Chaos around a H\'enon-Heiles-inspired exact perturbation of a black hole

A solution of the Einstein's equations that represents the superposition of a Schwarszchild black hole with both quadrupolar and octopolar terms describing a halo is exhibited. We show that this solution, in the Newtonian limit, is an analog to the well known H\'enon-Heiles potential. The integrability of orbits of test particles moving around a black hole representing the galactic center is studied and bounded zones of chaotic behavior are found.Comment: 7 pages Revte

Is Hilbert space discrete?

We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert space is discrete. We give some simple examples involving qubits and the Schrodinger wavefunction, and discuss implications for quantum information and quantum gravity.Comment: 4 pages, revtex, 1 figur

The Semiclassical Limit of Loop Quantum Cosmology

The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit \gamma \to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the volume eigenvalues, and the simultaneous limit is technically the same as the classical limit \hbar \to 0, l \to \infty of angular momentum in quantum mechanics. Possible lessons for semiclassical states at the dynamical level in the full theory of quantum geometry are mentioned.Comment: 10 page

Tinted Semi-Transparent Solar Panels Allow Concurrent Production of Crops and Electricity on the Same Cropland

Agrivoltaics describes concurrent agricultural production of crops and photovoltaic generation of electricity on the same cropland. By using tinted semi-transparent solar panels, this study introduces a novel element to transform the concept of agrivoltaics from just solar-sharing to selective utilisation of different light wavelengths. Agrivoltaic growth of basil and spinach was tested. When compared with classical agriculture, and based on the feed-in-tariff of the experimental location, agrivoltaic co-generation of biomass and electricity is calculated to result in an estimated financial gross gain up to +2.5% for basil and +35% for spinach. Marketable biomass yields did not change significantly for basil, while a statistically significant loss was observed for spinach. This was accompanied by a relative increase in the protein content for both plants grown under agrivoltaic conditions. Agrivoltaics implemented with tinted solar panels improved the biomass production per unit amount of solar radiation up to 68%, with up to 63% increase in the ratio of leaf and stem biomass to root. Agrivoltaics can enrich the portfolio of farmers, mitigate risks associated with climate, and vastly enhance global photovoltaics capacity without compromising agricultural production.Leverhulme Trust RPG-2015-393 Italian Ministry of University and Research (to co-author A Schievano

The Value of Singularities

We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a stable ground state. This argument applies both to classical extensions of general relativity, and to candidate quantum theories of gravity.Comment: 5 pages, no figures; a few clarifying comments adde

Chaos in black holes surrounded by gravitational waves

The occurrence of chaos for test particles moving around Schwarzschild black holes perturbed by a special class of gravitational waves is studied in the context of the Melnikov method. The explicit integration of the equations of motion for the homoclinic orbit is used to reduce the application of this method to the study of simple graphics.Comment: 15 pages, LaTex

Network Cosmology

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology

Divergences problem in black hole brick-wall model

In this work we review, in the framework of the so-called brick wall model, the divergence problem arising in the one loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. Particularly we find that, if one imposes that entanglement entropy is equal to the Bekenstein-Hawking one, the model gives problematic results. Then a proposal of solution to the divergence problem is made following the zeroth law of black hole mechanics.Comment: 19 pages, reviseted-extended version accepted by Phys. Rev.

Entanglement entropy, black holes and holography

We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of holography as an upper bound on the realizable entropy (entanglement or von Neumann) of a region, rather than on the dimension of its Hilbert space.Comment: 4 pages, revte

Black hole entropy: statistical mechanics agrees thermodynamics

We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to 't Hooft and regularized by Pauli-Villars.Comment: 10 pages, latex. Some new discussion added. Version to appear in Phys Rev.