Myungseok Eune, Wontae Kim
We reconsider a recently proposed action for a free particle which is compatible with Hořava-Lifshitz gravity, and then obtain the subluminal and the superluminal limits without gauge ambiguity in terms of Hamiltonian formulation.
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On the Lifshitz black brane geometry of an Einstein-Maxwell-dilaton gravity, we holographically investigate electric DC conductivities and the role of impurity in a non-relativistic Lifshitz medium with two different charge carriers, impurity and Lifshitz matter. The conductivity carried by Lifshitz matter is proportional to the square of temperature, while that carried by impurity crucially depends on the bulk coupling parameter \g. For \g < -2, impurity at high temperature can change the electric property of the Lifshitz medium significantly so that the Lifshitz matter with impurity can show…
This note is devoted to the study of Hamiltonian formalism of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended Horava-Lifshitz gravities and show that these theories have many unusual and interesting properties.
In this note we study the relation between F(R) and scalar tensor Horava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance corresponding scalar tensor theory has more complicated form than in case of the full diffeomorphism invariant F(R) theory of gravity. We also show that in the low energy limit this theory flows to the relativistic scalar tensor theory of gravity.
We fermionize the two-dimensional free Lifshitz scalar field in order to identify what the gauge covariant couplings are, and then they are bosonized back to get the gauged Lifshitz scalar field theories. We show that they give the same physical modes with those of the corresponding Lorentz invariant gauged scalar theories, although the dispersion relations are different.
With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Hořava-Lifshitz gravity. It is shown that, when the parameter of Hořava-Lifshitz gravity $ω\rightarrow \infty$, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hořava-Lifshitz gravity.
We investigate the dynamics of a scalar field governed by the Lifshitz-type action which should appear naturally in Horava-Lifshitz gravity. The wave of the scalar field may propagate with any speed without an upper bound. To preserve the causality, the action cannot have a generic form. Due to the superluminal propagation, a formation of a singularity may cause the breakdown of the predictability of the theory. To check whether such a catastrophe could occur in Horava-Lifshitz gravity, we investigate the dynamics of a dust. It turns out that the dust does not collapse completely to form a sin…
We discuss a class of supersymmetric type II non-relativistic solutions with exact or asymptotic scale invariance. As already emerged from previous investigations, we find a clear correspondence between anisotropic d-dimensional vacua and relativistic solutions in (d + 1)-dimensions. We will show that supersymmetric four-dimensional Poincare' invariant backgrounds in type IIB can descend to analogous solutions with anisotropic scaling in t and (x, y). This result can be applied to scale invariant theories, domain walls interpolating between four-dimensional Lifshitz vacua and more general solu…
We investigate several aspects of exact black hole solutions in asymptotically Lifshitz spacetime, which were proposed in 0812.0530. Firstly, we calculate the tidal forces and find that in the near horizon region of such black hole backgrounds, the tidal forces diverge in the near extremal limit. Secondly, we evaluate the Wilson loops in both extremal and finite temperature cases. Finally, we obtain the corresponding shear viscosity and square of the sound speed and find that the ratio of shear viscosity to entropy density takes the universal value $1/4π$ in arbitrary dimensions while the squa…
We construct Horava-Lifshitz gravities that are invariant under anisotropic Weyl scaling. This construction is based on an extension of the group of symmetries of healthy extended Horava-Lifshitz gravity and RFDiff invariant Horava-Lifshitz gravity. We find their Hamiltonian formulation and determine their constraint structure.
We reassess the conclusion by Klusoň (J. High Energy Phys. 1007 (2010) 038) that the Hamiltonian formulation of the healthy extended Hořava-Lifshitz gravity does not present any problem.
Notes on exact solvability for rotating and pulsating strings in nonrelativistic Lifshitz background
本文在非相对论平面 Lifshitz 时空中构造旋转与脉动探针弦的一维可解模型，将其约化为 Neumann-Rosochatius 系统并得到色散关系。
We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in arXiv:1604.05092 [hep-th]. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicate…
In this note we construct asymptotically Lifshitz spacetimes in the Chern-Simons formulation of three dimensional higher spin gravity and relate the resulting theories to integrable systems which are elements of the KdV hierarchy.
This short note is devoted to the canonical analysis of the Horava-Lifshitz gravity with mixed derivative terms that was proposed in arXiv:1604.04215. We determine the algebra of constraints and we show that there is one additional scalar degree of freedom with respect to the non-projectable Horava-Lifshitz gravity.
A note on the holographic time-like entanglement entropy in Lifshitz theory
本文在三维Lifshitz时空中检验多种全息类时间纠缠熵提案，发现结果一致，且TEE的实部与虚部均依赖各向异性参数。
In this paper we continue the study of the Hamiltonian formalism of the healthy extended Horava-Lifshitz gravity. We find the constraint structure of given theory and argue that this is the theory with the second class constraints. Then we discuss physical consequence of this result. We also apply the Batalin-Tyutin formalism of the conversion of the system with the second class constraints to the system with the first class constraints to the case of the healthy extended Horava-Lifshitz theory. As a result we find new theory of gravity with structure that is different from the standard formul…
We employ the matching method to analytically investigate the holographic superconductors with Lifshitz scaling in an external magnetic field. We discuss systematically the restricted conditions for the matching method and find that this analytic method is not always powerful to explore the effect of external magnetic field on the holographic superconductors unless the matching point is chosen in an appropriate range and the dynamical exponent $z$ satisfies the relation $z=d-1$ or $z=d-2$. From the analytic treatment, we observe that Lifshitz scaling can hinder the condensation to be formed, w…
We perform the phase space analysis in terms of the linearization technique in the Hořava-Lifshitz gravity with the softly broken detailed balance condition. It can be shown that the bouncing universe appears only for the positive spatial curvature of $k=+1$, and it is possible to obtain oscillating universe with the help of the negative dark radiation and the negative cosmological constant.
In this note, we discuss the renormalizability of Horava-Lifshitz-type gravity theories. Using the fact that Horava-Lifshitz gravity is very closely related to the stochastic quantization of topologically massive gravity, we show that the renormalizability of HL gravity only depends on the renormalizability of topologically massive gravity. This is a consequence of the BRST and time-reversal symmetries pertinent to theories satisfying the detailed balance condition.
We investigate the Lifshitz black holes from the Hořava-Lifshitz gravity by comparing with the Lifshitz black hole from the 3D new massive gravity. We note that these solutions all have single horizons. These black holes are very similar to each other when studying their thermodynamics. It is shown that a second order phase transition is unlikely possible to occur between $z=3,2$ Lifshitz black holes and $z=1$ Hořava black hole.
In this note we searched for a family of solutions with Caustic singularity in non relativistic-renormalizable Ho$\check {\textbf{r}}$ava-Lifshitz (HL)theory without the general covariant. We show that in infrared (IR) limit and with a deviation from $λ=1$ we have no caustic singularity. Also in ultraviolet (UV) regime and for Ricci flat 3-dimensional (3d) spaces and codimension 1 and for $λ\neq1$ the non linear terms should help bouncing this kind of most dangerous would be caustics. But if 3d curvature does not vanish, higher curvature terms do help caustics even in codimension one. Thus the…
In this note we examine whether spherically symmetric solutions in Covariant Horava Lifshitz Gravity can reproduce Newton's Law in the IR limit λ->1. We adopt the position that the auxiliary field A is independent of the space-time metric [10,11], and we assume, as in [4], that $λ$ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ->1, unless λdoes not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby Thompson approach [4] in which A is assumed as a pa…
In this short note, we are going to classify the cosmological evolutions in the recently proposed, nonrelativistic gravitational theory, the Hořava-Lifshitz (HL) theory. We consider the original HL theory (theory I), and the modified version obtained by an analytic continuation of parameters (theory II). We discuss the possiblilities of cosmological evolutions with arbitrary matter.
Recently, Hořava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply the scale invariant primordial perturbation can be generated in any expansion of early universe with a\sim t^n and n>1/3, which, in this note, will be validated by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. However, it is found that it seems that if we require the efolding number of primordial perturbation is suitable for observable universe, n>1 still need to be satisfied, unless the …
The aim of this note is to explore Susskind's proposal [arXiv:1802.01198] on the connection between operator size in chaotic theories and the bulk momentum of a particle falling into black holes (see also [arXiv:1804.04156, 1806.05574, 1904.12819, 1912.05996, 2006.03019] for more recent generalizations), in a broad class of models involving Gauss-Bonnet(GB) and Lifshitz-Hyperscaling violating theories in AdS. For Gauss-Bonnet black holes, the operator size is seen to be suppressed as the coupling constant $λ$ is increased. For the Lifshitz-hyperscaling violating theories characterised by the p…
Holographic relationships between entanglement entropy on the boundary of a spacetime and the area of minimal surfaces in the bulk provide an important entry in the bulk/boundary dictionary. While constructing the necessary causal and entanglement wedges is well understood in asymptotically AdS spacetimes, less is known about the equivalent constructions in spacetimes with different asymptotics. In particular, recent attempts to construct entanglement and causal wedges for asymptotically Lifshitz solutions in relativistic gravitational theories have proven problematic. We note a simple observa…
We study the holographic dark energy on the subject of Ho$\check{r}$ava-Lifshitz gravity with a time dependent gravitational constant (G(t)), in the non-flat space-time. We obtain the differential equation that specify the evolution of the dark energy density parameter based on varying gravitational constant. we find out a relation for the state parameter of the dark energy equation to low redshifts which containing varying $G$ correction.
Induced current by a magnetic flux in $(1+2)-$dimensional conical spacetime in a Ho{ř}ava-Lifshitz Lorentz-violating scenario
研究在Hořava-Lifshitz洛伦兹破缺场景下，磁通量在$(2+1)$维锥形时空中诱导的玻色子流真空期望值，考虑圆形边界和Robin边界条件，通过Wightman函数得到解析表达式并分析边界诱导部分的渐近行为。
It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, we also obtain the corresponding dynamic equations by using the idea of emergence of space in the $f(R)$ theory and deformed Hořava-Lifshitz (HL) theory.
Quantum cosmology of the Friedmann-Lemaître-Robertson-Walker model with cosmological constant in the Ho$\check{\rm r}$ava-Lifshitz type gravity is studied in the phase space by means of the Wigner function. The modification of the usual general relativity description by the Ho$\check{\rm r}$ava-Lifshitz type gravity induces a new scenario for the origin of the Universe with an embryonic era where the Universe can exist classically before the tunneling process takes place and which gives rise to the current evolution of the Universe. The Wigner functions corresponding to the Hartle-Hawking, Vil…
We consider slowly rotating, stationary, axisymmetric black holes in the infrared limit of Horava-Lifshitz gravity. We show that such solutions do not exist, provided that they are regular everywhere apart from the central singularity. This has profound implications for the viability of the theory, considering the astrophysical evidence for the existence of black holes with non-zero spin. NOTE ADDED: A subtlety in the dynamical equivalence between Horava-Lifshitz gravity and Einstein-aether theory has been missed and this has seriously affected the conclusions of this paper. Please see arXiv:1…
In this short note, I present a generalization of a set of static D-dimensional (D >= 3) Lifshitz black holes, which are solutions of the gravitational model obtained by amending the cosmological Einstein theory with the addition of only the curvature-scalar-squared term and that are described by two parameters, to a more general class of exact, analytic solutions that involves an additional parameter which now renders them stationary. In the special D=3 and the dynamical exponent z=1 case, the parameters can be adjusted so that the solution becomes identical to the celebrated BTZ black hole m…
In this paper, we investigate the fermions Hawking radiation and quasinormal modes in infra-red modified Ho$\check{r}$ava-Lifshitz gravity under tunneling and perturbation perspectives.Firstly, through the fermions tunneling in IR modified Ho$\check{r}$ava-Lifshitz gravity,we obtain the Hawking radiation emission rate, tunneling temperature and entropy for the Kehagias-Sfetsos black hole. It is found that the results of fermions tunneling are in consistence with the thermodynamics results obtained by calculating surface gravity.Secondly, we numerically calculate the lowing quasinormal modes fr…
The modified field equations are written in logarithmic and power law versions of entropy corrected models in Einstein's gravity in the background of FRW universe. In one section, a brief review of the Ho$\check{\text r}$ava-Lifshitz gravity is discussed and the modified field equations in logarithmic and power law versions of entropy corrected models in Ho$\check{\text r}$ava-Lifshitz gravity are formulated. The stability analysis for these models are performed by describing the dynamical system. In another section, a brief review of the fractal universe is presented and the modified field eq…
In this note we study the linear dynamics of scalar graviton in a de Sitter background in the infrared limit of the healthy extension of Hořava-Lifshitz gravity with the dynamical critical exponent $z=3$. Both our analytical and numerical results show that the non-zero Fourier modes of scalar graviton oscillate with an exponentially damping amplitude on the sub-horizon scale, while on the super-horizon scale, the phases are frozen and they approach to some asymptotic values. In addition, as the case of the non-zero modes on super-horizon scale, the zero mode also initially decays exponentially…
Lifshitz critical points meet Zamolodchikov perturbation theory
本文研究了二维耦合最简CFT模型，通过Zamolodchikov大$m$展开揭示了Lifshitz临界点和远红外旋转对称性的出现。
Horava-Lifshitz gravity, a recent proposal for a UV-complete renormalizable gravity theory, may lead to a bouncing cosmology. In this note we argue that Horava-Lifshitz cosmology may yield a concrete realization of the matter bounce scenario, and thus give rise to an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. In this scenario, quantum vacuum fluctuations exit the Hubble radius in the pre-bounce phase and the spectrum is transformed into a scale-invariant one on super-Hubble scales before the bounce because the long wavelength modes undergo …
Motivated by recent logarithmic entropy of Ho$\check{r}$ava-Lifshitz gravity, we investigate Hawking radiation for Kehagias-Sfetsos black hole from tunneling perspective. After considering the effect of self-gravitation, we calculate the emission rate and entropy of quantum tunneling by using Kraus-Parikh-Wilczek method. Meanwhile, both massless and massive particles are considered in this letter. Interestingly, two types tunneling particles have the same emission rate $Γ$ and entropy $S_b$ whose analytical formulae are $Γ= \exp{[π(r_{in}^2 - r_{out}^2t)/2 + π/α\ln r_{in}/r_{out}]}$ and $S_b =…
We study condensation for non-relativistic matter in a Hořava-Lifshitz black hole without the condition of the detailed balance. We show that, for the fixed non-relativistic parameter $α_2$ (or the detailed balance parameter $ε$), it is easier for the scalar hair to form as the parameter $ε$ (or $α_2$) becomes larger, but the condensation is not affected by the non-relativistic parameter $β_2$. We also find that the ratio of the gap frequency in conductivity to the critical temperature decreases with the increase of $ε$ and $α_2$, but increases with the increase of $β_2$. The ratio can reduce …
In this paper we present the spectrum of entropy/area for Kehagias-Sfetsos (KS) black hole in Ho$\check{\textbf{r}}$ava-Lifshitz (HL)gravity via quasi-normal modes (QNM) approach. We show that in the massive case the mass parameter $μ$ disappears in the entropy spectrum and only the quasinormal modes modified by a term which is proportional to the mass square term. Our calculations show that the charge like parameter $\frac{1}{2ω}=Q^{2}$ appears in the surface gravity and our calculations can be applied to any spherically symmetric spacetime which has only one physically acceptable horizon. Ou…
A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity. The theory explicitly breaks Lorentz invariance, which introduces an apparent extra scalar degree of freedom. In this note, we show that the low energy limit of (non-projectible) Horava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, which is minimally coupled to Einstein gravity. This imp…
We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho${\rm\check{r}}$ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.
By using the canonical Hamiltonian method, we obtain the mass and entropy of the black holes with general dynamical coupling constant $λ$ in Hoř ava-Lifshitz Gravity. Regardless of whether the horizon is sphere, plane or hyperboloid, we find these black holes are thermodynamically stable in some parameter space and unstable phase also exists in other parameter space. The relation between the entropy and horizon area of the black holes has an additional coefficient depending on the coupling constant $λ$, compared to the $λ=1$ case. For $λ=1$, the well-known coefficient of one quarter is recover…
We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this respect, although being fully relativistic, it results to be locally anisotropic in the time-like and space-like directions defined by a family of irrotational observers. We show that this theory propagates generically three degrees of freedom: two of them are related to the four-dimensional diffeomorphism invariant graviton (the metric) and one is related …
Detailed balance and projectability conditions are two main assumptions when Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz (HL) theory. While the latter represents an important ingredient, the former often believed needs to be abandoned, in order to obtain an ultraviolet stable scalar field, among other things. In this paper, because of several attractive features of this condition, we revisit it, and show that the scalar field can be stabilized, if the detailed balance condition is allowed to be softly broken. Although this is done explicitly in the non-relati…
Vanishing Compactness Gap and Fermionic Compact Dark Matter in Hořava-Lifshitz Gravity
在霍罗维茨-利夫希茨引力中，黑洞与中子星的紧致性间隙可能消失，费米子质量决定是否存在紧致对象，可能解释暗物质特性。
In this work, we have investigated the validity of GSL of thermodynamics in a universe (open, closed and flat) governed by Ho$\check{\text r}$ava-Lifshitz gravity. If the universe contains barotropic fluid the corresponding solutions have been obtained. The validity of GSL have been examined by two approaches: (i) robust approach and (ii) effective approach. In robust approach, we have considered the universe contains only matter fluid and the effect of the gravitational sector of HL gravity was incorporated through the modified black hole entropy on the horizon. Effective approach is that all…
Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
本研究通过规范su$(1,2)\oplus$u$(1)$代数探究三维扭转牛顿-卡当引力，用Chern-Simons理论构建作用量，揭示其新特征，复现Schrödinger引力并解释相关真空解对应关系，重新探讨代数对应关系的起源。
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