Gravitation and Astrophysics

Preface.

CONTENTS.

No abstract received.

In string theories, extra dimensions must be compactified. The possibility that gravity can have large radii of compactification leads to a violation of the inverse square law at submillimeter distances. We are preparing a null test of Newton's law with a resolution of one part in 10³ at 100 μm, which will probe the extra dimensions down to 10 μm. The experiment will be cooled to 2 K. To minimize Newtonian errors, a near null source in the form of a circular disk of large diameter-to-thickness ratio is employed. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a distance of 150 mm. The signal is detected by a superconducting differential accelerometer. We discuss the design and principle of this experiment and report the progress.

No abstract received.

This is a study of the behavior of wave equations in conformally compactified spacetimes suited to the use of computational boundaries beyond Scri+. There light cones may be adjusted for computational convenience and/or Scri+ may be converted to a spacelike hypersurface just outside a de Sitter horizon. Our preliminary numerical implementation excises the physically unnecessary universe somewhat beyond this outer horizon. As an entry level example we study a formulation of the Maxwell equations and causal relations for an outer boundary in that example. We find that an initial central pulse propagates to and through Scri+ in an (hyperboloidal) coordinate time comparable to the pulse width, and that the the numerical evolution remains stable for several times that long. This is a proposal for outer boundary conditions and wave extraction in numerical relativity for which further tests and development would be needed prior to an implementation in full GR.

We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical black hole evolution calculations. We use excision to evolve rapid-rotating Kerr-Schild black holes, and obtain accurate and stable simulations for specific angular momenta J/M of up to about 0.9M.

Discovery of present acceleration of the Universe, dark matter and dark energy problems are great challenges to modern physics, which may bring to a new revolution. Integrable multidimensional models of gravitation and cosmology make up one of the proper approaches to study basic issues and, in particular, strong field objects, the Early and present Universe and black hole physics ^1,2. Problems of the absolute G measurements and its possible time and range variations, which are reflections of the unification problem are discussed. A need for further measurements of G and its possible variations (also in space) is pointed out.

We revise the stability of the tracking solutions and briefly review the potentials of quintessence models. We discuss the evolution of linear perturbations for V(ϕ) = V₀ exp(λϕ²/2) potential in which the scalar field is non-minimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. We find that the phenomenology of this model is consistent with current observations up to the coupling power n_c ≤ 0.01 while adopting the current parameters measured by WMAP, , , , and h = 0.70. Upcoming cosmic microwave background observations continuing to focus on resolving the higher peaks may put strong constraints on the strength of the coupling.

In 1955, Lee and Yang discussed a new massless gauge field based on the established conservation of baryon number. They predicted the existence of a very weak repulsive force between baryons. Such a repulsive long-range force may be the physical origin of the dark-energy-induced acceleration of the expansion of the universe. The accelerated Wu transformation of spacetime based on limiting Lorentz and Poincaré invariance is employed to investigate the Wu-Doppler effects in which the source and observer have linearly accelerated motion. The results are applied to discuss experimental detections of the accelerated expansion of the universe.

It is the common consensus that the expansion of a universe always slows down if the gravity provided by the energy sources therein is attractive. To examine this point we find counter-examples for a spherically symmetric dust fluid described by the Lemaitre-Tolman-Bondi solution. As suggested by these counter-intuitive examples, the effects of inhomogeneities on the evolution of the space-time geometry (such as the cosmic evolution) should be restudied, and the intuition about general relativity is yet to be built.

The inflationary Big Bang model based on general relativity, inflation and cosmological principle is consistent with the current observational data from WMAP. In this talk I review some issues in the inflationary Big Bang model and discuss hot thermal inflation in detail.

We study the accelerating cosmological model with a static traversable wormhole to see the relation of wormhole to the dark energy. In this model, the phantom energy is considered as the engine of the acceleration of the universe. It is shown that the time to the 'Big Rip', that is derived by using the phantom energy, will be delayed for a sufficient wormhole distribution.

We do not know the basic ingredient of the universe. A model is proposed in which dark energy is identified as Bose-Einstein condensation of some boson field. A global cosmic acceleration cause by such condensation and the rapid local collapses into black holes of the condensation are examined. We propose a novel mechanism of inflation due to the steady flow of condensation, and the early formation of highly non-linear objects.

Gravitational Lensing is an important tool to understand the "missing mass" problem, especially for Modified Gravity. Recently, Bekenstein proposed a relativistic gravitation theory for Modified Newtonian Dynamics (MOND) paradigm which resolves the "missing mass" problem well on abnormal dynamical behaviors in extragalactic region. Our work follow Bekenstein's approach to investigating gravitational lensing to get theoretical prediction.

On geometrical grounds, the cosmological constant problem turns out to be an artifact due to the unfounded link of this fundamental constant to vacuum energy density of quantum fluctuations.

We determined the central black hole mass (M) for 25 γ-ray-loud blazars using their available variability timescales. In this method, the absorption effect depends on the γ-ray energy, emission size and property of the accretion disk. Using the intrinsic γ-ray luminosity as a fraction λ of the Eddington luminosity, and the optical depth equal to unity, we can determine the upper limit of the central black hole masses. We found that the black hole masses range between 10⁷ M_⊙ and 10⁹ M_⊙ when λ = 0.1 and 1.0 are adopted. For the black hole mass there is no clear difference between BLs and FSRQs, which suggests that the central black hole masses do not play an important role in the evolutionary sequence of blazars or there is no evolution between BLs and FSRQs.

The extraction of gravitational potential energy from matter which accretes into the deep potential well of black holes is believed to be the central engine of several important energetic sources in the Universe, such as active galactic nucleus (AGNs), gamma ray bursts (GRBs), X-ray binaries (XRBs), and so on. In this talk, I give a brief review of our recent works on black hole astrophysics. These works include: the possible observational properties of the afterglow of ultra-luminous quasars; the observed profile of an emission line from the conical jets around rotating a black hole; the temporal evolution of the hyperaccretion flow under beta equilibrium; and the relationship between the lack of type I x-ray bursts in XRBs and the evidence for black hole event horizons.

In this paper, we review the problem of the anomalous acceleration of Pioneer 10 and 11 in the region of the deep space (> 10AU), which is un-modelled sunward constant acceleration (8.74 ± 1.33) × 10^-8cm/s². The anomalous acceleration has been discovered for long time ago (1992) by Anderson et al., but recently it is confirmed further more after excluding almost all of known conventional physical errors. The Pioneer anomaly is so called the third dark cloud over the general relativity besides the dark matter and the dark energy. We also briefly introduce several published explanation on the Pioneer anomaly by means of conventional physics or new physics, but none of them is fully successful or commonly acceptable in our point view. A new plan to launch a mission to explore the Pioneer anomaly is mentioned in the paper. In the second part, we initiate the possible influence from the anomalous acceleration on the orbit motion of eight planets as a perturbation (pericenter-shift and radiu-shift) is calculated by us. To compare with the present observational precision, such kind of influence definitely does not exist for the bounded orbit motion of eight planets. Therefore we believe that, if the weak equivalence principle is correct everywhere, it is impossible to explain the Pioneer anomaly by means of any revising gravitational theory based on the general relativity.

In this paper we deduce a quite general formula which allows the relation of clock rates at two different space time points to be discussed. In the case of a perturbed Robertson-Walker metric, our analysis leads to an equation which includes the Hubble redshift, the Doppler effect, the gravitational redshift and the Rees-Sciama effects. In the case of the solar system, when the 2PN metric is substituted into the general formula, the comparison of the clock rates on both the earth and a space station could be made. It might be useful for the discussion on the precise measurements on future ACES and ASTROD.

Sub-millisecond pulsars should be triaxial (Jacobi ellipsoids), which may not spin down to super-millisecond periods via gravitation wave radiation during their lifetimes if they are extremely low mass bare strange quark stars. It is addressed that the spindown of sub-millisecond pulsars would be torqued dominantly by gravitational wave radiation (with braking index n ≃ 5). The radio luminosity of sub-millisecond pulsars could be high enough to be detected in advanced radio telescopes. Sub-millisecond pulsars, if detected, should be very likely quark stars with low masses and/or small equatorial ellipticities.

If gravitons are super-strong interacting particles and the low-temperature graviton background exists, the basic cosmological conjecture about the Dopplerian nature of redshifts may be false. In this case, a full magnitude of cosmological redshift would be caused by interactions of photons with gravitons. Non-forehead collisions with gravitons will lead to a very specific additional relaxation of any photonic flux. It gives a possibility of another interpretation of supernovae 1a data - without any kinematics. A quantum mechanism of classical gravity based on an existence of this sea of gravitons is described for the Newtonian limit. This mechanism needs graviton pairing and "an atomic structure" of matter for working it. If the considered quantum mechanism of classical gravity is realized in the nature, then an existence of black holes contradicts to Einstein's equivalence principle. In this approach the two fundamental constants – Hubble's and Newton's ones - should be connected between themselves. Every massive body would be decelerated due to collisions with gravitons that may be connected with the Pioneer 10 anomaly.

We discuss the random motion of an electron driven by quantum electromagnetic fluctuations at finite temperature in the Minkowski spacetime and calculate the mean squared fluctuations in the velocity of the electron. We find that at very late times, this random motion leads to a kinetic energy, e²/(6mβ²), for the electron, which may be interpreted as a shift in its rest mass, or mass renormalization. However, our result differs from that of other earlier works on temperature-dependent quantum-electrodynamic corrections to the inertial mass. It is argued that our calculations are gauge invariant while the gauge invariance of other earlier works remains unclear.

This report is an extension of the talk given at ICGA7. We present a brief review on quantum gravity phenomenology at first, focusing on the fate of Lorentz symmetry at Planck scale. Then we investigate its possible impacts on the study of black holes physics. We argue that modified dispersion relations may require a modification of Bekenstein entropy bound, leading to a correction to the Bekenstein-Hawking entropy formula for black holes. In particular one specific modified dispersion relation is proposed in the context of doubly special relativity, which changes the picture of Hawking radiation and can prevent black holes from total evaporation.

We analyze the interaction of a uniformly accelerated detector with a quantum field in (3+1)D spacetime and derive the two-point correlation functions of the detector and of the field separately with full account of their interplay. We find that there does exist a positive radiated flux of quantum nature emitted by the detector in steady state, with a hint of certain features of the Unruh effect. We further verify that only some part of the radiation is conserved with the total energy of the dressed detector. Since this part of the radiation ceases in steady state, the hint of the Unruh effect in late-time radiated flux is actually not directly from the energy flux that the detector experiences in Unruh effect.

The operational meaning of quantum fluctuations of spacetime geometry will be discussed. Three potential signatures of these fluctuations will be considered: luminosity fluctuations of a distant source, angular blurring of images, and broadening of spectral lines. To leading order, luminosity fluctuations arise only from passive geometry fluctuations, those driven by quantum fluctuations of the stress tensor. This effect can be described by a Langevin version of the Raychaudhuri equation. Angular blurring and line broadening can arise both from passive fluctuations and from the active fluctuations of the quantized gravitational field, and can be given a unified geometrical description using the Riemann tensor correlation function.

Pair production itself prevents the development of dyadospheres, hypothetical macroscopic regions where the electric field exceeds the critical Schwinger value. Pair production is a self-regulating process that would discharge a growing electric field, in the example of a hypothetical collapsing charged stellar core, before it reached 6% of the minimum dyadosphere value, keeping the pair production rate more than 26 orders of magnitude below the dyadosphere value.

No abstract received.

Using quadratic spinor techniques we demonstrate that the Immirzi parameter can be expressed as ratio between scalar and pseudo-scalar contributions in the theory and can be interpreted as a measure of how Einstein gravity differs from a generally constructed covariant theory for gravity. This interpretation is independent of how gravity is quantized. One of the important advantage of deriving the Immirzi parameter using the quadratic spinor techniques is to allow the introduction of renormalization scale associated with the Immirzi parameter through the expectation value of the spinor field upon quantization.

We discuss the phenomenon of quantum entanglement between relatively accelerating observers, illustrating that it is an observer-dependent concept due to its degradation from the Rindler vacuum.

We give a progress report of our research on spacetime fluctuations induced by quantum fields in an evaporating black hole and a black hole in quasi-equilibrium with its Hawking radiation. We note the main issues involved in these two classes of problems and outline the key steps for a systematic quantitative investigation. This report contains unpublished new ideas for further studies.

Primordial black holes have important observational implications through Hawking evaporation and gravitational radiation as well as being a candidate for cold dark matter. Those black holes are assumed to have formed in the early universe typically with the mass scale contained within the Hubble horizon at the formation epoch and subsequently accreted mass surrounding them. Numerical relativity simulation shows that primordial black holes of different masses do not accrete much, which contrasts with a simplistic Newtonian argument. We see that primordial black holes larger than the 'super-horizon' primordial black holes have decreasing energy and worm-hole like struture, suggesting the formation through quamtum processes.

In de Sitter space, de Sitter invariant special relativity can be established more or less parallel to the Einstein special relativity, based on the principle of special relativity and the postulate of two-universal constants. There are two kinds of simultaneity. One is the Beltrami-time simultaneity. By using the simultaneity, a new kind of inertial motion and a series of classical observables can be defined. In addition, the temperature of the horizon of de Sitter space for a set of inertial observers should be zero! Therefore, there is no need to explain the statistical origin of the entropy for the horizon of de Sitter space. Another is the proper-time simultaneity. With the proper-time simultaneity, the metric takes the Robertson-Walker-like form, which shows that the space has positive spatial curvature of order Λ. This has already been shown by the CMB power spectrum from WMAP and should be further confirmed in future. The existence of the two kinds of simultaneity also makes possible to explain the cosmic background or origin of inertial motion. Further, in de Sitter invariant special relativity, dynamics for a particle, including the pseudo-Hamiltonian mechanics, can be established. The non-relativistic limit of de Sitter invariant special relativity gives rise to the Newton-Hooke mechanics. The possibility of a test of de Sitter invariant special relativity is also studied tentatively. Finally, a kind of the doubly special relativity may be viewed as the de Sitter invariant special relativity in energy-momentum space.

Scalar field contribution to entropy is studied in arbitrary D-dimensional one parameter rotating spacetime by semiclassical method. By introducing the zenithal angle dependent cutoff parameter, the generalized area law is derived. The non-rotating limit can be taken smoothly and it yields known results. The derived area law is applied to the Kerr-Newman black hole in (3+1) dimension. This work is the collaboration with K. Ishi-moto, K.K. Nandi and K. Shigemoto of the paper ¹.

The super-Hamiltonian of 4-dimensional gravity as simplified by Ashtekar through the use of gauge potential and densitized triad variables can furthermore be succinctly expressed as a Poisson bracket between the volume element and other fundamental gauge-invariant elements of 3-geometry. This observation naturally suggests a reformulation of non-perturbative quantum gravity wherein the Wheeler-DeWitt Equation is identical to the requirement of the vanishing of the corresponding commutator. Moreover, this reformulation singles out spin network states as the preeminent basis for expansion of all physical states.

Non-singular space-times are given which model the formation of a Bardeen black hole from an initial vacuum region and its subsequent evaporation to a vacuum region. The black hole consists of a compact space-time region of trapped surfaces, with inner and outer boundaries which join circularly as a single smooth trapping horizon.

The final fate of Gregory-Laflamme instability is one of the most interesting problems in higher-dimensional black hole physics. In this article, non-uniform black strings with a gauge charge are constructed by static perturbations. Then, their thermodynamical stability is analyzed. It is found that in sufficiently non-extremal regions, the non-uniform black strings can be thermodynamically favored over the uniform ones in a large range of spacetime dimensions, which is realized only for higher dimensions (> 13) in vacuum spacetime.

We obtain a general spherically symmetric solution of a null dust fluid in n(≥ 4)-dimensions in Gauss-Bonnet gravity. This solution is a generalization of the n-dimensional Vaidya-(anti)de Sitter solution in general relativity. For n = 4, the Gauss-Bonnet term in the action does not contribute to the field equations, so that the solution coincides with the Vaidya-(anti)de Sitter solution. Using the solution for n ≥ 5 with a specific form of the mass function, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed and its properties are quite different between n = 5 and n ≥ 6. In the n ≥ 6 case, a massless ingoing null naked singularity is formed, while in the n = 5 case, a massive timelike naked singularity is formed, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than that in the general relativistic case. These naked singularities can be globally naked when the null dust fluid is turned off after a finite time and the field settles into the empty asymptotically flat spacetime. This paper is based on¹.

A gyraton is an object moving with the speed of light and having finite energy and internal angular momentum (spin). We study gyraton solutions of the Einstein-Maxwell gravity and in supergravity. We demonstrate that in the both cases the solutions in 4 and higher dimensions reduce to linear problems in a Euclidean space.

We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). Using the hyperspherical coordinate system for a flat base space, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we present general solutions, which include the BMPV black hole and the Brinkmann wave solution. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field , which is a rotational part of gravity, is self-dual. We also construct a supersymmetric rotating black hole in a compactified 4-dimensional spacetime by superposing an infinite number of BMPV black holes.

We study global properties for wave maps on black holes.

By studying the canonical expression of quasilocal energy-flux that follows from the Einstein's equations, I find geometric conditions for purely in- or out-going gravitational radiation of the most general type at a finite distance. These conditions are the vanishing of the transverse traceless parts of the second fundamental forms of a 2-surface with respect to the in- or out-going null vector fields normal to the surface. I also discuss the quasilocal momentum conservation equation, which has a remarkably similar structure with the Navier-Stokes equation for a viscous fluid. The deviation from the affinity of the parameter of the in-going null geodesies turns out to play the role of the coefficient of viscosity, whereas the scalar curvature of 2-surface is like a local pressure. Thus, Einstein's field equations, which consist of the Hamilton's equations of motion and a set of quasilocal conservation equations, describe a dissipative system of the Einstein's gravitation.

Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only on the world-line. We consider point particle interacting with scalar, vector (electromagnetic) and linearized gravitational fields in the (generally non-vacuum) curved space-time. To properly renormalize the self-action in the gravitational case, we use a manifestly reparameterization-invariant formulation of the theory. Scalar and vector divergences are shown to cancel for a certain ratio of the corresponding charges. We also report on a modest progress in extending the results for the gravitational radiation reaction to the case of non-vacuum background.

We have studied the famous classical pseudotensors in the small region limit, both inside matter and in vacuum. A recent work [Deser et al. 1999 CQG 16, 2815] had found one combination of the Einstein and Landau-Lifshitz expressions which yields the Bel-Robinson tensor in vacuum. Using similar methods we found another independent combination of the Bergmann-Thomson, Papapetrou and Weinberg pseudotensors with the same desired property. Moreover we have constructed an infinite number of additional new holonomic pseudotensors satisfying this important positive energy requirement, all seem quite artificial. On the other hand we found that Møller's 1961 tetrad-teleparallel energy-momentum expression naturally has this Bel-Robinson property.

We review the recently developed program for constructing and studying solutions of the Einstein constraint equations using gluing techniques. We discuss what we believe are sharp conditions sufficient for a pair of solutions to admit gluing via a connected sum or "wormhole", and describe how one carries out the gluing. We also discuss a number of useful applications.

We propose a reformulation of general relativity by making the Abelian decomposition of Einstein's theory. Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the Einstein's gravitational connection into the restricted part made of the maximal Abelian subgroup of Lorentz group and the valence part which transforms covariantly under Lorentz group. With the decomposition we reconstruct Einstein's theory as a restricted theory of gravitation which has the valence part as the gravitational source.

The Hamiltonian includes a boundary term which determines the quasi-local values and the boundary conditions. Using our covariant Hamiltonian formalism we found four particular quasi-local energy-momentum boundary term expressions. Here we show how a fundamental Hamiltonian identity naturally leads to the associated quasi-local energy flux expressions. For electromagnetism one of the four is distinguished by gauge invariance; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two choices correspond to quasi-local expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux. Again there is a distinguished expression: the one which is covariant.

The Hamiltonian for a gravitating region necessarily includes a boundary term. Its role is to determine the quasi-local values and, via the vanishing of the boundary term in the variation of the Hamiltonian (required for a well defined Hamiltonian), the boundary conditions. With this boundary variation principle, the Hamiltonian formalism tames the ambiguities inherent in the traditional approaches to the (quasi-)localization of energy-momentum. Using our covariant Hamiltonian formalism, we identified special boundary terms associated with particular physical boundary conditions. In the radiating regime the Hamiltonian fails to be "well defined". This led to new energy flux expressions. We here report on new results for homogeneous cosmologies, the small region limit, and positivity. Although there are many possibilities for the boundary term (reflecting the many choices for the boundary conditions and reference), we found that one expression is distinguished.

A smooth, three-dimensional submanifold of spacetime is a dynamical untrapped hypersurface if it can be foliated by a family of closed 2-manifolds S such that each foliation is an untrapped (mean convex) surface. If further on each leaf S, the dual expansion vector is tangent to the dynamical untrapped hypersurface, then it is called a stationary untrapped hypersurface. Note that for an untrapped surface S, the dual expansion vector is unique, always timelike and it is the direction for zero expansion. Thus for stationary untrapped hypersurfaces, the dual expansion vector plays the role which the stationary Killing vector plays for stationary black holes. We show that Hamiltonian for the spatial hypersurface associated with the timelike vector extended by the dual expansion vector for each leaf is well-defined for stationary untrapped hypersurface, and thus provides a definition of total energy-momentum for the region with the boundary S. For dynamical untrapped hypersurface, there does not exist a Hamiltonian in general, but a gravitational radiation energy flux can be obtained.

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