Horizon energy and angular momentum from a Hamiltonian perspective

Classical black holes and event horizons are highly non-local objects, defined in terms of the causal past of future null infinity. Alternative, (quasi)local definitions are often used in mathematical, quantum, and numerical relativity. These include apparent, trapping, isolated, and dynamical horizons, all of which are closely associated to two-surfaces of zero outward null expansion. In this paper we show that three-surfaces which can be foliated with such two-surfaces are suitable boundaries in both a quasilocal action and a phase space formulation of general relativity. The resulting formalism provides expressions for the quasilocal energy and angular momentum associated with the horizon. The values of the energy and angular momentum are in agreement with those derived from the isolated and dynamical horizon frameworks.Comment: 39 pages, 3 figures, Final Version : content essentially unchanged but many small improvements made in response to referees, a few references adde

Fundamental properties and applications of quasi-local black hole horizons

The traditional description of black holes in terms of event horizons is inadequate for many physical applications, especially when studying black holes in non-stationary spacetimes. In these cases, it is often more useful to use the quasi-local notions of trapped and marginally trapped surfaces, which lead naturally to the framework of trapping, isolated, and dynamical horizons. This framework allows us to analyze diverse facets of black holes in a unified manner and to significantly generalize several results in black hole physics. It also leads to a number of applications in mathematical general relativity, numerical relativity, astrophysics, and quantum gravity. In this review, I will discuss the basic ideas and recent developments in this framework, and summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th International Conference on General Relativity and Gravitation, 8-13 July 2007, Sydney, Australi

P and T Violation From Certain Dimension Eight Weinberg Operators

Dimension eight operators of the Weinberg type have been shown to give important contributions to CP violating phenomena, such as the electric dipole moment of the neutron. In this note we show how operators related to these (and expected to occur on equal footing) can give rise to time-reversal violating phenomena such as atomic electric dipole moments. We also estimate the induced parity violating phenomena such as small ``wrong'' parity admixtures in atomic states and find that they are negligible. Uses harvmac.tex and epsf.tex; one figure submitted as a uuencoded, compressed EPS file.Comment: 6 pages, EFI-92-5

X-ray Absorption Fine Structure in Embedded Atoms

Oscillatory structure is found in the atomic background absorption in x-ray-absorption fine structure (XAFS). This atomic-XAFS or AXAFS arises from scattering within an embedded atom, and is analogous to the Ramsauer-Townsend effect. Calculations and measurements confirm the existence of AXAFS and show that it can dominate contributions such as multi-electron excitations. The structure is sensitive to chemical effects and thus provides a new probe of bonding and exchange effects on the scattering potential.Comment: 4 pages plus 2 postscript figures, REVTEX 3.

Marginally trapped tubes and dynamical horizons

We investigate the generic behaviour of marginally trapped tubes (roughly time-evolved apparent horizons) using simple, spherically symmetric examples of dust and scalar field collapse/accretion onto pre-existing black holes. We find that given appropriate physical conditions the evolution of the marginally trapped tube may be either null, timelike, or spacelike and further that the marginally trapped two-sphere cross-sections may either expand or contract in area. Spacelike expansions occur when the matter falling into a black hole satisfies $\rho - P \leq 1/A$, where $A$ is the area of the horizon while $\rho$ and $P$ are respectively the density and pressure of the matter. Timelike evolutions occur when $(\rho - P)$ is greater than this cut-off and so would be expected to be more common for large black holes. Physically they correspond to horizon "jumps" as extreme conditions force the formation of new horizons outside of the old.Comment: 31 pages, many figures. Final Version to appear in CQG: improvements include more complete references, a discussion of those references, Penrose-Carter diagrams for several of the spacetimes, and improved numerics for the scalar field

Classical dynamics and stability of collapsing thick shells of matter

We study the collapse towards the gravitational radius of a macroscopic spherical thick shell surrounding an inner massive core. This overall electrically neutral macroshell is composed by many nested delta-like massive microshells which can bear non-zero electric charge, and a possibly non-zero cosmological constant is also included. The dynamics of the shells is described by means of Israel's (Lanczos) junction conditions for singular hypersurfaces and, adopting a Hartree (mean field) approach, an effective Hamiltonian for the motion of each microshell is derived which allows to check the stability of the matter composing the macroshell. We end by briefly commenting on the quantum effects which may arise from the extension of our classical treatment to the semiclassical level.Comment: 16 pages in IOP style, 8 figures, accepted for publication in Class. Quantum Gra

Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries

A general recipe to define, via Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Noether conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.Comment: 29 pages with 1 figur

Black hole boundaries

Classical black holes and event horizons are highly non-local objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and numerical relativity. These include apparent, killing, trapping, isolated, dynamical, and slowly evolving horizons. All of these are closely associated with two-surfaces of zero outward null expansion. This paper reviews the traditional definition of black holes and provides an overview of some of the more recent work on alternative horizons.Comment: 27 pages, 8 figures, invited Einstein Centennial Review Article for CJP, final version to appear in journal - glossary of terms added, typos correcte

A hazard model of the probability of medical school dropout in the United Kingdom

From individual level longitudinal data for two entire cohorts of medical students in UK universities, we use multilevel models to analyse the probability that an individual student will drop out of medical school. We find that academic preparedness—both in terms of previous subjects studied and levels of attainment therein—is the major influence on withdrawal by medical students. Additionally, males and more mature students are more likely to withdraw than females or younger students respectively. We find evidence that the factors influencing the decision to transfer course differ from those affecting the decision to drop out for other reasons

Metabolic modeling for predicting VFA production from protein‐rich substrates by mixed‐culture fermentation

This is the peer reviewed version of the following article: Regueira, A, Lema, JM, Carballa, M, Mauricio‐Iglesias, M. Metabolic modeling for predicting VFA production from protein‐rich substrates by mixed‐culture fermentation. Biotechnology and Bioengineering. 2020; 117: 73– 84, which has been published in final form at https://doi.org/10.1002/bit.27177. This article may be used for non‐commercial purposes in accordance with Wiley Terms and Conditions for Use of Self‐Archived VersionsProteinaceous organic wastes are suitable substrates to produce high added‐value products in anaerobic mixed‐culture fermentations. In these processes, the stoichiometry of the biotransformation depends highly on operational conditions such as pH or feeding characteristics and there are still no tools that allow the process to be directed toward those products of interest. Indeed, the lack of product selectivity strongly limits the potential industrial development of these bioprocesses. In this work, we developed a mathematical metabolic model for the production of volatile fatty acids from protein‐rich wastes. In particular, the effect of pH on the product yields is analyzed and, for the first time, the observed changes are mechanistically explained. The model reproduces experimental results at both neutral and acidic pH and it is also capable of predicting the tendencies in product yields observed with a pH drop. It also offers mechanistic insights into the interaction among the different amino acids (AAs) of a particular protein and how an AA might yield different products depending on the relative abundance of other AAs. Particular emphasis is placed on the utility of this mathematical model as a process design tool and different examples are given on how to use the model for this purposeThe authors would like to acknowledge the support of the Spanish Ministry of Education (FPU14/05457) and project BIOCHEM (ERA-IB-2 7th call, ERA-IB-16-052) funded by MINECO (PCIN 2016-102). A. Regueira would like to thank the CRETUS Strategic Partnership (ED431E 2018/01), for a research stay grant. A. Regueira, M. Miguel-Mauricio and J. M. Lema belong to the Galician Competitive Research Group ED431C2017/029 and to the CRETUS Strategic Partnership, both programmes are co-funded by FEDER (UE)S