Showing papers on "Gravitation published in 1999"

An Alternative to compactification

Abstract: Conventional wisdom states that Newton's force law implies only four noncompact dimensions. We demonstrate that this is not necessarily true in the presence of a nonfactorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.

The Gravitational Action in Asymptotically AdS and Flat Spacetimes

Abstract: The divergences of the gravitational action are analyzed for spacetimes that are asymptotically anti-de Sitter and asymptotically flat. The gravitational action is rendered finite using a local counterterm prescription, and the relation of this method to the traditional reference spacetime is discussed. For AdS, an iterative procedure is devised that determines the counterterms efficiently. For asymptotically flat space, we use a different method to derive counterterms which are sufficient to remove divergences in most cases.

Negative specific heat in astronomy, physics and chemistry

Abstract: Starting from Antonov's discovery that there is no maximum to the entropy of a gravitating system of point particles at fixed energy in a spherical box if the density contrast between centre and edge exceeds 709, we review progress in the understanding of gravitational thermodynamics. We pinpoint the error in the proof that all systems have positive specific heat and say when it can occur. We discuss the development of the thermal runaway in both the gravothermal catastrophe and its inverse. The energy range over which microcanonical ensembles have negative heat capacity is replaced by a first order phase transition in the corresponding canonical ensembles. We conjecture that all first order phase transitions may be viewed as caused by negative heat capacities of units within them. We find such units in the theory of ionization, chemical dissociation and in the Van der Waals gas so these concepts are applicable outside the realm of stars, star clusters and black holes.

Large N phases, gravitational instantons, and the nuts and bolts of AdS holography

Abstract: Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity ~at least with a negative cosmological constant! can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay, and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taubbolt spacetimes, and compare them to a ~211!-dimensional conformal field theory~at large N! compactified on a squashed three-sphere and on the twisted plane. @S0556-2821~99!06302-X#

Quadrupole Moments of Rotating Neutron Stars

Abstract: Numerical models of rotating neutron stars are constructed for four equations of state using the computer code RNS written by Stergioulas. For five selected values of the star's gravitational mass (in the interval between 1.0 and 1.8 solar masses) and for each equation of state, the star's angular momentum is varied from J=0 to the Keplerian limit J=Jmax. For each neutron star configuration, we compute Q, the quadrupole moment of the mass distribution. We show that for given values of M and J, |Q| increases with the stiffness of the equation of state. For fixed mass and equation of state, the dependence on J is well reproduced with a simple quadratic fit, Q -aJ2/Mc2, where c is the speed of light and a is a parameter of order unity depending on the mass and the equation of state.

Isolated horizons: The Classical phase space

Abstract: A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are “isolated” near future time-like infinity or for a finite time interval The underlying space-times need not admit a stationary Killing field even in a neighborhood of the horizon; rather, the physical assumption is that neither matter fields nor gravitational radiation fall across the portion of the horizon under consideration A precise notion of non-rotating isolated horizons is formulated to capture these ideas With these boundary conditions, the gravitational action fails to be differentiable unless a boundary term is added at the horizon The required term turns out to be precisely the Chern-Simons action for the self-dual connection The resulting symplectic structure also acquires, in addition to the usual volume piece, a surface term which is the Chern-Simons symplectic structure We show that these modifications affect in subtle but important ways the standard discussion of constraints, gauge and dynamics In companion papers, this framework serves as the point of departure for quantization, a statistical mechanical calculation of black hole entropy and a derivation of laws of black hole mechanics, generalized to isolated horizons It may also have applications in classical general relativity, particularly in the investigation of of analytic issues that arise in the numerical studies of black hole collisions Typeset using REVTEX

Short-range tests of the equivalence principle

Abstract: The most precise tests of the equivalence principle, the underlying symmetry of general relativity, are made by comparing the accelerations of test bodies toward a massive attractor. The equivalence principle, which states that gravitation is locally equivalent to an acceleration of the reference frame, predicts that these gravitational accelerations will be identical if tidal forces can be neglected. The classic Princeton @1# and Moscow @2# equivalence-principle tests compared the accelerations of Al and Au or Pt test bodies toward the Sun, implicitly assuming that any violation of the equivalence principle, or more precisely the universality of free fall ~UFF!, would have an infinite range. This was a natural assumption in a classical context where the equivalence principle can be viewed in Newtonian terms; i.e., are gravitational and inertial masses identical? However, in a quantum context it is natural to view equivalence principle tests as probes for new Yukawa interactions arising from exchange of exotic, low-mass bosons. In this context the tests should be sensitive to UFF violation over a broad variety of Yukawa length scales and should utilize a variety of test bodies whose relevant properties, such as binding energy per unit mass, atomic charge Z, neutron-to-proton ratio N/Z, etc., differ by the greatest practical amount. Such UFF tests are powerful probes of new physics because interactions arising from exchange of scalar or vector bosons generically violate the UFF ~see Ref. @3#!. We have undertaken a series of experiments with the goal of testing the UFF with as much generality as is practical. In designing these tests, we imagine UFF-violating interactions arising from the exchange of scalar or vector bosons of mass mb . These will produce a potential between point bodies with a Yukawa form

Effective Field Theory for a Three-Brane Universe

Abstract: A general effective field theory formalism is presented which describes the low-energy dynamics of a 3-brane universe. In this scenario an arbitrary four-dimensional particle theory, such as the standard model, is constrained to live on the world volume of a (3+1)-dimensional hypersurface, or {open_quotes}3-brane,{close_quotes} which in turn fluctuates in a higher-dimensional, gravitating spacetime. The inclusion of chiral fermions on the 3-brane is given careful treatment. The power counting needed to renormalize quantum amplitudes of the effective theory is also discussed. The effective theory has a finite domain of validity, restricting it to processes at low enough energies that the internal structure of the 3-brane cannot be resolved. {copyright} {ital 1999} {ital The American Physical Society}

Black holes, shock waves, and causality in the AdS/CFT correspondence

Abstract: We find the expectation value of the energy-momentum tensor in the CFT corresponding to a moving black hole in AdS. Boosting the black hole to the speed of light, keeping the total energy fixed, yields a gravitational shock wave in AdS. The analogous procedure on the field theory side leads to ``light cone'' states, i.e., states with energy-momentum tensor localized on the light cone. The correspondence between the gravitational shock wave and these light cone states provides a useful tool for testing causality. We show, in several examples, how the CFT reproduces the causal relations in AdS.

Cosmological constraints on theories with large extra dimensions

Abstract: In theories with large extra dimensions, constraints from cosmology lead to non-trivial lower bounds on the gravitational scale M, corresponding to upper bounds on the radii of the compact extra dimensions. These constraints are especially relevant to the case of two extra dimensions, since only if M is 10 TeV or less do deviations from the standard gravitational force law become evident at distances accessible to planned sub-mm gravity experiments. By examining the graviton decay contribution to the cosmic diffuse gamma radiation, we derive, for the case of two extra dimensions, a conservative bound M > 110TeV, corresponding to r{sub 2} 6.5/{radical}h TeV, or r{sub 2} < .015hmm.

Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space

Abstract: Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity to 3d and 4d, in the form of field theories over group manifolds. We show that the Barrett-Crane quantum gravity model arises naturally from a theory of this type, but restricted to the homogeneous space S^3=SO(4)/SO(3), as a term in its Feynman expansion. From such a perspective, 4d quantum spacetime emerges as a Feynman graph, in the manner of the 2d matrix models. This formalism provides a precise meaning to the ``sum over triangulations'', which is presumably necessary for a physical interpretation of a spin foam model as a theory of gravity. In addition, this formalism leads us to introduce a natural alternative model, which might have relevance for quantum gravity.

Isolated Horizons: the Classical Phase Space

Abstract: A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are ``isolated'' near future time-like infinity or for a finite time interval. The underlying space-times need not admit a stationary Killing field even in a neighborhood of the horizon; rather, the physical assumption is that neither matter fields nor gravitational radiation fall across the portion of the horizon under consideration. A precise notion of non-rotating isolated horizons is formulated to capture these ideas. With these boundary conditions, the gravitational action fails to be differentiable unless a boundary term is added at the horizon. The required term turns out to be precisely the Chern-Simons action for the self-dual connection. The resulting symplectic structure also acquires, in addition to the usual volume piece, a surface term which is the Chern-Simons symplectic structure. We show that these modifications affect in subtle but important ways the standard discussion of constraints, gauge and dynamics. In companion papers, this framework serves as the point of departure for quantization, a statistical mechanical calculation of black hole entropy and a derivation of laws of black hole mechanics, generalized to isolated horizons. It may also have applications in classical general relativity, particularly in the investigation of of analytic issues that arise in the numerical studies of black hole collisions.

Phenomenology of low quantum gravity scale models

Abstract: We study some phenomenological implications of models where the scale of quantum gravity effect lies much below the four-dimensional Planck scale. These models arise from M-theory vacua where either the internal space volume is large or the string coupling is very small. We provide a critical analysis of ways to unify electroweak, strong, and gravitational interactions in M theory. We discuss the relations between different scales in two M vacua: type I strings and Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Witten supergravity models. The latter allows possibilities for an 11-dimensional scale at TeV energies with one large dimension below separating our four-dimensional world from a hidden one. Different mechanisms for breaking supersymmetry (gravity mediated, gauge mediated, and Scherk-Schwarz mechanisms) are discussed in this framework. Some phenomenological issues such as dark matter (with masses that may vary in time), origin of neutrino masses, and axion scale are discussed. We suggest that these are indications that the string scale may be lying in the ${10}^{10}--{10}^{14 }$GeV region.

Trans-Planckian Redshifts and the Substance of the Space-Time River

Abstract: Trans-Planckian redshifts in cosmology and outside black holes may provide windows on a hypothetical short distance cutoff on the fundamental degrees of freedom. In cosmology, such a cutoff seems to require a growing Hilbert space, but for black holes, Unruh’s sonic analogy has given rise to both field theoretic and lattice models demonstrating how such a cutoff in a fixed Hilbert space might be compatible with a low energy effective quantum field theory of the Hawking effect. In the lattice case, the outgoing modes arise via a Bloch oscillation from ingoing modes. A short distance cutoff on degrees of freedom is incompatible with local Lorentz invariance, but may nevertheless be compatible with general covariance if the preferred frame is defined non-locally by the cosmological background. Pursuing these ideas in a different direction, condensed matter analogs may eventually allow for laboratory observations of the Hawking effect. This paper introduces and gives a fairly complete but brief review of the work that has been done in these areas, and tries to point the way to some future directions. It was inspiring to be in Kyoto with the purpose of looking forward toward the next century of gravitational physics. The present century gave us general relativity, with its profound and beautiful understanding of gravitation. In this view, we can think of spacetime as a river, and of gravitation as the inhomogeneity of the flow. At the YKIS99 meeting we heard about vortices, waves, bifurcations, and stones in the river. The subject of my talk was a question about the substance of the river itself: the ancient question whether space and time are continuous or discrete. The ultraviolet divergences of quantum field theory and the infinite curvature singularities of general relativity call for a fundamental short distance cutoff of some kind. Perhaps spacetime is locally discrete, or perhaps locality itself is not valid, as string theory suggests. But to learn something about the physics of the cutoff we must find a way to access that remote territory. The modern viewpoint 1) is that quantum field theory is an effective description of collective degrees of freedom of an underlying medium whose nature remains unknown, and need not be known, in order to do physics below some cutoff momentum scale. However, there are two familiar settings in which the usual separation between long and short distance scales breaks down, and the short distance physics is, potentially, unmasked. These are the expansion of the universe, and the event horizon of a black hole. In both cases there is a tremendous, trans-Planckian, redshift. The redshift at a black hole horizon means that the low energy effective field

Some remarks on theories with large compact dimensions and TeV-scale quantum gravity

Abstract: We comment on some implications of theories with large compactification radii and TeV-scale quantum gravity. These include the behavior of high-energy gravitational scattering cross sections and consequences for ultra-high-energy cosmic rays and neutrino scattering, the question of how to generate naturally light neutrino masses, the issue of quark-lepton unification, the equivalence principle, and the cosmological constant.

Scalar mesostatic field with regard for gravitational effects

Abstract: (Foreword by translator.) The aim of present translation is to clarify the historically important question who was the pioneer in obtaining of exact static solutions of Einstein equations minimally coupled with scalar field. Usually, people cite the works by Janis, Newman, Winicour (Phys. Rev. Lett. 20 (1968) 878) and others authors whereas it is clear that JNW rediscovered (in other coordinates) the Fisher's solution which was obtained 20 years before, in 1947. Regrettably, up to now I continue to meet many papers (even very fresh ones) whose authors evidently do not know about the Fisher's work, so I try to remove this gap by virtue of present translation and putting it into the LANL e-print archive. (Original Abstract.) It is considered the scalar mesostatic field of a point source with the regard for spacetime curvature caused by this field. For the field with $\mass = 0$ the exact solution of Einstein equations was obtained. It was demonstrated that at small distance from a source the gravitational effects are so large that they cause the significant changes in behavior of meson field. In particular, the total energy of static field diverges logarithmically.

Stochastic background of gravitational waves generated by a cosmological population of young, rapidly rotating neutron stars

Abstract: We estimate the spectral properties of the stochastic background of gravitational radiation emitted by a cosmological population of hot, young, rapidly rotating neutron stars. Their formation rate as a function of redshift is deduced from an observation-based determination of the star formation history in the Universe, and the gravitational energy is assumed to be radiated during the spin-down phase associated with the newly discovered r-mode instability. We calculate the overall signal produced by the ensemble of such neutron stars, assuming various cosmological backgrounds. We find that the spectral strain amplitude has a maximum ≈ (2-4)× 10-26Hz-1/2 , at frequencies ≈ (30-60) Hz, while the corresponding closure density, h2ΟGW, has a maximum amplitude plateau of ≈ (2.2-3.3) × 10-8 in the frequency range (500-1700) Hz. We compare our results with a preliminary analysis done by Owen et al., and discuss the detectability of this background.

Particlelike solutions of the Einstein-Dirac equations

Abstract: The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well-behaved even for strong coupling.

Compactification for a three-brane universe

Abstract: A fully realistic and systematic effective field theory model of a 3-brane universe is constructed. It consists of a six-dimensional gravitating spacetime, containing several, approximately parallel (3+1)-dimensional defects, or ``3-branes.'' The standard model particles are confined to live on one of the 3-branes while different four-dimensional field theories may inhabit the others, in literally a case of ``parallel universes.'' The effective field theory is valid up to the six-dimensional Planck scale, where it must be replaced by a more fundamental theory of gravity and 3-brane structure. Each 3-brane induces a conical geometry in the two dimensions transverse to it. Collectively, the curvature induced by the 3-branes can compactify the extra dimensions into a space of spherical topology. It is possible to take the six-dimensional Planck scale to be not much larger than the weak scale, and the compact space not much smaller than a millimeter, thereby realizing the recent proposal by Arkani-Hamed, Dimopoulos and Dvali for eliminating the gauge hierearchy problem. In this case, an extra force is required to stabilize the compact space against collapse. This is provided by a six-dimensional (compact) U(1) gauge field with a magnetic flux quantum trapped in the compact space. The nature of the cosmological constant problem in this scenario is discussed.

Global effects due to cosmic defects in Kaluza-Klein theory

Abstract: Using Kaluza-Klein theory we study the quantum mechanics of a scalar particle in the background of a magnetic cosmic string and in the background of a chiral cosmic string. We show that the wave functions, the phase shifts, and scattering amplitudes associated with the particle depend on the global features of those spacetimes. These dependences represent gravitational analogues of the well-known Aharonov-Bohm effect. In addition, we discuss the Landau levels in the presence of a cosmic string in the framework of Kaluza-Klein theory.

Branes for Higgs phases and exact conformal field theories

Abstract: We consider multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang-Mills theories with ZN symmetric vacua. In certain energy regimes, we find a description in terms of a generalized wormhole solution that corresponds to the SL(2,)/U(1) × SU(2)/U(1) exact conformal field theory. We show that U-dualities map these backgrounds to purely gravitational ones and comment on the relation to the black holes arising from intersecting D1- and D5-branes. We also discuss supersymmetric properties of the various solutions and the relation to 2-dim solitons, on flat space, of the reduced axion--dilaton gravity equations. Finally, we address the problem of understanding other supergravity solutions from the multicenter ones. As prototype examples we use rotating D3-branes and NS5- and D5-branes associated to non-Abelian duals of 4-dim hyper-Kahler metrics with SO(3) isometry.

A global isostatic gravity model of the earth

Abstract: The long-wavelength features of the external gravity field of the Earth contain the gravitational signal from deep-seated lateral mass and density inhomogeneities sustained by dynamic Earth mantle processes. To interpret the observed gravity field with respect to mantle dynamics and structures, it is essential first to remove the lithosphere-induced anomalous gravitational potential, which is generated by the topographic surface load and its isostatically compensating masses. Based upon the most recent global compilation of crustal thickness and density data and the age distribution of cooling oceanic lithosphere, residual topography and gravity are calculated by subtracting the ‘known’ crustal and oceanic lithosphere compensating masses and gravitational effects from the surface fields. Empirical admittances between residual topography and gravity are then computed to estimate the effective depths of the remaining compensating masses, which are not explained by the initial data and model assumptions. This additional compensation is eventually placed by adjusting the density in the uppermost mantle between the Moho and, on average, 70 km depth, with a maximum of 118 km under Tibet. The lithospheric mass distribution is used in a subsequent forward computation to create a global model of the lithosphere-induced gravitational potential. The resulting isostatic model is considered to be valid for spatial wavelengths longer than 500 km. The isostatic lithosphere model field, expressed in terms of both gravity and geoid heights, is subtracted from the observed free-air gravity field to yield a global set of 1° × 1° isostatic gravity disturbances and from a satellite-derived long-wavelength geoid to yield the isostatic residual geoid. The comparison of residual (mantle) gravity, residual topography and isostatic corrected gravity allows us to identify the main characteristics of the underlying mantle; for example, dynamic support by mantle flow of the North Atlantic topographic high. Applying the isostatic correction, the overall pattern of the geoid becomes smoother and the most pronounced features, which are separated in the observed geoid, tend to get connected to larger structures. These results stress the importance of separation of the lithospheric gravitational impact for a correct interpretation of the external gravity field, even in its very long-wavelength constituents. Also, the isostatic corrected geoid spectrum reveals a stronger decrease in power from degree 3 to degree 4 and degree 5 to degree 6, which is in accordance with seismological models of deep-mantle structures.

Big bang nucleosynthesis and tensor-scalar gravity

Abstract: Big Bang Nucleosynthesis (BBN) is studied within the framework of a two-parameter family of tensor-scalar theories of gravitation, with nonlinear scalar-matter coupling function a(phi). We run a BBN code modified by tensor-scalar gravity, and impose that the theoretically predicted BBN yields of Deuterium, Helium and Lithium lie within some conservative observational ranges. It is found that large initial values of a(phi) (corresponding to initial cosmological expansion rates much larger than standard) are compatible with observed BBN yields. However, the BBN-inferred upper bound on the cosmological baryon density is insignificantly modified by considering tensor-scalar gravity. Taking into account the effect of e^+ e^- annihilation together with the subsequent effect of the matter-dominated era (which both tend to decouple phi from matter), we find that the present value of the scalar coupling, i.e. the present level of deviation from Einstein's theory, must be, for compatibility with BBN, smaller than alpha_0^2 0.5.

Metric preheating and limitations of linearized gravity

Abstract: Recently it has become clear that the resonant amplification of quantum field fluctuations at preheating must be accompanied by resonant amplification of scalar metric perturbations, since the two are united by Einstein's equations. Furthermore, this "metric preheating" enhances particle production and leads to gravitational rescattering effects even at linear order. In multi-field models with strong preheating (q \gg 1), metric perturbations are driven nonlinear, with the strongest amplification typically on super-Hubble scales (k \to 0). This amplification is causal, being due to the super- Hubble coherence of the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Einstein field equations, irrespective of the amount of fine-tuning of the initial conditions. This has serious implications at all scales - from the large-angle cosmic microwave background (CMB) anisotropies to primordial black holes. We investigate the (q,k) parameter space in a two-field model, and introduce the time to nonlinearity, t_{nl}, as the timescale for the breakdown of the linearized Einstein equations. Backreaction effects are expected to shut down the linear resonances, but cannot remove the existing amplification, which threatens the viability of strong preheating when confronted with the CMB. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. Finally we rank known classes of inflation from strongest (chaotic and strongly coupled hybrid inflation) to weakest (hidden sector, warm inflation) in terms of the distortion of the primordial spectrum due to these resonances in preheating.

The imprint of the equation of state on the axial w‐modes of oscillating neutron stars

Abstract: We discuss the dependence of the pulsation frequencies of the axial quasi-normal modes of a non-rotating neutron star upon the equation of state describing the star interior. The continued fraction method has been used to compute the complex frequencies for a set of equations of state based on different physical assumptions and spanning a wide range of stiffness. The numerical results show that axial gravitational waves carry relevant information on both the structure of neutron star matter and the nature of the hadronic interactions.