308 research outputs found

### 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

### 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

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