A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics

This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation ("the cell problem"), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.Comment: 32 page

Soliton Solutions to the Einstein Equations in Five Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS$_{5}/\Gamma$, but have less energy than AdS$_{5}/\Gamma$. We present evidence that these solutions are the lowest-energy states within their asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title changed by journal from original title "Eguchi-Hanson Solitons

Hawking radiation from extremal and non-extremal black holes

The relationship between Hawking radiation emitted by non extremal and extremal Reissner Nordstrom black holes is critically analyzed. A careful study of a series of regular collapsing geometries reveals that the stress energy tensor stays regular in the extremal limit and is smoothly connected to that of non extremal black holes. The unexpected feature is that the late time transients which played little role in the non extremal case are necessary to preserve the well defined character of the flux in the extremal case. The known singular behavior of the static energy density of extremal black holes is recovered from our series by neglecting these transients, when performing what turns out to be an illegitimate late time limit. Although our results are derived in two dimensional settings, we explain why they should also apply to higher dimensional black holes.Comment: 18 pages, late

Dark Matter from R^2-gravity

The modification of Einstein gravity at high energies is mandatory from a quantum approach. In this work, we point out that this modification will necessarily introduce new degrees of freedom. We analyze the possibility that these new gravitational states can provide the main contribution to the non-baryonic dark matter of the Universe. Unfortunately, the right ultraviolet completion of gravity is still unresolved. For this reason, we will illustrate this idea with the simplest high energy modification of the Einstein-Hilbert action: R^2-gravity.Comment: 5 pages, 2 figure

Novel black hole bound states and entropy

We solve for the spectrum of the Laplacian as a Hamiltonian on $\mathbb{R}^{2}-\mathbb{D}$ and in $\mathbb{R}^{3}-\mathbb{B}$. A self-adjointness analysis with $\partial\mathbb{D}$ and $\partial\mathbb{B}$ as the boundary for the two cases shows that a general class of boundary conditions for which the Hamiltonian operator is essentially self-adjoint are of the mixed (Robin) type. With this class of boundary conditions we obtain "bound state" solutions for the Schroedinger equation. Interestingly, these solutions are all localized near the boundary. We further show that the number of bound states is finite and is in fact proportional to the perimeter or area of the removed \emph{disc} or \emph{ball}. We then argue that similar considerations should hold for static black hole backgrounds with the horizon treated as the boundary.Comment: 13 pages, 3 figures, approximate formula for energy spectrum added at the end of section 2.1 along with additional minor changes to comply with the version accepted in PR

How red is a quantum black hole?

Radiating black holes pose a number of puzzles for semiclassical and quantum gravity. These include the transplanckian problem -- the nearly infinite energies of Hawking particles created near the horizon, and the final state of evaporation. A definitive resolution of these questions likely requires robust inputs from quantum gravity. We argue that one such input is a quantum bound on curvature. We show how this leads to an upper limit on the redshift of a Hawking emitted particle, to a maximum temperature for a black hole, and to the prediction of a Planck scale remnant.Comment: 3 pages, essay for the Gravity Research Foundatio

Massless and massive graviton spectra in anisotropic dilatonic braneworld cosmologies

We consider a braneworld model in which an anisotropic brane is embedded in a dilatonic background. We solve the background solutions and study the behavior of the perturbations when the universe evolves from an inflationary Kasner phase to a Minkowski phase. We calculate the massless mode spectrum, and find that it does not differ from what expected in standard four-dimensional cosmological models. We then evaluate the spectrum of both light (ultrarelativistic) and heavy (nonrelativistic) massive modes, and find that, at high energies, there can be a strong enhancement of the Kaluza-Klein spectral amplitude, which can become dominant in the total spectrum. The presence of the dilaton, on the contrary, decrease the relative importance of the massive modes.Comment: 18 pages, 4 figures, Typos correction

Asymptotic Symmetries of Rindler Space at the Horizon and Null Infinity

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.Comment: 37 pages, 4 figures. Version 3: New Section 5 adde

Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry

We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant $G_{eff}$ and two parameters $\Sigma$ and $\eta$, which along with the perturbation equation of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation for the scale factor $a$ in terms of time $t$ and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model.Comment: 9 pages, 3 figures, uses revtex4, added Appendix and references, minor changes, accepted in Phys. Rev. D (to appear

Very Light Cosmological Scalar Fields from a Tiny Cosmological Constant

We discuss a mechanism which generates a mass term for a scalar field in an expanding universe. The mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry which is however broken in the gravitational sector. The mass is comparable today to the Hubble time. This scalar field could thus impact our universe today and for example be at the origin of a time variation of the couplings and masses of the parameters of the standard model.Comment: 11 page