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Non-perturbative analysis of the constraints and the positivity of the energy of the complete Horava theory
High Energy Physics - Theory · Submitted 10 May 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using it we prove the positivity of the energy of the effective action under consideration.
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The abstract, sentence by sentence
We perform a non-perturbative analysis to the Hamiltonian constraint of the lowest-order effective action of the complete Horava theory, which includes a (\partial_i \ln N)^2 term in the Lagrangian. We cast this constraint as a partial differential equation for N and show that the solution exists and is unique under a condition of positivity for the metric and its conjugate momentum. We interpret this condition as the analog of the positivity of the spatial scalar curvature in general relativity. From the analysis we extract several general properties of the solution for N: an upper bound on its absolute value and its asymptotic behavior. In particular, we find that the asymptotic behavior is different to that of general relativity, which has consequences on the evolution of the initial data and the calculus of variations. Similarly, we proof the existence and uniqueness of the solution of the equation for the Lagrange multiplier of the theory. We also find a relationship between the expression of the energy and the solution of the Hamiltonian constraint. Using it we prove the positivity of the energy of the effective action under consideration. Minkowski spacetime is obtained from Horava theory at minimal energy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We perform a non-perturbative analysis to the Hamiltonian constraint of the lowest-order effective action of the complete Horava theory, which includes a (\partial_i \ln N)^2 term in the Lagrangian. | contribution 0.88 | 0.96 | 0.05 | asserted 0.99 |
| s1 | We cast this constraint as a partial differential equation for N and show that the solution exists and is unique under a condition of positivity for the metric and its conjugate momentum. | result 0.63 | 0.96 | 0.15 | asserted 1.00 |
| s2 | We interpret this condition as the analog of the positivity of the spatial scalar curvature in general relativity. | interpretation 1.00 | 0.83 | 0.08 | asserted 0.98 |
| s3 | From the analysis we extract several general properties of the solution for N: an upper bound on its absolute value and its asymptotic behavior. | result 0.94 | 0.97 | 0.08 | asserted 1.00 |
| s4 | In particular, we find that the asymptotic behavior is different to that of general relativity, which has consequences on the evolution of the initial data and the calculus of variations. | result 0.59 | 0.94 | 0.10 | asserted 1.00 |
| s5 | Similarly, we proof the existence and uniqueness of the solution of the equation for the Lagrange multiplier of the theory. | result 0.90 | 0.95 | 0.06 | asserted 1.00 |
| s6 | We also find a relationship between the expression of the energy and the solution of the Hamiltonian constraint. | result 0.83 | 0.95 | 0.07 | asserted 1.00 |
| s7 | Using it we prove the positivity of the energy of the effective action under consideration. | result 0.97 | 0.96 | 0.53 | asserted 1.00 |
| s8 | Minkowski spacetime is obtained from Horava theory at minimal energy. | result 0.96 | 0.67 | 0.20 | asserted 1.00 |
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Original abstract
We perform a non-perturbative analysis to the Hamiltonian constraint of the lowest-order effective action of the complete Horava theory, which includes a (\partial_i \ln N)^2 term in the Lagrangian. We cast this constraint as a partial differential equation for N and show that the solution exists and is unique under a condition of positivity for the metric and its conjugate momentum. We interpret this condition as the analog of the positivity of the spatial scalar curvature in general relativity. From the analysis we extract several general properties of the solution for N: an upper bound on its absolute value and its asymptotic behavior. In particular, we find that the asymptotic behavior is different to that of general relativity, which has consequences on the evolution of the initial data and the calculus of variations. Similarly, we proof the existence and uniqueness of the solution of the equation for the Lagrange multiplier of the theory. We also find a relationship between the expression of the energy and the solution of the Hamiltonian constraint. Using it we prove the positivity of the energy of the effective action under consideration. Minkowski spacetime is obtained from Horava theory at minimal energy.
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How the literature uses it
7 arXiv papers cite this in 8 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 2 papers
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From the Hamiltonian formalism of the Hořava gravity [ref] , we can obtain the Hamiltonian density $H$ via a Legendre transformation.
Constraints on Ho\v{r}ava-Lifshitz gravity from GRB 170817A · The model · 0.89
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We proceed to reformulate the action using the Hamiltonian formalism [ref] .
The anisotropic coupling of gravity and electromagnetism in Ho\v{r}ava-Lifshitz theory · Hořava-Lifshitz in five dimensions · 0.96
Cites it as background 3 papers
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Since the Hořava proposal [ref] and its consistent extension [ref] , many investigations have been devoted to corroborated the consistency of the theory as a possible candidate to describe a UV complete gravitational theory [ref] .
Wave zone of the Ho\v{r}ava--Lifshitz gravity coupled to a gauge vector · Introduction · 0.94
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The fixed values are equivalent to have set a Cartesian system at spatial infinity (see Ref. [ref] for a discussion on asymptotically flat conditions in the context of Hořava theory, where a definition of the spacetime metric does not exist).
Renormalization of the nonprojectable Horava theory · The classical theory · 0.85
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Thus we choose the minimal version. * Behavior of the shift function: Different versions of Hořava-Lifshitz gravity may have different dynamics and numbers of degrees of freedom, depending on the numbers of fields and numbers of first-class and second-class constraints (for example, see [ref] ).
Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect · Summary and Comments · 0.83
What it cites
Cites as background 1 paper
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For a perturbative analysis in the projectable case see, for example, Ref. [ref] .].
Perturbative instabilities in Horava gravity · Introduction · 0.93
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