scenario of an inflationary universe with accelerated expansion · Mandelung formalism · 0.90
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The cosmological constant is written by [ref] in terms of the matter fields $ψ_m$ and the scalar field $V_qu$, [equation] this is yet another point of similarity between the works of [ref] and [ref] , since the scalar field equation in [ref] has a functional form very similar to the form of [ref], and we have already demonstrated in [ref] that the field $ϕ$ associated with the Symmetric Special Relativity (SSR) kinematics has inflationary properties.
Bohmian mechanics versus Madelung quantum hydrodynamics · Mandelung formalism · 0.90
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The similarity of the action [ref] with the action of a k-essence model [ref] is remarkable.
k-Essence, superluminal propagation, causality and emergent geometry · NLKG-Mandelung's formalism and superfluids · 0.97
Cites as background 4 papers
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One of the open discussions is the relation with the simple connectedness of the space [ref] .
Iordanskii Force and the Gravitational Aharonov-Bohm effect for a Moving Vortex · The quantization of a superfluid · 0.81
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One of the open discussions is the relation with the simple connectedness of the space [ref] .
Relativistic superfluidity and vorticity from the nonlinear Klein-Gordon equation · The quantization of a superfluid · 0.81
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Let's now follow [ref] , [ref] , [ref] to review the concept of acoustic geometry.
Acoustic propagation in fluids: an unexpected example of Lorentzian geometry · Fluctuations in barotropic fluids $p=p(ρ)$ under Lorentz symmetry · 0.80
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