Tony Rothman

Bio: Tony Rothman is an academic researcher from Princeton University. The author has contributed to research in topics: General relativity & Hawking radiation. The author has an hindex of 20, co-authored 63 publications receiving 1148 citations. Previous affiliations of Tony Rothman include University of Texas at Austin & Bryn Mawr College.

Can Gravitons be Detected

Abstract: 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.

Behavior of chaotic inflation in anisotropic cosmologies with nonminimal coupling

Abstract: We review the behavior of the chaotic inflationary scenario in the minimally coupled anisotropic case and in the nonminimally coupled isotropic case. In the former, anisotropy enhances inflation. In the latter, positive nonminimal coupling introduces a singularity at a critical point \ensuremath{\varphi}${^}_{c}$ in the scalar field. The exact value of \ensuremath{\varphi}${^}_{c}$ depends on the coupling parameter \ensuremath{\xi}. This singularity cannot be exceeded, which precludes astrophysically sufficient inflation for \ensuremath{\xi}\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}2}$. We extend the analysis to anisotropic Bianchi models where a second singularity ${\ensuremath{\varphi}}_{c}$ appears, which further prevents inflation in these models for \ensuremath{\xi}\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}2}$.

Instability of Extremal Relativistic Charged Spheres

Abstract: 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-Nordstr\"om 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-Nordstr\"om 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 $m/Rl4/9$ stability limit for the Schwarzschild interior solution, the gravitational mass M does not. Indeed, the stability limit approaches ${R}_{+}$ as $Q\ensuremath{\rightarrow}M.$ In the Appendix we also argue that Hawking radiation will not lead to an extremal Reissner-Nordstr\"om black hole. All our results are consistent with the third law of black hole dynamics, as currently understood.

Nonthermal nature of incipient extremal black holes

Abstract: We examine particle production from spherical bodies collapsing into extremal Reissner-Nordstrom 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.

Black Hole Explosions

Abstract: QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Proton Conductivity: Materials and Applications

Abstract: In this review the phenomenon of proton conductivity in materials and the elements of proton conduction mechanismsproton transfer, structural reorganization and diffusional motion of extended moietiesare discussed with special emphasis on proton chemistry. This is characterized by a strong proton localization within the valence electron density of electronegative species (e.g., oxygen, nitrogen) and self-localization effects due to solvent interactions which allows for significant proton diffusivities only when assisted by the dynamics of the proton environment in Grotthuss and vehicle type mechanisms. In systems with high proton density, proton/proton interactions lead to proton ordering below first-order phase transition rather than to coherent proton transfers along extended hydrogen-bond chains as is frequently suggested in textbooks of physical chemistry. There is no indication for significant proton tunneling in fast proton conduction phenomena for which almost barrierless proton transfer is suggest...

The fundamental constants and their variation: observational and theoretical status

Abstract: This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion of the role of fundamental constants, their definition and link with metrology, it reviews the various constraints on the variation of the fine-structure constant, the gravitational, weak- and strong-interaction couplings and the electron-to-proton mass ratio. The review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant, and (3) to point out the underlying hypotheses. Such an investigation is of importance in comparing the different results and in understanding the recent claims of the detection of a variation of the fine-structure constant and of the electron-to-proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories, and other alternative theories. Cosmological implications of these results are also discussed. The links with the tests of general relativity are emphasized.

Imaging standing waves in a two-dimensional electron gas

Abstract: ELECTRONS occupying surface states on the close-packed surfaces of noble metals form a two-dimensional nearly free electron gas1–3. These states can be probed using the scanning tunnelling microscope (STM), providing a unique opportunity to study the local properties of electrons in low-dimensional systems4. Here we report the direct observation of standing-wave patterns in the local density of states of the Cu(lll) surface using the STM at low temperature. These spatial oscillations are quantum-mechanical interference patterns caused by scattering of the two-dimensional electron gas off step edges and point defects. Analysis of the spatial oscillations gives an independent measure of the surface state dispersion, as well as insight into the interaction between surface-state electrons and scattering sites on the surface.