Higher Curvature Gravity and the Holographic fluid dual to flat spacetime

Recent works have demonstrated that one can construct a (d+2) dimensional solution of the vacuum Einstein equations that is dual to a (d+1) dimensional fluid satisfying the incompressible Navier-Stokes equations. In one important example, the fluid lives on a fixed timelike surface in the flat Rindler spacetime associated with an accelerated observer. In this paper, we show that the shear viscosity to entropy density ratio of the fluid takes the universal value 1/4\pi in a wide class of higher curvature generalizations to Einstein gravity. Unlike the fluid dual to asymptotically anti-de Sitter spacetimes, here the choice of gravitational dynamics only affects the second order transport coefficients. We explicitly calculate these in five-dimensional Einstein-Gauss-Bonnet gravity and discuss the implications of our results.Comment: 13 pages; v2: modified abstract, added references; v3: added clarifying comments, modified discussio

Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories

We derive the equations of motion for Palatini F(R) gravity by applying an entropy balance law T dS= \delta Q+\delta N to the local Rindler wedge that can be constructed at each point of spacetime. Unlike previous results for metric F(R), there is no bulk viscosity term in the irreversible flux \delta N. Both theories are equivalent to particular cases of Brans-Dicke scalar-tensor gravity. We show that the thermodynamical approach can be used ab initio also for this class of gravitational theories and it is able to provide both the metric and scalar equations of motion. In this case, the presence of an additional scalar degree of freedom and the requirement for it to be dynamical naturally imply a separate contribution from the scalar field to the heat flux \delta Q. Therefore, the gravitational flux previously associated to a bulk viscosity term in metric F(R) turns out to be actually part of the reversible thermodynamics. Hence we conjecture that only the shear viscosity associated with Hartle-Hawking dissipation should be associated with irreversible thermodynamics.Comment: 12 pages, 1 figure; v2: minor editing to clarify Section III, fixed typos; v3: fixed typo

Viability of vector-tensor theories of gravity

We present a detailed study of the viability of general vector-tensor theories of gravity in the presence of an arbitrary temporal background vector field. We find that there are six different classes of theories which are indistinguishable from General Relativity by means of local gravity experiments. We study the propagation speeds of scalar, vector and tensor perturbations and obtain the conditions for classical stability of those models. We compute the energy density of the different modes and find the conditions for the absence of ghosts in the quantum theory. We conclude that the only theories which can pass all the viability conditions for arbitrary values of the background vector field are not only those of the pure Maxwell type, but also Maxwell theories supplemented with a (Lorentz type) gauge fixing term.Comment: 13 pages, 2 figures, 1 table. Final version to appear in JCA

Spontaneous Lorentz Violation and the Long-Range Gravitational Preferred-Frame Effect

Lorentz-violating operators involving Standard Model fields are tightly constrained by experimental data. However, bounds are more model-independent for Lorentz violation appearing in purely gravitational couplings. The spontaneous breaking of Lorentz invariance by the vacuum expectation value of a vector field selects a universal rest frame. This affects the propagation of the graviton, leading to a modification of Newton's law of gravity. We compute the size of the long-range preferred-frame effect in terms of the coefficients of the two-derivative operators in the low-energy effective theory that involves only the graviton and the Goldstone bosons.Comment: 11 pages, no figures, revtex4. v4: Replaced to match version to appear in Phys. Lett. B (minor corrections of form

Dispersive fields in de Sitter space and event horizon thermodynamics

When Lorentz invariance is violated at high energy, the laws of black hole thermodynamics are apparently no longer satisfied. To shed light on this observation, we study dispersive fields in de Sitter space. We show that the Bunch-Davies vacuum state restricted to the static patch is no longer thermal, and that the Tolman law is violated. However we also show that, for free fields at least, this vacuum is the only stationary stable state, as if it were in equilibrium. We then present a precise correspondence between dispersive effects found in de Sitter and in black hole metrics. This indicates that the consequences of dispersion on thermodynamical laws could also be similar.Comment: 19 pages. Black and White version on Phys.Rev.D serve

Local Entropy Current in Higher Curvature Gravity and Rindler Hydrodynamics

In the hydrodynamic regime of field theories the entropy is upgraded to a local entropy current. The entropy current is constructed phenomenologically order by order in the derivative expansion by requiring that its divergence is non-negative. In the framework of the fluid/gravity correspondence, the entropy current of the fluid is mapped to a vector density associated with the event horizon of the dual geometry. In this work we consider the local horizon entropy current for higher-curvature gravitational theories proposed in arXiv:1202.2469, whose flux for stationary solutions is the Wald entropy. In non-stationary cases this definition contains ambiguities, associated with absence of a preferred timelike Killing vector. We argue that these ambiguities can be eliminated in general by choosing the vector that generates the subset of diffeomorphisms preserving a natural gauge condition on the bulk metric. We study a dynamical, perturbed Rindler horizon in Einstein-Gauss-Bonnet gravity setting and compute the bulk dual solution to second order in fluid gradients. We show that the corresponding unambiguous entropy current at second order has a manifestly non-negative divergence.Comment: 28 pages, 2 appendices; v2: added references, fixed typos, one clarifying commen

Anomalies in Superfluids and a Chiral Electric Effect

We analyze the chiral transport terms in relativistic superfluid hydrodynamics. In addition to the spontaneously broken symmetry current, we consider an arbitrary number of unbroken symmetries and extend the results of arXiv:1105.3733. We suggest an interpretation of some of the new transport coefficients in terms of chiral and gravitational anomalies. In particular, we show that with unbroken gauged charges in the system, one can observe a chiral electric conductivity - a current in a perpendicular direction to the applied electric field. We present a motivated proposal for the value of the associated transport coefficient, linking it to the triangle anomaly. Along the way we present new arguments regarding the interpretation of the anomalous transport coefficients in normal fluids. We propose a natural generalization of the chiral transport terms to the case of an arbitrary number of spontaneously broken symmetry currents.Comment: 30 pages; v2: Onsager-relations argument corrected, references added; v3: fixed missing line in eq. (38

Modified Dispersion Relations from the Renormalization Group of Gravity

We show that the running of gravitational couplings, together with a suitable identification of the renormalization group scale can give rise to modified dispersion relations for massive particles. This result seems to be compatible with both the frameworks of effective field theory with Lorentz invariance violation and deformed special relativity. The phenomenological consequences depend on which of the frameworks is assumed. We discuss the nature and strength of the available constraints for both cases and show that in the case of Lorentz invariance violation, the theory would be strongly constrained.Comment: revtex4, 9 pages, updated to match published versio

More about spontaneous Lorentz-violation and infrared modification of gravity

We consider a model with Lorentz-violating vector field condensates, in which dispersion laws of all perturbations, including tensor modes, undergo non-trivial modification in the infrared. The model is free of ghosts and tachyons at high 3-momenta. At low 3-momenta there are ghosts, and at even lower 3-momenta there exist tachyons. Still, with appropriate choice of parameters, the model is phenomenologically acceptable. Beyond a certain large distance scale and even larger time scale, the gravity of a static source changes from that of General Relativity to that of van Dam--Veltman--Zakharov limit of the Fierz--Pauli theory. Yet the late time cosmological evolution is always determined by the standard Friedmann equation, modulo small correction to the ``cosmological Planck mass'', so the modification of gravity cannot by itself explain the accelerated expansion of the Universe. We argue that the latter property is generic in a wide class of models with condensates.Comment: 15 pages, 1 figure, JHEP3.cls; Added reference

The universal viscosity to entropy density ratio from entanglement

We present evidence that the universal Kovtun-Son-Starinets shear viscosity to entropy density ratio of 1/4\pi can be associated with a Rindler causal horizon in flat spacetime. Since there is no known holographic (gauge/gravity) duality for this spacetime, a natural microscopic explanation for this viscosity is in the peculiar properties of quantum entanglement. In particular, it is well-known that the Minkowski vacuum state is a thermal state and carries an area entanglement entropy density in the Rindler spacetime. Based on the fluctuation-dissipation theorem, we expect a similar notion of viscosity arising from vacuum fluctuations. Therefore, we propose a holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk. We calculate this viscosity assuming a minimally coupled scalar field theory and find that the ratio with respect to the entanglement entropy density is exactly 1/4\pi in four dimensions. The issues that arise in extending this result to non-minimally coupled scalar fields, higher spins, and higher dimensions provide interesting hints about the relationship between entanglement entropy and black hole entropy.Comment: 30 pages; v2: footnote added, minor editin