Geometrothermodynamics for Black holes and de Sitter Space

In this report, a general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald's method using geometrical language, e.g$.$, via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The correspondence between the thermodynamics and general relativity can be seen clearly by comparing the two expressions. This comparison requires a modification of Wald's method. The new method is applied to Schwarzschild, Kerr, and Kerr--Newman black holes and de Sitter space. The results are consistent with previous results obtained using various independent methods. This strongly supports the validity of the area theorem for black holes.Comment: 14 page

Quantum effects of black holes and the cosmological constant problem

A quantum equation of gravity is proposed using geometric quantization of general relativity. Quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are provided by solving a quantum equation of gravity requiring a stationary phase and also using the Einstein-Brillouin-Keller (EBK) quantization condition, and they are consistent each other. WKB method is also applied to the McVittie-Thakurta metric, which is describing a system consists of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and scalar field are investigated in detail. A number density of black holes in the universe is obtained using statistical mechanics on a system consisting of black holes and a scalar filed. A possible solution for the cosmological constant problem is proposed in basis of a statistical consideration.Comment: 13 pages, 1 figur

Consistent simulation of non-resonant diphoton production at hadron collisions with a custom-made parton shower

We have developed a Monte Carlo event generator for non-resonant diphoton ($\gamma\gamma$) production at hadron collisions in the framework of GR@PPA, which consistently includes additional one-jet production. The jet-matching method developed for initial-state jet production has been extended to the final state in order to regularize the final-state QED divergence in the $qg \rightarrow \gamma\gamma + q$ process. A QCD/QED-mixed parton shower (PS) has been developed to complete the matching. The PS has the capability of enforcing hard-photon radiation, and small-$Q^{2}$ photon radiations that are not covered by the PS are supplemented by using a fragmentation function. The generated events can be passed to general-purpose event generators in order to perform the simulations down to the hadron level. Thus, we can simulate the isolation requirements that must be applied in experiments at the hadron level. The simulation results are in reasonable agreement with the predictions from RESBOS and DIPHOX. The simulated hadron-level events can be further fed to detector simulations in order to investigate the detailed performance of experiments.Comment: 23 pages, 15 figure

GR@PPA 2.9: radiation matching for simulating photon production processes in hadron collisions

We release an event generator package, GR@PPA 2.9, for simulating the direct (single) photon and diphoton (double photon) production in hadron collisions. The included programs were used in our previous studies, in which we have explicitly shown large contributions from parton-associated processes. The programs consistently combine simulations based on matrix elements with parton-shower simulations that reproduce the multiple parton radiation and quark fragmentation to photons. The matrix elements include associated parton production processes up to two partons. We provide instructions for the installation and execution of the programs in this article. The practical performance is also presented.Comment: 11 page

Single-W production to test triple gauge boson couplings at LEP

We present a study of single-W production ($e^+e^-\to e^-\bar{\nu}_e W^+$) as a new probe of the anomalous couplings at the LEP energy region. We introduce simple cuts to separate the single-W process from W-pair production and have performed cross-section calculations using 4-fermion generator ``grc4f''. The cross-section of the single-W process is found to be large enough to detect at LEP experiments in the near future. In addition, a high sensitivity to the anomalous coupling of the $WW\gamma$ vertex is expected since the amplitude of the $WW\gamma$ diagram makes a dominant contribution in this process. We have found that the cross-section measurement of the single-W process in the LEP2 energy region can give complementary bounds on the anomalous couplings to those obtained from W-pair analysis.Comment: revised version, to appear in Physics Letters

Thermodynamics for Trajectories of a Mass Point

On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated geometrically as dynamical variables. Statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamic variables are introduced through a partition function based on a canonical ensemble of trajectories. Within this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. The relationships between classical and quantum mechanics are discussed from this statistical mechanical viewpoint. The maximum entropy principle is shown to provide a unified view of both classical and quantum mechanics.Comment: 22 pages, 1 figur