Publisher’s Note: Quantizing Hořava-Lifshitz gravity via causal dynamical triangulations [Phys. Rev. D<b>85</b>, 044027 (2012)]

Anderson, Caroline F.; Carlip, Steven; Cooperman, Joshua H.; Hořava, Petr; Kommu, Rajesh; Zulkowski, Patrick R.

doi:10.1103/physrevd.85.049904

Cited by 20 publications

(24 citation statements)

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“…Following the ideas [57,58,59,56] one could, e.g., use the foliated flow equation to study diffusion processes on spatial slices and examine if these can be matched to the CDT data recently reported in [60]. This may shed new light on the question whether the continuum limit of CDT corresponds to an isotropic or anisotropic gravity theory as suggested in [61,62]. The trace of the heat kernel has the well-known asymptotic expansion for s → 0…”

Section: Discussionmentioning

confidence: 99%

A functional renormalization group equation for foliated spacetimes

Rechenberger

Saueressig

2013

J. High Energ. Phys.

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We derive an exact functional renormalization group equation for the projectable version of Hořava-Lifshitz gravity. The flow equation encodes the gravitational degrees of freedom in terms of the lapse function, shift vector and spatial metric and is manifestly invariant under background foliation-preserving diffeomorphisms. Its relation to similar flow equations for gravity in the metric formalism is discussed in detail, and we argue that the space of action functionals, invariant under the full diffeomorphism group, forms a subspace of the latter invariant under renormalization group transformations. As a first application we study the RG flow of the Newton constant and the cosmological constant in the ADM formalism. In particular we show that the non-Gaussian fixed point found in the metric formulation is qualitatively unaffected by the change of variables and persists also for Lorentzian signature metrics.

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Section: Discussionmentioning

confidence: 99%

A functional renormalization group equation for foliated spacetimes

Rechenberger

Saueressig

2013

J. High Energ. Phys.

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“…Moreover, the positive semidefinite function (16) has the correct qualitative features of a probability density measured within CDT, making a future comparison between these more detailed spectral properties of the underlying quantum spacetimes meaningful. 4 The averaged squared displacement of the test particle implied by (16) is easily found to be…”

Section: A Diffusion In Nonlinear Timementioning

confidence: 99%

“…In other words, a classical random walk is used to capture the fractal features of the geometry. The probe particle thereby has equal probabilities for moving from its current simplex to one of its neighbors in each time step [1,[3][4][5]. This construction implies that, after each time step, the probe particle has to be located somewhere on the geometry, guaranteeing a positive semidefinite probability density P (x, x ′ , σ).…”

Section: Introductionmentioning

confidence: 99%

“…causal dynamical triangulations (CDT) in four [1,2] and three spacetime dimensions [3,4], Euclidean dynamical triangulations (EDT) [5], loop quantum gravity (LQG) [6], asymptotically safe gravity (or quantum Einstein gravity, QEG) [7][8][9][10], nonlocal gravity [11], and also Hořava-Lifshitz (HL) gravity [12,13]. Remarkably, many of these works assess that d S = 2 at microscopic scales [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Probing the quantum nature of spacetime by diffusion

2013

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Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semidefinite probability densities, applicable to asymptotically safe gravity, Hořava-Lifshitz gravity and loop quantum gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime.

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“…But for the general solutions (9), the curvature singularities at r = 0 in (14) and (15) are covariant in the foliation preserving diffeomorphism such that they are physical singularities. For asymptotically AdS, i.e., Λ < 0 2 , the solution (9) has two horizons generally where f and N vanish simultaneously, i.e., the apparent and Killing horizons coincide, and the Hawking temperature for the outer horizon r + is given by…”

Section: The Rotating Black Hole In Three-dimensional Hořava Gravitymentioning

confidence: 99%

The rotating black hole in renormalizable quantum gravity: The three-dimensional Hořava gravity case

Park

2013

Physics Letters B

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Recently Hořava proposed a renormalizable quantum gravity, without the ghost problem, by abandoning Einstein's equal-footing treatment of space and time through the anisotropic scaling dimensions. Since then various interesting aspects, including the exact black hole solutions have been studied but no rotating black hole solutions have been found yet, except some limiting cases. In order to fill the gap, I consider a simpler three-dimensional set-up with z = 2 and obtain the exact rotating black hole solution. This solution has a ring curvature singularity inside the outer horizon, like the four-dimensional Kerr black hole in Einstein gravity, as well as a curvature singularity at the origin. The usual mass bound works also here but in a modified form. Moreover, it is shown that the conventional first law of thermodynamics with the usual Hawking temperature and chemical potential does not work, which seems to be the genuine effect of Lorentz-violating gravity due to lack of the absolute horizon.

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Publisher’s Note: Quantizing Hořava-Lifshitz gravity via causal dynamical triangulations [Phys. Rev. D85, 044027 (2012)]

Cited by 20 publications

References 0 publications

A functional renormalization group equation for foliated spacetimes

A functional renormalization group equation for foliated spacetimes

Probing the quantum nature of spacetime by diffusion

The rotating black hole in renormalizable quantum gravity: The three-dimensional Hořava gravity case

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