# Bassetto, Ciafaloni, Marchesini ## Jet Structure and Infrared Sensitive Quantities in Perturbative QCD \[Links: [Inspire](https://inspirehep.net/literature/201902)\] \[Abstract: Infrared sensitive measurements in hard scattering include $x$- and $p_\perp$-distributions at the phase space boundary (where soft emision is depressed) and jet multiplicity distributions (where it is emphasized). We review QCD results for these quantities and the corresponding infrared resummation techniques. Particular emphasis is put on the structure of the jet final state and its phenomenological consequences.\] # Bohigas, Giannoni, Schmit ## Characterization of chaotic quantum spectra and universality of level fluctuation laws \[Links: [inspire](https://inspirehep.net/literature/194582)\] \[Abstract: It is found that the level fluctuations of the quantum Sinai's billiard are consistent with the predictions of the Gaussian orthogonal ensemble of random matrices. This reinforces the belief that level fluctuation laws are universal.\] # Gibbons, Hawking, Horowitz, Perry ## Positive mass theorems for black holes \[Links: [Springer](https://link.springer.com/article/10.1007/BF01213209), [PDF](https://link.springer.com/content/pdf/10.1007/BF01213209.pdf)\] \[Abstract: We extend Witten's proof of the [[0116 Positive energy theorem|positive mass theorem]] at spacelike infinity to show that the mass is positive for initial data on an asymptotically flat spatial hypersurface $\Sigma$ which is regular outside an apparent horizon $H$. In addition, we prove that if a black hole has electromagnetic charge, then the mass is greater than the modulus of the charge. These results are also valid for the Bondi mass at null infinity. Finally, in the case of the Einstein equation with a negative cosmological constant, we show that a suitably defined mass is positive for data on an asymptotically anti-de Sitter surface $\Sigma$ which is regular outside an [[0226 Apparent horizon|apparent horizon]]. \] ## Refs - an earlier work that works for initial surfaces without a horizon: [[AbbottDeser1982]] ## Summary - extends [[0116 Positive energy theorem|positive mass theorem]] to initial surfaces in AdS that contains a horizon # Hartle, Hawking ## Wave Function of the Universe \[Links: [Inspire](https://inspirehep.net/literature/192909)\] \[Abstract: The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt]] second-order functional differential equation. We put forward a proposal for the wave function of the "ground state" or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple [[0254 Minisuperspace|minisuperspace]] model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and $\Lambda>0$. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.\] ## Reference - this is the original work on [[0162 No-boundary wavefunction|Hartle-Hawking state]] # Hawking, Page ## Thermodynamics of black holes in AdS \[Links: [Springer](https://link.springer.com/article/10.1007/BF01208266)\] \[Abstract: \] ## Summary - BH in AdS is different from BH in flat space thermodynamically: - characteristic scale $\sim l_{AdS}$ above which temperature (by asymptotic observer) increases with size of the BH - => positive specific heat => can be in stable equilibrium with radiation at a fixed temperature - => canonical ensemble exists - c.f. in flat space, need to put gravity in a box by hand - there is a phases transition called [[0012 Hawking-Page transition]] # Migdal ## Loop Equations and $1/N$ Expansion \[Links: [Inspire](https://inspirehep.net/literature/203384)\] # Teitelboim ## Gravitation and Hamiltonian Structure in Two Space-Time Dimensions \[Links: [Inspire](https://inspirehep.net/literature/194389)\] \[Abstract: In two spacetime dimensions a c-number (“Schwinger term”, “central charge”) is allowed in the algebra of surface deformations. A non-trivial analog of gravitation theory in two dimensional spacetime is built upon this fact, with the inverse of the central charge playing the role of the gravitational constant. Classically the analog with gravitation theory is only partial in that the hamiltonian constraints cannot be imposed, but it becomes complete at the quantum level.\] # Teyssandier, Tourrenc ## The Cauchy problem for the $R+R^2$ theories of gravity without torsion \[Links: [J.Math.Phys](https://aip.scitation.org/doi/10.1063/1.525659)\] \[Abstract: The exterior Cauchy problem is discussed for the fourth‐order theories of gravity derived from the Lagrangian densities $L=(-g)^{1 / 2}\left(R+(1 / 2) a R^2+b R_{\mu \nu} R^{\mu\nu}\right)-\chi L_m$. When $b \ne 0$, the Cauchy problem can be solved by the standard method already used in general relativity. When $b=0$, the problem cannot be formulated as in the case where $b\ne0$, since the corresponding fourth‐order theory is shown to be equivalent to a second‐order [[0140 Scalar-tensor theory|scalar–tensor theory]]. This scalar–tensor theory is proved to coincide with one of the models of gravity proposed by O’Hanlon in order to present a covariant version of the massive dilaton theory suggested by Fujii. This result is generalised: The models of O’Hanlon are shown to be indistinguishable from the fourth‐order theories derived from the Lagrangian densities $L=(-g)^{1 / 2} F(R)-\chi L_m$, where $F$ is any real function such that $F''(R)$ does not identically vanish.\] ## Summary - shows that $f(R)$ is equivalent to a [[0140 Scalar-tensor theory|scalar-tensor theory]] - also studies the Cauchy problem for $R+R^2+R_{\mu\nu}R^{\mu\nu}$ # Wolpert ## On the Symplectic Geometry of Deformations of a Hyperbolic Surface \[Links: [DOI](https://doi.org/10.2307/2007075)\]