Schwarzschild Geometry Emerging from Matrix Models

We demonstrate how various geometries can emerge from Yang-Mills type matrix models with branes, and consider the examples of Schwarzschild and Reissner-Nordstroem geometry. We provide an explicit embedding of these branes in R^{2,5} and R^{4,6}, as well as an appropriate Poisson resp. symplectic structure which determines the non-commutativity of space-time. The embedding is asymptotically flat with asymptotically constant \theta^{\mu\nu} for large r, and therefore suitable for a generalization to many-body configurations. This is an illustration of our previous work arXiv:1003.4132, where we have shown how the Einstein-Hilbert action can be realized within such matrix models.Comment: 21 pages, 1 figur

And what if gravity is intrinsically quantic ?

Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum loop gravity are based on a quantum field theory - the latter is a quantum field theory of connections on a SU(2) group manifold and former a quantum field theory in two dimensional spaces. Here we argue that there is a very close relation between quantum mechanics and gravity. Without gravity quantum mechanics becomes ambiguous. We consider this observation as the evidence for an intrinsic relation between these fundamental laws of nature. We suggest a quantum role and definition for gravity in the context of a quantum universe, and present a preliminary formulation for gravity in a system with a finite number of particles.Comment: 8 pages, 1 figure. To appear in the proceedings of the DICE2008 conference, Castiglioncello, Tuscany, Italy, 22-26 Sep. 2008. V2: some typos remove

Gravity and compactified branes in matrix models

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor \theta^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.Comment: 35 pages. V2: substantially revised and improved, conclusion weakened. V3: some clarifications, published version. V4: minor correctio

Bubbles in galactic haloes

We briefly discuss a possible interconnection of vertical HI structures observed in the Milky Way Galaxy with large scale blow-outs caused by the explosions of multiple clustered SNe. We argue that the observed OB associations can produce only about 60 such events, or approximately one chimney per 3 kpc$^2$ within the solar circle. We also discuss the overall properties of HI shells in nearby face-on galaxies and the distribution of H$\alpha$ and dust in edge-on galaxies. We argue that the presence of dust in galactic haloes may indicate that radiation pressure is the most probable mechanism capable of transporting dust to large heights above the galactic plane. In order to make this possible, the galactic magnetic field must have a strong vertical component. We mention that SNe explosions can initiate the Parker instability which in turn creates large scale magnetic loops with a strong vertical component. Recent observations of nearby edge-on galaxies favour this suggestion.Comment: 11 pages, 4 Figs, Talk at the JENAM, May 29 -- June 3, 2000, Mosco

Emergent Geometry and Quantum Gravity

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of symplectic structure \omega in terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page

Emergent Geometry and Gravity from Matrix Models: an Introduction

A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semi-classical limit. The relation to noncommutative gauge theory and the role of UV/IR mixing is explained. Several types of geometries are identified, in particular "harmonic" and "Einstein" type of solutions. The physics of the harmonic branch is discussed in some detail, emphasizing the non-standard role of vacuum energy. This may provide new approach to some of the big puzzles in this context. The IKKT model with D=10 and close relatives are singled out as promising candidates for a quantum theory of fundamental interactions including gravity.Comment: Invited topical review for Classical and Quantum Gravity. 57 pages, 5 figures. V2,V3: minor corrections and improvements. V4,V5: some improvements, refs adde

The structured environments of embedded star-forming cores. PACS and SPIRE mapping of the enigmatic outflow source UYSO 1

The intermediate-mass star-forming core UYSO 1 has previously been found to exhibit intriguing features. While deeply embedded and previously only identified by means of its (sub-)millimeter emission, it drives two powerful, dynamically young, molecular outflows. Although the process of star formation has obviously started, the chemical composition is still pristine. We present Herschel PACS and SPIRE continuum data of this presumably very young region. The now complete coverage of the spectral energy peak allows us to precisely constrain the elevated temperature of 26 - 28 K for the main bulge of gas associated with UYSO1, which is located at the interface between the hot HII region Sh 2-297 and the cold dark nebula LDN 1657A. Furthermore, the data identify cooler compact far-infrared sources of just a few solar masses, hidden in this neighbouring dark cloud.Comment: accepted contribution for the forthcoming Herschel Special Issue of A&A, 5 pages (will appear as 4-page letter in the journal), 6 figure file

Matrix geometries and Matrix Models

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.Comment: 20 page

3D Continuum radiative transfer in complex dust configurations around young stellar objects and active nuclei II. 3D Structure of the dense molecular cloud core Rho Oph D

Constraints on the density and thermal 3D structure of the dense molecular cloud core Rho Oph D are derived from a detailed 3D radiative transfer modeling. Two ISOCAM images at 7 and 15 micron are fitted simultaneously by representing the dust distribution in the core with a series of 3D Gaussian density profiles. Size, total density, and position of the Gaussians are optimized by simulated annealing to obtain a 2D column density map. The projected core density has a complex elongated pattern with two peaks. We propose a new method to calculate an approximate temperature in an externally illuminated complex 3D structure from a mean optical depth. This T(tau)-method is applied to a 1.3 mm map obtained with the IRAM 30m telescope to find the approximate 3D density and temperature distribution of the core Rho Oph D. The spatial 3D distribution deviates strongly from spherical symmetry. The elongated structure is in general agreement with recent gravo-turbulent collapse calculations for molecular clouds. We discuss possible ambiguities of the background determination procedure, errors of the maps, the accuracy of the T(tau)-method, and the influence of the assumed dust particle sizes and properties.Comment: 16 pages, 12 figure