Lightcone reference for total gravitational energy

We give an explicit expression for gravitational energy, written solely in terms of physical spacetime geometry, which in suitable limits agrees with the total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for asymptotically flat spacetimes and with the Abbot-Deser energy for asymptotically anti-de Sitter spacetimes. Our expression is a boundary value of the standard gravitational Hamiltonian. Moreover, although it stands alone as such, we derive the expression by picking the zero-point of energy via a ``lightcone reference.''Comment: latex, 7 pages, no figures. Uses an amstex symbo

Clustered spatially and temporally resolved global heat and cooling energy demand in the residential sector

Climatic conditions, population density, geography, and settlement structure all have a strong influence on the heating and cooling demand of a country, and thus on resulting energy use and greenhouse gas emissions. In particular, the choice of heating or cooling system is influenced by available energy distribution infrastructure, where the cost of such infrastructure is strongly related to the spatial density of the demand. As such, a better estimation of the spatial and temporal distribution of demand is desirable to enhance the accuracy of technology assessment. This paper presents a Geographical Information System methodology combining the hourly NASA MERRA-2 global temperature dataset with spatially resolved population data and national energy balances to determine global high-resolution heat and cooling energy density maps. A set of energy density bands is then produced for each country using K-means clustering. Finally, demand profiles representing diurnal and seasonal variations in each band are derived to capture the temporal variability. The resulting dataset for 165 countries, published alongside this article, is designed to be integrated into a new integrated assessment model called MUSE (ModUlar energy systems Simulation Environment)but can be used in any national heat or cooling technology analysis. These demand profiles are key inputs for energy planning as they describe demand density and its fluctuations via a consistent method for every country where data is available

Chiral black hole in three-dimensional gravitational Chern-Simons

A chiral black hole can be defined from the three-dimensional pure gravitational Chern-Simons action as an independent gravitational theory. The third order derivative of the Cotton tensor gives a dimensional constant which plays a role of the cosmological constant. The handedness of angular momentum depends on the signature of the Chern-Simons coefficient. Even in the massless black hole which corresponds to the static black hole, it has a nonvanishing angular momentum. We also study statistical entropy and thermodynamic stability.Comment: 6 pages, a reference added, minor changes to introductio

(2,2)-Formalism of General Relativity: An Exact Solution

I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede

Quantization of AdS_3 Black Holes in External Fields

2+1-dimensional Anti-deSitter gravity is quantized in the presence of an external scalar field. We find that the coupling between the scalar field and gravity is equivalently described by a perturbed conformal field theory at the boundary of AdS_3. We derive the explicit form of this coupling, which allows us to perform a microscopic computation of the transition rates between black hole states due to absorption and induced emission of the scalar field. Detailed thermodynamic balance then yields Hawking radiation as spontaneous emission, and we find agreement with the semiclassical result, including greybody factors. This result also has application to four and five dimensional black holes in supergravity. However, since we only deal with gravitational degrees of freedom, the approach is not based on string theory, and does not depend, either, on the validity of Maldacena's AdS/CFT conjecture.Comment: 12 pages, Late

Elastic cavitation, tube hollowing, and differential growth in plants and biological tissues

Elastic cavitation is a well-known physical process by which elastic materials under stress can open cavities. Usually, cavitation is induced by applied loads on the elastic body. However, growing materials may generate stresses in the absence of applied loads and could induce cavity opening. Here, we demonstrate the possibility of spontaneous growth-induced cavitation in elastic materials and consider the implications of this phenomenon to biological tissues and in particular to the problem of schizogenous aerenchyma formation

Graviton-Graviton Scattering, Bel-Robinson and Energy (Pseudo)-Tensors

Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, B_{\m\n\a\b}, and as the "current-current interaction" square of gravitational energy pseudo-tensors t_{\a\b},we find an exact tensor-square root equality B_{\mn\a\b} = \pa^2_\mn t_{\a\b}, for a combination of Einstein and Landau-Lifschitz t_\ab, in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by polynomials in the curvature.Comment: 7 page

Relativistic conservation laws and integral constraints for large cosmological perturbations

For every mapping of a perturbed spacetime onto a background and with any vector field $\xi$ we construct a conserved covariant vector density $I(\xi)$, which is the divergence of a covariant antisymmetric tensor density, a "superpotential". $I(\xi)$ is linear in the energy-momentum tensor perturbations of matter, which may be large; $I(\xi)$ does not contain the second order derivatives of the perturbed metric. The superpotential is identically zero when perturbations are absent. By integrating conserved vectors over a part \Si of a hypersurface $S$ of the background, which spans a two-surface \di\Si, we obtain integral relations between, on the one hand, initial data of the perturbed metric components and the energy-momentum perturbations on \Si and, on the other hand, the boundary values on \di\Si. We show that there are as many such integral relations as there are different mappings, $\xi$'s, \Si's and \di\Si's. For given boundary values on \di\Si, the integral relations may be interpreted as integral constraints (e.g., those of Traschen) on local initial data including the energy-momentum perturbations. Conservation laws expressed in terms of Killing fields \Bar\xi of the background become "physical" conservation laws. In cosmology, to each mapping of the time axis of a Robertson-Walker space on a de Sitter space with the same spatial topology there correspond ten conservation laws. The conformal mapping leads to a straightforward generalization of conservation laws in flat spacetimes. Other mappings are also considered. ...Comment: This paper, published 7 years ago, was found useful by some researchers but originally was not put on the gr-qc website. Now it has been retyped with very minor changes: few wordings have been modified and several misprints occurring in the printed version correcte