Session X4: Einstein Prize and New Methods for Old Problems in Gravitational Physics

Tuesday, May 3, 2011

We present some observations about certain unusual geometric structures that appear in both Minkowski space and asymptotically flat space-times. Three different types of light-cones are considered: ordinary real light-cones in Minkowski space, M, complex light-cones in the complexified Minkowski space, M$_{C}$,(Minkowski coordinates x$^{a}$ go to complex z$^{a}$) and third, virtual light-cones in asymptotically flat space-times. All three types are defined at future null infinity, I$^+$, (I$^+$ defined by the endpoints of infinite extensions of future directed null geodesics) via the vanishing of the shear of the null geodesics lying in the null surface. The virtual light-cones appear to converge to points in an auxiliary virtual space, H-space. Cones are labeled by their apex coordinate x$^{a}$ or z$^{a}$. Two applications are discussed. The first begins with asymptotically flat Maxwell fields written as W=E+iB. On each light cone, with apex x$^{a}$, extracting the l=1 harmonic of the Maxwell field determines the complex electromagnetic dipole moment, D$_{E\&M}=$D$_{E}+iD_{M}$. D$_{E\&M}$, a function of x$^{a}$, can be analytically extending into M$_{C}$. Its zero set, points in M$_{C}$ where D$_{E\&M}$(z$^{a}$) vanishes, is a complex curve called the complex center of charge world-line. The second application virtually repeats the Maxwell case but now for asymptotically flat Einstein/Einstein-Maxwell fields. In the asymptotic region of each virtual light-cone, extracting the l=1 harmonics from the asymptotic gravitational field (the Weyl tensor) yields the complex gravitational dipole, D$_{Grav}=$D$_{Mass}+$iD$_{Spin}$. Each cone is labeled by its H-space apex z$^{a}$. D$_{Grav}$(z$^{a}$) is thus a function on H-space. Its zero set determines an H-space curve: the complex center of mass world-line. Interior space-time physical quantities and dynamics, (e.g. center of mass, spin, angular momentum, linear momentum, force, eqs. of motion) are identified at I$^+$ and described in terms of this complex world-line.   

Tuesday, May 3, 2011

The gravitational redshift was the first consequence of General Relativity described by Einstein, and its measurement remains fundamental to our confidence in the theory. Clock comparison tests have reached an accuracy of 7$\times $10$^{-5}$. We have performed redshift experiments based on matter waves, in which redshift anomalies modify material particles' Compton frequencies. These have reached an accuracy of 7$\times $10$^{-9}$. For verifying the Einstein Equivalence Principle (EEP), these experiments are complemented by tests of Lorentz symmetry and universality of free fall (UFF). However, these tests are interrelated, as the proper time experienced by a clock or a matter wave is maximized on a geodesic, which relates the acceleration of free fall to the redshift. Here, we present a comprehensive framework for tests of the EEP, based on the Standard Model Extension. It shows that whether redshift measurements are related to measurements of UFF or not depends on the mechanism underlying the violation of the EEP, not on whether clocks or matter waves are used. Therefore, matter wave tests and clock comparisons are both valid measurements of the gravitational redshift and can probe violations of EEP that tests of UFF alone cannot probe. This framework also allows us to propose new tests of relativistic gravity: Searching for velocity- dependent effects and measuring force-free effects of gravity. Velocity-dependent effects of gravity are a consequence of nonlinear terms in the metric, which are proportional to 1/$c^{4}$ that have never been measured in the laboratory but are responsible for the perihelion shift of mercury. Force-free effects of gravity are in analogy to the Aharonov-Bohm effect, in which a matter wave is phase-shifted by the existence of a potential even though there is no electric or magnetic field and, thus, no force.   

Tuesday, May 3, 2011

Violation of unitarity in black hole evaporation has been puzzling physicist since the seminal work of Hawking in the seventies. Although there are hopes for a resolution of the problem in a full theory of quantum gravity, it has eluded us so far. Even less ambitious efforts considering only quantum corrections beyond the external field approximation have proven hard to attack in 4 dimensions. All these obstacles directed researchers to investigate the black hole evaporation problem in simpler 2-dimensional models. In this talk, we will present results on a new investigation of one of these models, the 2-dimensional Callan-Giddings-Harvey-Strominger (CGHS) model. Using a combination of analytical and high precision numerical tools, we are able to resolve CGHS black hole evaporation within the mean field approximation all the way to the point where the black hole area vanishes. Our results confirm some of the assumptions of the standard paradigm, and strongly suggest the recovery of unitarity within the full quantum theory. On the other hand, there are several surprising new results, in particular remarkable universal behavior in the evaporation of initially macroscopic black holes. This suggests that information about the collapsing matter that formed the black hole can not be recovered from the evaporation radiation. Though this separation of the questions of information loss and unitarity is peculiar to the 2-dimensional model, insights into the higher dimensional case can still be garnered.