Chaos and Symmetry in String Cosmology

We review the recently discovered interplay between chaos and symmetry in the general inhomogeneous solution of many string-related Einstein-matter systems in the vicinity of a cosmological singularity. The Belinsky-Khalatnikov-Lifshitz-type chaotic behaviour is found, for many Einstein-matter models (notably those related to the low-energy limit of superstring theory and M-theory), to be connected with certain (infinite-dimensional) hyperbolic Kac-Moody algebras. In particular, the billiard chambers describing the asymptotic cosmological behaviour of pure Einstein gravity in spacetime dimension d+1, or the metric-three-form system of 11-dimensional supergravity, are found to be identical to the Weyl chambers of the Lorentzian Kac-Moody algebras AE_d, or E_{10}, respectively. This suggests that these Kac-Moody algebras are hidden symmetries of the corresponding models. There even exists some evidence of a hidden equivalence between the general solution of the Einstein-three-form system and a null geodesic in the infinite dimensional coset space E_{10} / K(E_{10}), where K(E_{10}) is the maximal compact subgroup of E_{10}.Comment: 14 pages, one diagram; invited talk at the 11th Marcel Grossmann Meeting on Recent Developments in General Relativity, Berlin, Germany, 23-29 July 200

The general relativistic two body problem

The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently introduced approach to the motion and radiation of (comparable mass) binary systems: the Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of its recent developments. Several recent comparisons between EOB predictions and Numerical Relativity (NR) simulations have shown the aptitude of the EOB formalism to provide accurate descriptions of the dynamics and radiation of various binary systems (comprising black holes or neutron stars) in regimes that are inaccessible to other analytical approaches (such as the last orbits and the merger of comparable mass black holes). In synergy with NR simulations, post-Newtonian (PN) theory and Gravitational Self-Force (GSF) computations, the EOB formalism is likely to provide an efficient way of computing the very many accurate template waveforms that are needed for Gravitational Wave (GW) data analysis purposes.Comment: 43 pages, 4 figures, to appear in the Brumberg Festschrift, edited by S. M. Kopeikein, and to be published by de Gruyter, Berlin, 2014. arXiv admin note: substantial text overlap with arXiv:1212.316

Quantum strings and black holes

The transition between (non supersymmetric) quantum string states and Schwarzschild black holes is discussed. This transition occurs when the string coupling $g^2$ (which determines Newton's constant) increases beyond a certain critical value $g_c^2$. We review a calculation showing that self-gravity causes a typical string state of mass $M$ to shrink, as the string coupling $g^2$ increases, down to a compact string state whose mass, size, entropy and luminosity match (for the critical value $g_c^2 \sim (M \sqrt{\alpha'})^{-1}$) those of a Schwarzschild black hole. This confirms the idea (proposed by several authors) that the entropy of black holes can be accounted for by counting string states. The level spacing of the quantum states of Schwarzschild black holes is expected to be exponentially smaller than their radiative width. This makes it very difficult to conceive (even Gedanken) experiments probing the discreteness of the quantum energy levels of black holes.Comment: 11 pages, plenary talk given at the 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, Rome, Italy, 2-9 July 200

High-energy gravitational scattering and the general relativistic two-body problem

A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the 2-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.Comment: 25 pages, 5 figure