New Developments and Perspectives in General Relativity and Cosmology.

摘要

General Relativity is almost 100 years old. Classically, Einstein's theory, is a geometric theory with a metric equating gravity and acceleration. This Principle of Equivalence determines the kinematics. Padmanabhan uses accelerated Rindler frames to derive general relativistic actions, including the Einstein-Hilbert action, and the Einstein equations. This determines the dynamics.;There is another formulation of General Relativity due to Gockeler and Schucker, a gauge theory in terms of differential forms, which reduces to the Einstein-Hilbert action and implies the Einstein equations including torsion.;My thesis, "New Developments and Perspectives in General Relativity and Cosmology", contains, in part:;• Padmanabhan discovered a differential relation between the volume and surface terms for generalized Lagrangians in Einstein-Hilbert type actions. I found a generalization of this using the Gockeler and Schucker form from which Padmanabhan's relations can be deduced under contraction. The new formulation constrains the curvature and torsion and allows other generalizations.;• Padmanabhan has recently derived Einstein's Equations from thermodynamical assumptions on the surface term in the Action. Horizons which block information are a relatively new feature in Physics. Padmanabhan has done alot in advancing the goal of elucidating the relation between General Relativity, Thermodynamics, and Quantum Theory.;• Hawking found that black holes radiate in a thermal spectrum and calculated the temperature. This (nonquantum) temperature is novel in General Relativity.;• Unruh and others found vacuum states which exhibit thermal properties dependent on the motion of the observer. Vacuums are nonunique in noninertial frames and curved spacetimes.;• Recent observations indicate the presence of an unclustered material acting like a fluid with negative pressure causing the acceleration of the Universe and amounting to about 70% of its energy density. The simplest explanation for this Dark Energy is the Cosmological Constant. Padmanabhan has derived the correct value for this vacuum energy by gauging away the bulk value and evaluating the vacuum fluctuations in terms of surface dimensions.;• There has been considerable progress recently in understanding the History on the Universe, although there remains much is unknown. This is the Standard Model of Cosmology. The Standard Model of Particle Physics and the gauge theory of General Theory of Relativity are not only the current fundamental theories of physics but also the way the Universe has evolved.;• Despite the progress of the Ashtekar formulation, the development of spin foams, and String theory with its spin-2 graviton, there does not exist a complete theory of Quantum Gravity. The search continues for the microscopic spacetime degrees of freedom and the gravitational notions of energy and entropy.