Quantum nature of black holes

I reconsider Hawking's analysis of the effects of gravitational collapse on quantum fields, taking into account interactions between the fields. The ultra-high energy vacuum fluctuations, which had been considered to be an awkward peripheral feature of the analysis, are shown to play a key role. By interactions, they can scatter particles to, or create pairs of particle at, ultra-high energies. The energies rapidly become so great that quantum gravity must play a dominant role. Thus the vicinities of black holes are essentially quantum-gravitational regimes.Comment: 7 pages, 5 figures. Honorable mention in the 2004 Gravity Research Foundation Essay Competitio

In an expanding universe, what doesn't expand?

The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general expansion, but a much more subtle question is whether bound systems expand partially. In this paper, a very definitive answer is given for a very simple system: a classical "atom" bound by electrical attraction. With a mathemical description appropriate for undergraduate physics majors, we show that this bound system either completely follows the cosmological expansion, or -- after initial transients -- completely ignores it. This "all or nothing" behavior can be understood with techniques of junior-level mechanics. Lastly, the simple description is shown to be a justifiable approximation of the relativistically correct formulation of the problem.Comment: 8 pages, 9 eps figure

Tuning the stochastic background of gravitational waves using the WMAP data

The cosmological bound of the stochastic background of gravitational waves is analyzed with the aid of the WMAP data, differently from lots of works in literature, where the old COBE data were used. From our analysis, it will result that the WMAP bounds on the energy spectrum and on the characteristic amplitude of the stochastic background of gravitational waves are greater than the COBE ones, but they are also far below frequencies of the earth-based antennas band. At the end of this letter a lower bound for the integration time of a potential detection with advanced LIGO is released and compared with the previous one arising from the old COBE data. Even if the new lower bound is minor than the previous one, it results very long, thus for a possible detection we hope in the LISA interferometer and in a further growth in the sensitivity of advanced projects.Comment: 9 pages, 2 figures, published in Modern Physics Letters A. arXiv admin note: substantial text overlap with arXiv:0901.119

Towards a closed differential aging formula in special relativity

It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and its calculation in terms of the proper acceleration history of the timelike curve would provide an important tool for the autonomous spacetime navigation of non-inertial observers. I give a solution in 3+1 dimensions which holds whenever the acceleration is decomposed with respect to a lightlike transported frame (lightlike transport will be defined), the analogous and more natural problem for a Fermi-Walker decomposition being still open.Comment: Latex2e, 6 pages, 1 figure, uses psfrag. Contribution to the Proceedings of The Spanish Relativity Meeting (ERE 2006), Palma de Mallorca, Spain September 4-8, 200

Quantum Perfect-Fluid Kaluza-Klein Cosmology

The perfect fluid cosmology in the 1+d+D dimensional Kaluza-Klein spacetimes for an arbitrary barotropic equation of state $p= n \rho$ is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. For the first case of the stiff fluid $n=1$ we exactly solve the Wheeler-DeWitt equation when the $d$ space is flat. After the superposition of the solutions we analyze the Bohmian trajectories of the final-stage wave-packet functions and show that the flat $d$ spaces and the compact $D$ spaces will eventually evolve into finite scale functions. For the second case of $n \approx 1$, we use the approximated wavefunction in the Wheeler-DeWitt equation to find the analytic forms of the final-stage wave-packet functions. After analyzing the Bohmian trajectories we show that the flat $d$ spaces will be expanding forever while the scale function of the contracting $D$ spaces would not become zero within finite time. Our investigations indicate that the quantum effect in the quantum perfect-fluid cosmology could prevent the extra compact $D$ spaces in the Kaluza-Klein theory from collapsing into a singularity or that the "crack-of-doom" singularity of the extra compact dimensions is made to occur at $t=\infty$.Comment: Latex 18 pages, add section 2 to introduce the quantization of perfect flui

Regularization of the second-order gravitational perturbations produced by a compact object

The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined. Here we construct well-defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the potential gravitational-waves. Construction of templates with desired accuracy for extreme mass ratio binaries, in which a compact-object inspirals towards a supermassive black-hole, requires calculation of the second-order gravitational perturbations produced by the compact-object.Comment: 12 pages, discussion expanded, to be published in Phys. Rev. D Rapid Communicatio

Supersymmetric quantum cosmological billiards

D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.Comment: 4 pages. v2: Added ref. Version to be published in PR

Population bound effects on bosonic correlations in non-inertial frames

We analyse the effect of bounding the occupation number of bosonic field modes on the correlations among all the different spatial-temporal regions in a setting in which we have a space-time with a horizon along with an inertial observer. We show that the entanglement between A (inertial observer) and R (uniformly accelerated observer) depends on the bound N, contrary to the fermionic case. Whether or not decoherence increases with N depends on the value of the acceleration a. Concerning the bipartition A-antiR (Alice with an observer in Rindler's region IV), we show that no entanglement is created whatever the value of N and a. Furthermore, AR entanglement is very quickly lost for finite N and for infinite N. We will study in detail the mutual information conservation law found for bosons and fermions. By means of the boundary effects associated to N finiteness, we will show that for bosons this law stems from classical correlations while for fermions it has a quantum origin. Finally, we will present the strong N dependence of the entanglement in R-antiR bipartition and compare the fermionic cases with their finite N bosonic analogs. We will also show the anti-intuitive dependence of this entanglement on statistics since more entanglement is created for bosons than for their fermion counterparts.Comment: revtex 4, 12 pages, 10 figures. Added Journal ref

Decay of the Maxwell field on the Schwarzschild manifold

We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of $t^{-1}$ for all components of the Maxwell field. We use vector field methods and do not require a spherical harmonic decomposition. In outgoing regions, where the Regge-Wheeler tortoise coordinate is large, $r_*>\epsilon t$, we obtain decay for the null components with rates of $|\phi_+| \sim |\alpha| < C r^{-5/2}$, $|\phi_0| \sim |\rho| + |\sigma| < C r^{-2} |t-r_*|^{-1/2}$, and $|\phi_{-1}| \sim |\underline{\alpha}| < C r^{-1} |t-r_*|^{-1}$. Along the event horizon and in ingoing regions, where $r_*<0$, and when $t+r_*1$, all components (normalized with respect to an ingoing null basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior region.Comment: 37 pages, 5 figure

A new perspective on Gravity and the dynamics of Spacetime

The Einstein-Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self contained, perspective on gravity and (ii) a concrete mathematical framework in which the description of spacetime dynamics by Einstein's equations is similar to the description of a continuum solid in the thermodynamic limit.Comment: Based on the Essay selected for Honorable Mention in the Gravity Research Foundation Essay Contest, 2005; to appear in the special issue of IJMP