Session D8 - Classical Gravitation.
ORAL session, Saturday afternoon, May 01
Governor's Square 17, Adam's Mark Hotel

[D8.001] Cosmology, cohomology, and compactification

Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. More precisely, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form admits a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.

[D8.002] Power-laws from critical gravitiational collapse: The mass distribution of subsolar objects

At large mass, the initial mass function [IMF], which describes the size distribution of stellar objects, is characterized by a power-law with the Salpeter exponent. At small [substellar] mass, theory indicates that there must be some change in this power law. Indeed, direct observation indicates that the IMF is certainly modified below approximately one-tenth of a solar mass. We demonstrate that at very low mass the IMF should again be given by a power law with an exponent opposite in sign to the high-mass exponent. Furthermore, we verify that this low-mass exponent is in principle calculable via dynamical systems theory applied to gravitational collapse. Observational data indicate a broad agreement with the sign of the low-mass exponent, and a preponderance of evidence pointing to a critical mass-scaling exponent approximately equal to two.

[D8.003] Higher-Derivative Palatini Gravity and the Accelerating Universe

It has been suggested that higher-derivative gravity could give a classical explanation to the observed acceleration of the Universe. Others have objected, citing inconsistencies with solar-system observations.

It was recently noted that when higher-derivative gravity is obtained through the Palatini variational principle, the resulting theory is no longer in conflict with solar-system observations. A controversy has started on the question of consistency with certain laboratory electron scattering experiments.

In my talk I will note that any higher-derivative Palatini theory is necessarily non-metric. Specifically, if particles are assumed to move along geodesics, the mass of particles is not conserved. Although Lorentz-invariance violations may be too small to be detected in the laboratory, they may have observable effects at the cosmological scale.

[D8.004] The Kerr-Schild Method in 2+1 Gravity

The Kerr-Schild method has proved to be a powerful tool for generating many of the most recurrent solutions of Einstein equations. We show here that this method works with the same efficiency in (2+1) dimensions. Our examples are the BTZ metric and the magnetic solution in (2 + 1) gravity. In both cases we have reobtained the known solutions and extended them to include new ones that contain charge and angular momentum. Following the same thread, we have extended the Dray and t'Hooft solution to this lower dimension case. This exact solution of Einstein equations, includes a null particle travelling along the event horizon of a black hole. These results underline the unifying character of this approach, several solutions of Einstein equations find their way through this formalism. Also, the simplicity of this approach and the existence of programs for algebraic manipulation of the Einstein equations overcome the main difficulty of this method: the physical interpretation of the resulting equations.

[D8.005] The Schwarzschild solution in the DGP model

We discuss the Schwarzschild solution in the Dvali-Gabadadze-Porrati (DGP) model. We obtain two different perturbative expansions which are valid in two distinct domains, respectively, separated by a critical radius. We show that this critical radius can be determined by the lowest-order contributions to the two perturbative expansions. At large distances, the solution is the standard solution of the linearized Einstein equations obtained by DGP. At distances below the critical radius on the brane, the perturbative expansion yields the four-dimensional Schwarzschild solution. This is similar to the Vainshtein solution in massive gravity demonstrating the absence of the van Dam-Veltman-Zakharov (vDVZ) discontinuity.

[D8.006] Perturbative calculation of quasi-normal modes of Schwarzschild black holes

We discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies of a four-dimensional Schwarzschild black hole by expanding around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. We obtain an explicit expression for the first-order correction and arbitrary spin. Our results are in agreement with the results from WKB and numerical analyses in the case of scalar and gravitational waves.

[D8.007] The Newtonian Mercury Perihelion, Light Bending and General Relativity

The 43 arc seconds per century of Mercury's perihelion advance (3.8 x 10 ^-12 of the total) are accounted for by an Electromagnetic, Gravitational coupling function respective to the precise 2/3 ratio of day-to-year of Mercury and \textbfNuclear Quantum Gravitation^\copyright . The slight rotation and the drag of the other planets cause the Sun's Electromagnetic domains-fields to rotate-change that small amount. This is absolutely a Newtonian, \textbfNuclear Quantum Gravitation^\copyright effect and not a General Relativity effect. General Relativity cannot have an effect at a distance from a gravitating body. There has been no proven mechanism of this. Fallacy tensors and time-space do not produce tangible results. They do not function. Further, General Relativity fails the Cavendish experiment. Where in the equations of General Relativity is there the ability for two bodies of any size to attract each other? Other so-called proofs of General Relativity such as light bending near the Sun are also incorrect and false.

Part D of program listing