Freeman Dyson has questioned whether any conceivable experiment in the real universe can detect a single graviton. If not, is it meaningful to talk about gravitons as physical entities? We attempt to answer Dyson's question and find it is possible concoct an idealized thought experiment capable of detecting one graviton; however, when anything remotely resembling realistic physics is taken into account, detection becomes impossible, indicating that Dyson's conjecture is very likely true. We also point out several mistakes in the literature dealing with graviton detection and production.

We examine particle production from spherical bodies collapsing into extremal Reissner-Nordström black holes. Kruskal coordinates become ill-defined in the extremal case, but we are able to find a simple generalization of them that is good in this limit. The extension allows us to calculate the late-time worldline of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential fall-off of a nonextremal black hole. Therefore, although the vanishing of the stress tensor's expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.

With the question, "Can relativistic charged spheres form extremal black holes?" in mind, we investigate the properties of such spheres from a classical point of view. The investigation is carried out numerically by integrating the Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding interior Reissner-Nordström solutions for these objects. We consider both constant density and adiabatic equations of state, as well as several possible charge distributions, and examine stability by both a normal mode and an energy analysis. In all cases, the stability limit for these spheres lies between the extremal (Q = M ) limit and the black hole limit (R = R + ). That is, we find that charged spheres undergo gravitational collapse before they reach Q = M , suggesting that extremal Reissner-Nordtröm black holes produced by collapse are ruled out. A general proof of this statement would support a strong form of the cosmic censorship hypothesis, excluding not only stable naked singularities, but stable extremal black holes. The numerical results also indicate that although the interior mass-energy m(R) obeys the usual m/R < 4/9 stability limit for the Schwarzschild interior solution, the gravitational mass M does not. Indeed, the stability limit approaches R + as Q → M . In the Appendix we also argue that Hawking radiation will not lead to an extremal ReissnerNordström black hole. All our results are consistent with the third law of black hole dynamics, as currently understood.

No abstract

Graviton absorption cross sections and emission rates for hydrogen are calculated by both semi-classical and field theoretic methods. We point out several mistakes in the literature concerning spontaneous emission of gravitons and related phenomena, some of which are due to a subtle issue concerning gauge invariance of the linearized interaction Hamiltonian. PACS: 03.65. Sq, 04.30.Db, 04.30.Nk, 95.30.Cq, 95.30.Sf