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On the role of boundary conditions within Ho\v{r}ava-Lifshitz gravity
High Energy Physics - Theory · Submitted 29 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Subsequently, we show that, whenever bound states are absent, one can associate to each admissible boundary condition a ground and a KMS state whose associated two-point correlation function is of local Hadamard form.
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The abstract, sentence by sentence
On a class of four-dimensional Lifshitz spacetimes with critical exponent $z=2$, including a hyperbolic and a spherical Lifshitz topological black hole, we consider a real Klein-Gordon field. Using a mode-decomposition, we split the equation of motion into a radial and into an angular component. As first step, we discuss under which conditions on the underlying parameters, we can impose to the radial equation boundary conditions of Robin type and whether bound state solutions do occur. Subsequently, we show that, whenever bound states are absent, one can associate to each admissible boundary condition a ground and a KMS state whose associated two-point correlation function is of local Hadamard form.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | On a class of four-dimensional Lifshitz spacetimes with critical exponent $z=2$, including a hyperbolic and a spherical Lifshitz topological black hole, we consider a real Klein-Gordon field. | background 0.52 | 0.58 | 0.03 | asserted 0.85 |
| s1 | Using a mode-decomposition, we split the equation of motion into a radial and into an angular component. | method 1.00 | 0.94 | 0.02 | asserted 1.00 |
| s2 | As first step, we discuss under which conditions on the underlying parameters, we can impose to the radial equation boundary conditions of Robin type and whether bound state solutions do occur. | contribution 0.62 | 0.84 | 0.06 | unclear 0.51 |
| s3 | Subsequently, we show that, whenever bound states are absent, one can associate to each admissible boundary condition a ground and a KMS state whose associated two-point correlation function is of local Hadamard form. | result 0.99 | 0.92 | 0.61 | asserted 1.00 |
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The paper
Original abstract
On a class of four-dimensional Lifshitz spacetimes with critical exponent $z=2$, including a hyperbolic and a spherical Lifshitz topological black hole, we consider a real Klein-Gordon field. Using a mode-decomposition, we split the equation of motion into a radial and into an angular component. As first step, we discuss under which conditions on the underlying parameters, we can impose to the radial equation boundary conditions of Robin type and whether bound state solutions do occur. Subsequently, we show that, whenever bound states are absent, one can associate to each admissible boundary condition a ground and a KMS state whose associated two-point correlation function is of local Hadamard form.
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How the literature uses it
1 arXiv paper cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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In this paper we shall not give all the details of the latter, see [ref] , rather we focus on the construction of ground states admitting generalized $(γ,v)$-Robin boundary conditions.
Hidden freedom in the mode expansion on static spacetimes · The quantum dynamics · 0.86
What it cites · 25 sentences without a confident label
Builds on 2 papers
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Inspired by these works we consider a massive, real scalar field, with an arbitrary coupling to scalar curvature and we investigate whether one can extend the class of admissible boundary conditions on a four dimensional Lifshitz spacetime with dynamical critical exponent $z=2$ and on its generalizations to a hyperbolic and to a spherical Lifshitz topological black hole, as determined in [ref] .
Lifshitz Topological Black Holes · Introduction · 0.83
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Here we confirm and extend the results of [ref] , in which it was shown the occurrence of instabilities for a scalar field on Lifshitz spacetime for a specific range of the field parameters.
Boundary conditions for scalars in Lifshitz · Introduction · 0.94
Uses the method or tool of 3 papers
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In particular, here we follow the same nomenclature and strategy outlined in [ref] to which we refer for further details.
Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions · The radial equation on Lifshitz spacetime · 0.98
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Since the integrand has no poles within the contour, by the same argument of [ref] , or by a direct application of Jordan's Lemma, the arc integrals vanish.
Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions · Two-point functions on Lifshitz spacetime $𝖫𝗂𝖿_0$ · 0.87
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On the other hand, one can compute the transition rate of an Unruh-DeWitt detector in a $𝖫𝗂𝖿_κ$ spacetime, following the same prescription of [ref] unveiling in particular how such detector distinguishes among the three Lifshitz spacetimes considered, or how it interacts differently with a massless hyperbolic black hole or with a Lifshitz topological black holes.
Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect · Conclusion · 0.93
Compares with 1 paper
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Comparing them with topological black holes within Einstein gravity [ref] , we observe that compact sections at fixed $r$ and $t$ can also be obtained for Lifshitz topological black holes by suitable identifications in the spatial coordinates.
Topological Black Holes -- Outside Looking In · Hor̆ava-Lifshitz solutions · 1.00
Cites as support 2 papers
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A two-point function as constructed above, of the form [ref], satisfies the canonical commutation relations and characterizes a ground-state of local Hadamard form [ref] .
Passivity and microlocal spectrum condition · The construction of physically-sensible two-point functions · 1.00
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As a consequence, whenever such bound states do appear, it is not possible to construct the two-point function of a ground state associated to the underlying scalar field, as already observed in [ref] .
Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions · Introduction · 0.98
Cites as background 12 papers
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Here we do not enter into the details of such property, leaving an interested reader to the review [ref] or to [ref] .
Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction · Two-point functions for general boundary conditions · 0.96
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In the quest of finding a quantization scheme for the gravitational field, Hor̆ava-Lifshitz gravity, [ref] , was first introduced as a theory in which the underlying spacetime possesses a time coordinate $t$ and spatial counterparts $x$ appearing with a different scaling behaviour [equation] While we will not focus on the developments towards a quantum theory of gravitation, referring an interested reader to the recent review [ref] , we stress that also different applications of these models have been discussed ranging from cosmology, to quantum critical systems [ref] , to condensed matter physics, see e.g. [ref] and references therein, and to the AdS/CFT correspondence.
General Covariance in Gravity at a Lifshitz Point · Introduction · 1.00
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In the quest of finding a quantization scheme for the gravitational field, Hor̆ava-Lifshitz gravity, [ref] , was first introduced as a theory in which the underlying spacetime possesses a time coordinate $t$ and spatial counterparts $x$ appearing with a different scaling behaviour [equation] While we will not focus on the developments towards a quantum theory of gravitation, referring an interested reader to the recent review [ref] , we stress that also different applications of these models have been discussed ranging from cosmology, to quantum critical systems [ref] , to condensed matter physics, see e.g. [ref] and references therein, and to the AdS/CFT correspondence.
Lectures on holographic methods for condensed matter physics · Introduction · 1.00
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