Showing papers on "Gravitation published in 2002"

The Holographic principle

Abstract: There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.

Modified Newtonian dynamics as an alternative to dark matter

Abstract: ▪ Abstract Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below ao ≈ 10−8 cm/s2 ≈ cHo/6 the effective gravitational attraction approaches , where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V4 that forms the basis for the observed luminosity–rotation velocity relation—the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to superclusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extention of MOND to cosmology and structure formation.

From AdS/CFT correspondence to hydrodynamics. II. Sound waves

Abstract: As a non-trivial check of the non-supersymmetric gauge/gravity duality, we use a near-extremal black brane background to compute the retarded Green's functions of the stress-energy tensor in = 4 super-Yang-Mills (SYM) theory at finite temperature. For the long-distance, low-frequency modes of the diagonal components of the stress-energy tensor, hydrodynamics predicts the existence of a pole in the correlators corresponding to propagation of sound waves in the = 4 SYM plasma. The retarded Green's functions obtained from gravity do indeed exhibit this pole, with the correct values for the sound speed and the rate of attenuation.

Gravitational Energy in Quadratic-Curvature Gravities

Abstract: We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D = 4, all purely quadratic models admit constant curvature vacua with arbitrary Λ, and E is the “cosmological” Abbott-Deser (AD) expression; instead, E always vanishes in flat, Λ = 0, background. For combined Einstein-quadratic curvature systems without explicit Λ-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Λ-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.

Relativistic simulations of rotational core collapse - II. Collapse dynamics and gravitational radiation

Abstract: We have performed hydrodynamic simulations of relativistic rotational supernova core collapse in axisymmetry and have computed the gravitational radiation emitted by such an event. The Einstein equations are formulated using the confor- mally flat metric approximation, and the corresponding hydrodynamic equations are written as a first-order flux-conservative hyperbolic system. Details of the methodology and of the numerical code have been given in an accompanying paper. We have simulated the evolution of 26 models in both Newtonian and relativistic gravity. The initial configurations are dierentially rotat- ing relativistic 4=3-polytropes in equilibrium which have a central density of 10 10 gc m 3 . Collapse is initiated by decreasing the adiabatic index to some prescribed fixed value. The equation of state consists of a polytropic and a thermal part for a more realis- tic treatment of shock waves. Any microphysics like electron capture and neutrino transport is neglected. Our simulations show that the three dierent types of rotational supernova core collapse and gravitational waveforms identified in previous Newtonian simulations (regular collapse, multiple bounce collapse, and rapid collapse) are also present in relativistic gravity. However, ro- tational core collapse with multiple bounces is only possible in a much narrower parameter range in relativistic gravity. The relativistic models cover almost the same range of gravitational wave amplitudes (4 10 21 h TT 3 10 20 for a source at a distance of 10 kpc) and frequencies (60 Hz 1000 Hz) as the corresponding Newtonian ones. Averaged over all models, the total energy radiated in the form of gravitational waves is 8:2 10 8 Mc 2 in the relativistic case, and 3:6 10 8 Mc 2 in the Newtonian case. For all collapse models that are of the same type in both Newtonian and relativistic gravity, the gravitational wave signal is of lower amplitude. If the collapse type changes, either weaker or stronger signals are found in the relativistic case. For a given model, relativistic gravity can cause a large increase of the characteristic signal frequency of up to a factor of five, which may have important consequences for the signal detection. Our study implies that the prospects for detection of gravita- tional wave signals from axisymmetric supernova rotational core collapse do not improve when taking into account relativistic gravity. The gravitational wave signals obtained in our study are within the sensitivity range of the first generation laser interfer- ometer detectors if the source is located within the Local Group. An online catalogue containing the gravitational wave signal amplitudes and spectra of all our models is available at the URL http://www.mpa-garching.mpg.de/Hydro/hydro.html.

The scaling evolution of the cosmological constant

Abstract: In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the ``cosmological constant'' is not a constant in a quantum field theory context, still less should be zero. In this paper we continue with previous work, and derive the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time. At higher energies the calculation is performed in a sharp cut off approximation. We assess, in two different frameworks, whether the scaling dependences of the cosmological and gravitational constants spoil primordial nucleosynthesis. Finally, the cosmological implications of the running of the cosmological constant are discussed.

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Space-Time

Abstract: We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, Agile-Boltztran, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in self-consistent simulations of stellar core collapse and postbounce evolution. It implements a dynamically adaptive grid in comoving coordinates. Most macroscopically interesting physical quantities are defined by expectation values of the distribution function. We optimize the finite differencing of the microscopic transport equation for a consistent evolution of important expectation values. We test our code in simulations launched from progenitor stars with 13 solar masses and 40 solar masses. ~0.5 s after core collapse and bounce, the protoneutron star in the latter case reaches its maximum mass and collapses further to form a black hole. When the hydrostatic gravitational contraction sets in, we find a transient increase in electron flavor neutrino luminosities due to a change in the accretion rate. The muon- and tauon-neutrino luminosities and rms energies, however, continue to rise because previously shock-heated material with a non-degenerate electron gas starts to replace the cool degenerate material at their production site. We demonstrate this by supplementing the concept of neutrinospheres with a more detailed statistical description of the origin of escaping neutrinos. We compare the evolution of the 13 solar mass progenitor star to simulations with the MGFLD approximation, based on a recently developed flux limiter. We find similar results in the postbounce phase and validate this MGFLD approach for the spherically symmetric case with standard input physics.

Relativistic simulations of rotational core collapse. II. Collapse dynamics and gravitational radiation

Abstract: We have performed hydrodynamic simulations of relativistic rotational supernova core collapse in axisymmetry and have computed the gravitational radiation emitted by such an event. Details of the methodology and of the numerical code have been given in an accompanying paper. We have simulated the evolution of 26 models in both Newtonian and relativistic gravity. Our simulations show that the three different types of rotational supernova core collapse and gravitational waveforms identified in previous Newtonian simulations (regular collapse, multiple bounce collapse, and rapid collapse) are also present in relativistic gravity. However, rotational core collapse with multiple bounces is only possible in a much narrower parameter range in relativistic gravity. The relativistic models cover almost the same range of gravitational wave amplitudes and frequencies as the corresponding Newtonian ones. For a given model, relativistic gravity can cause a large increase of the characteristic signal frequency of up to a factor of five, which may have important consequences for the signal detection. The gravitational wave signals obtained in our study are within the sensitivity range of the first generation laser interferometer detectors if the source is located within the Local Group.

Artificial black holes

Abstract: Contents: Introduction and Survey (M Visser) Acoustic Black Holes in Dilute Bose-Einstein Condensates (L Garay) Slow Light (U Leonhardt) Black Hole and Baby Universe in a Thin Film of 3He-A (T Jacobson & T Koike) Measurability of Dumb Hole Radiation? (W Unruh) Effective Gravity and Quantum Vacuum in Superfluids (G Volovik) Emergent Relativity and the Physics of Black Hole Horizons (G Chapline et al.) Quasi-Gravity in Branes (B Carter) Towards a Collective Treatment of Quantum Gravitational Interactions (R Parentani) Role of Sonic Metric in Relativistic Superfluid (B Carter) Effective Geometry in Nonlinear Field Theory (Electrodynamics and Gravity) (M Novello) Non-Inertial Quantum Mechanical Fluctuations (H Rosu) Phonons and Forces: Momentum versus Pseudomomentum (M Stone) Coda (M Visser) Appendix: Elements of General Relativity (M Visser).

Studies of the Relativistic Binary Pulsar PSR B1534+12. I. Timing Analysis

Abstract: We have continued our long-term study of the double neutron star binary pulsar PSR B1534+12, using new instrumentation to make very high precision measurements at the Arecibo Observatory. We have significantly improved our solution for the astrometric, spin, and orbital parameters of the system as well as for the five "post-Keplerian" orbital parameters that can be used to test gravitation theory. The results are in good agreement with the predictions of general relativity. With the assumption that general relativity is the correct theory of gravity in the classical regime, our measurements allow us to determine the masses of the pulsar and its companion neutron star with high accuracy: 1.3332 ± 0.0010 M☉ and 1.3452 ± 0.0010 M☉, respectively. The small but significant mass difference is difficult to understand in most evolutionary models, as the pulsar is thought to have been born first from a more massive progenitor star and then undergone a period of mass accretion before the formation of the second neutron star. PSR B1534+12 has also become a valuable probe of the local interstellar medium. We have now measured the pulsar distance to be 1.02 ± 0.05 kpc, giving a mean electron density along this line of sight of 0.011 cm-3. We continue to measure a gradient in the dispersion measure, though the rate of change is now slower than in the first years after the pulsar's discovery.

Three-dimensional numerical general relativistic hydrodynamics. II. Long-term dynamics of single relativistic stars

Abstract: This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The following aspects of our code have been validated: the generation of initial data representing perturbed general relativistic polytropic models ~both rotating and nonrotating!, the long-term evolution of relativistic stellar models, and the coupling of our evolution code to analysis modules providing, for instance, the detection of apparent horizons or the extraction of gravitational waveforms. The tests involve single nonrotating stars in stable equilibrium, nonrotating stars undergoing radial and quadrupolar oscillations, nonrotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, nonrotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasiradial oscillations. We have carried out evolutions in full general relativity and compared the results to those obtained either with perturbation techniques, or with lower dimensional numerical codes, or in the Cowling approximation ~in which all the perturbations of the spacetime are neglected!. In all cases an excellent agreement has been found. The numerical evolutions have been carried out using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. In particular, we have found the ‘‘monotonized central differencing’’ limiter to be particularly effective in evolving the relativistic stellar models considered. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.

Relativistic simulations of rotational core collapse I. Methods, initial models, and code tests

Abstract: We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3 + 1 formalism and a conformally flat metric approximation of the Einstein equations. Within this approximation the ADM 3 + 1 equations reduce to a set of ve coupled non-linear elliptic equations for the metric components. The equations are discretized on a 2D grid in spherical polar coordinates and are solved by means of a Newton-Raphson iteration using a block elimination scheme to solve the diagonally dominant, sparse linear system arising within each iteration step. The relativistic hydrodynamics equations are formulated as a rst-order flux-conservative hyperbolic system and are integrated using high-resolution shock-capturing schemes based on Riemann solvers. We assess the quality of the conformally flat metric approximation for relativistic core collapse and present a comprehensive set of tests that the code successfully passed. The tests include relativistic shock tubes, the preservation of the rotation prole and of the equilibrium of rapidly and dierentially rotating neutron stars (approximated as rotating polytropes), spherical relativistic core collapse, and the conservation of rest-mass and angular momentum in dynamic spacetimes. The application of the code to relativistic rotational core collapse, with emphasis on the gravitational waveform signature, is presented in an accompanying paper.

Classical Mechanics: A Modern Perspective

Abstract: Part 1 Linear motion: Newtonian theory interactions the drag racer - frictional force sport parachuting - viscous force archery - spring force methods of solution simple harmonic oscillator damped harmonic motion forced oscillator with damping resonance. Part 2 Energy conservation: potential energy gravitational escape small oscillations three-dimensional motion - vector notation conservation forces in three dimensions motion in a plane simple pendulum coupled harmonic oscillators. Part 3 Lagrangian method: Lagrange's equations some Lagrangian applications the Lorentz force mechanical constraints Hamilton's equations. Part 4 Momentum conservation: rocket motion frames of reference elastic collisions - laboratory and center-of-mass systems collisions of billiard balls inelastic collisions scattering cross sections. Part 5 Angular-momentum conservation: central forces planetary motion eccentricity vector Kepler's laws satellites and spacecraft grand tours of the outer planets Rutherford scattering. Part 6 Particles systems and rigid bodies: center of mass and the two-body problem rotational equation of motion rigid bodies - static equilibrium statics and dynamics of a heavy string rotations of rigid bodies gyroscope effect the boomerang moments and produces of intertia single-axis rotations moments-of-intertia calculations impulses and billiard shots super-ball bounces. Part 7 Accelerated coordinate systems: transformation to moving coordinate frames fictitious forces motion on the earth Foucault's pendulum dynamical balance of a rigid body principal axes and Euler's equations the tennis racket theorem the earth as a free symmetric top - external observer spinning top, including gravity slipping tops - rising and sleeping the tippie-top. Part 8 Gravitation: attraction of a spherical body - Newton's theorem the tides gravity field of the earth. Part 9 Newtonian cosmology: the universe virial theorem dark matter cosmology. Part 10 Non-linear mechanics and the approach to chaos: the anharmonic oscillator the damped and driven anharmonic oscillator numerical solutions. Part 11 Relativity: the relativity idea Lorentz transformation consequences of relativity relativistic momentum and energy.

Relativistic simulations of rotational core collapse. I. Methods, initial models, and code tests

Abstract: We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3+1 formalism and a conformally flat metric approximation of the Einstein equations. The relativistic hydrodynamics equations are formulated as a first-order flux-conservative hyperbolic system and are integrated using high-resolution shock-capturing schemes based on Riemann solvers. We assess the quality of the conformally flat metric approximation for relativistic core collapse and present a comprehensive set of tests which the code successfully passed. The tests include relativistic shock tubes, the preservation of the rotation profile and of the equilibrium of rapidly and differentially rotating neutron stars (approximated as rotating polytropes), spherical relativistic core collapse, and the conservation of rest-mass and angular momentum in dynamic spacetimes. The application of the code to relativistic rotational core collapse, with emphasis on the gravitational waveform signature, is presented in an accompanying paper.

Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space

Abstract: We show that standard Einstein gravity coupled to a free conformal field theory (CFT) in anti-de Sitter space can undergo a Higgs phenomenon whereby the graviton acquires a nonzero mass (and three extra polarizations). We show that the essential ingredients of this mechanism are the discreteness of the energy spectrum in AdS space, and unusual boundary conditions on the elementary fields of the CFT. These boundary conditions can be interpreted as implying the existence of a 3-d defect CFT living at the boundary of AdS4. Our free-field computation sheds light on the essential, model-independent features of AdS4 that give rise to massive gravity.

Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation

Abstract: We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large-scale supercomputer. We take the typical grid size as (505, 505, 253) for (x, y, z) and the maximum grid size as (633, 633, 317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within ∼ 10% error) for the first time. To model neutron stars, we adopt a Γ -law equation of state in the form P =( Γ − 1)ρe, where P , ρ, e and Γ are the pressure, rest mass density, specific internal energy and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain.

Radion and holographic brane gravity

Abstract: The low energy effective theory for the Randall-Sundrum two brane system is investigated with an emphasis on the role of the non-linear radion in the brane world The equations of motion in the bulk is solved using a low energy expansion method This allows us, through the junction conditions, to deduce the effective equations of motion for the gravity on the brane It is shown that the gravity on the brane world is described by a quasi-scalar-tensor theory with a specific coupling function omega(Psi) = 3 Psi / 2(1-Psi) on the positive tension brane and omega(Phi) = -3 Phi / 2(1+Phi) on the negative tension brane, where Psi and Phi are non-linear realizations of the radion on the positive and negative tension branes, respectively In contrast to the usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two kinds of matter, namely, the matters on both positive and negative tension branes, with different effective gravitational coupling constants In particular, the radion disguised as the scalar fields Psi and Phi couples with the sum of the traces of the energy momentum tensor on both branes In the course of the derivation, it has been revealed that the radion plays an essential role to convert the non-local Einstein gravity with the generalized dark radiation to the local quasi-scalar-tensor gravity For completeness, we also derive the effective action for our theory by substituting the bulk solution into the original action It is also shown that the quasi-scalar-tensor gravity works as holograms at the low energy in the sense that the bulk geometry can be reconstructed from the solution of the quasi-scalar-tensor gravity

Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation

Abstract: We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large scale supercomputer. We take the typical grid size as (505,505,253) for (x,y,z) and the maximum grid size as (633,633,317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within $\sim 10%$ error) for the first time. To model neutron stars, we adopt a $\Gamma$-law equation of state in the form $P=(\Gamma-1)\rho\epsilon$, where P, $\rho$, $\varep$ and $\Gamma$ are the pressure, rest mass density, specific internal energy, and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain.

Quantum gravity and spin-1/2 particle effective dynamics

Abstract: Quantum gravity phenomenology opens up the possibility of probing Planck scale physics. Thus, by exploiting the generic properties that a semiclassical state of the compound system fermions plus gravity should have, an effective dynamics of spin-1/2 particles is obtained within the framework of loop quantum gravity. Namely, at length scales much larger than Planck length ${\mathcal{l}}_{P}\ensuremath{\sim}{10}^{\ensuremath{-}33}\mathrm{cm}$ and below the wavelength of the fermion, the spin-1/2 dynamics in flat spacetime includes Planck scale corrections. In particular we obtain modified dispersion relations in vacuo for fermions. These corrections yield a time of arrival delay of the spin-1/2 particles with respect to a light signal and, in the case of neutrinos, a novel flavor oscillation. To detect these effects the corresponding particles must be highly energetic and should travel long distances. Hence neutrino bursts accompanying gamma ray bursts or ultrahigh energy cosmic rays could be considered. Remarkably, future neutrino telescopes may be capable of testing such effects. This paper provides a detailed account of the calculations and elaborates on results previously reported in a Letter. These are further amended by introducing a real parameter $\ensuremath{\Upsilon}$ aimed at encoding our lack of knowledge of scaling properties of the gravitational degrees of freedom.

Induced Gravity on RS Branes

Abstract: It is shown that a localized four-dimensional Einstein term, induced by quantum corrections, modifies significantly the law of gravity in a Randall-Sundrum brane world. In particular, the short-distance behavior of gravity changes from five- to four-dimensional, while, depending on the values of parameters, there can be an intermediate range where gravity behaves as in five dimensions. The spectrum of graviton fluctuations around the brane, their relative importance for the gravitational force, and the relevance of their emission in the bulk for the brane cosmology are analysed. Finally, constraints on parameters are derived from energy loss in astrophysical and particle physics processes.

Heretics of the False Vacuum: Gravitational Effects On and Of Vacuum Decay 2

Abstract: This paper reexamines the question of vacuum decay in theories of quantum gravity. In particular it suggests that decay into stable flat or AdS vacua, never occurs. Instead, vacuum decay occurs, if at all, into a cosmological spacetime. If the latter has negative cosmological constant, it undergoes a Big Crunch, which suggests that the whole picture is inconsistent. The question of decay of de Sitter space must be very carefully defined.

Mass and gauge invariance: Holography for the Karch-Randall model

Abstract: We argue that the Karch-Randall compactification is holographically dual to a 4D conformal field theory coupled to gravity on anti--de Sitter space. Using this interpretation we recover the mass spectrum of the model. In particular, we find no massless spin-2 states. By giving a purely 4D interpretation to the compactification we make clear that it represents the first example of a local 4D field theory in which general covariance does not imply the existence of a massless graviton. We also discuss some variations of the Karch-Randall model discussed in the literature, and we examine whether its properties are generic to all conformal field theory.

Einstein billiards and overextensions of finite-dimensional simple Lie algebras

Abstract: In recent papers, it has been shown that (i) the dynamics of theories involving gravity can be described, in the vicinity of a spacelike singularity, as a billiard motion in a region of hyperbolic space bounded by hyperplanes; and (ii) that the relevant billiard has remarkable symmetry properties in the case of pure gravity in d+1 spacetime dimensions, or supergravity theories in 10 or 11 spacetime dimensions, for which it turns out to be the fundamental Weyl chamber of the Kac-Moody algebras AEd, E10, BE10 or DE10 (depending on the model). We analyse in this paper the billiards associated to other theories containing gravity, whose toroidal reduction to three dimensions involves coset models G/H (with G maximally non compact). We show that in each case, the billiard is the fundamental Weyl chamber of the (indefinite) Kac-Moody ``overextension'' (or ``canonical lorentzian extension'') of the finite-dimensional Lie algebra that appears in the toroidal compactification to 3 spacetime dimensions. A remarkable feature of the billiard properties, however, is that they do not depend on the spacetime dimension in which the theory is analyzed and hence are rather robust, while the symmetry algebra that emerges in the toroidal dimensional reduction is dimension-dependent.

Degeneracies and scaling relations in general power-law models for gravitational lenses

Abstract: ABSTRA C T The time-delay in gravitational lenses can be used to derive the Hubble constant in a relatively simple way. The results of this method are less dependent on astrophysical assumptions than in many other methods. For systems with accurately measured positions and time-delays, the most important uncertainty is related to the mass model used. Simple parametric models like isothermal ellipsoidal mass distributions seem to provide consistent results with a reasonably small scatter when applied to several lens systems. We discuss a family of models with a separable radial power law and an arbitrary angular dependence for the potential ca r b FOuU. Isothermal potentials are a special case of these models with ba 1. An additional external shear is used to take into account perturbations from other galaxies. Using a simple linear formalism for quadruple lenses, we can derive H0 as a function of the observables and the shear. If the latter is fixed, the result depends on the assumed power-law exponent according to H0/O2 2 bU/b. The effect of external shear is quantified by introducing a ‘critical shear’gc as a measure for the amount of shear that changes the result significantly. The analysis shows that in the general case H0 and gc do not depend on the position of the lens galaxy. Spherical lens models with images close to the Einstein radius with fitted external shear differ by a factor of b/2 from shearless models, leading to H0/ 2 2 b in this case. We discuss these results and compare them with numerical models for a number of real lens

The Maximum Tension Principle in General Relativity

Abstract: I suggest that classical General Relativity in four spacetime dimensions incorporates a Principal of Maximal Tension and give arguments to show that the value of the maximal tension is \(\frac{{c^4 }}{{4G}}\). The relation of this principle to other, possibly deeper, maximal principles is discussed, in particular the relation to the tension in string theory. In that case it leads to a purely classical relation between G and the classical string coupling constant α′ and the velocity of light c which does not involve Planck's constant.