Search

Spin foam models (SFMs) are covariant formulations of loop quantum gravity (LQG) in four dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying the Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity can arise as a low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter $\ensuremath{\delta}$ becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.

Lorentz violations in gravitational waves are investigated. Plane-wave solutions for arbitrary gauge-invariant violations in linearized gravity are constructed. Signatures of Lorentz violation include dispersion, birefringence, and anisotropies. Modifications to waves from coalescing compact binaries and to strain signals in gravitational-wave detectors are derived., Comment: 14 pages

We discuss the quantization of linearized gravity in the background de Sitter spacetime using a gauge-invariant formalism to write the perturbed gravitational field in the static patch. This field is quantized after fixing the gauge completely. The response rate of this field to monochromatic multipole sources is then computed in the thermal equilibrium state with the well known Gibbons-Hawking temperature. We compare this response rate with the one obtained in the Bunch-Davies-like vacuum state defined in the Poincar\'e patch. These response rates are found to be the same as expected. This agreement serves as a verification of the infrared finite graviton two-point function in the static patch of de Sitter spacetime found previously., Comment: 10 pages, no figures. Accepted for publication in Physical Review D

Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms that reside in the metric formulation of general relativity, in the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black hole entropy from the free energy due to the spacetime boundary. These results indicate that the vierbein formulation of gravity generally exhibits a well-posed action principle and readily admits the path-integral approach to quantization.

We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable properties: i) it has a well-defined Einstein gravity limit ii) it admits `Schwarzschild-like' solutions characterized by a single metric function iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein's gravity iv) Lovelock and quasi-topological gravities, as well as the recently developed Einsteinian cubic gravity [ArXiv:1607.06463] in four dimensions, are recovered as special cases. We perform a brief analysis of asymptotically flat black holes in this theory and study their thermodynamics., Comment: 19 pages, 1 figure

We analyze the gravitational radiation emitted from a particle in circular motion around a Schwarzschild black hole using the framework of quantum field theory in curved spacetime at tree level. The gravitational perturbations are written in a gauge-invariant formalism for spherically symmetric spacetimes. We discuss the results, comparing them to the radiation emitted by a particle when it is assumed to be orbiting a massive object due to a Newtonian force in flat spacetime., Comment: 13 pages, REVTeX, 10 figures

An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small bending-angle-approximation for a lens system where the source, lens and observer are co-aligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to non-existent null trajectories. The linear coefficient $\gamma$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by General Relativity for small $\gamma$., Comment: 22 pages, 8 figures

We study the spherically symmetric gravitational collapse of massless scalar matter field in asymptotic flat spacetime in $f(R)$ gravity. In the Einstein frame of $f(R)$ gravity, an additional scalar field arises due to the conformal transformation. We find that besides the usual competition between gravitational energy and kinetic energy in the process of gravitational collapse, the new scalar field brought by the conformal transformation adds one more competing force in the dynamical system. The dynamical competition can be controlled by tuning the amplitudes of the initial perturbations of the new scalar field and the matter field. To understand the physical reasons behind these phenomena, we analyze the gravitational potential behavior and calculate the Ricci scalar at center with the change of initial amplitudes of perturbations. We find rich physics on the formation of black holes through gravitational collapse in $f(R)$ gravity., 18pages, 5 figures, Accepted by PRD

We consider the $f(R,T)$ modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor of the matter, in order to investigate the dark-matter effects on the galaxy scale. We obtain the metric components for a spherically symmetric and static spacetime in the vicinity of general relativity solutions. However, we concentrate on a specific model of the theory where the matter is minimally coupled to the geometry, and derive the metric components in the galactic halo. Then, we fix the components by the rotational velocities of the galaxies for the model, and show that the mass corresponding to the interaction term (which appears in the Einstein modified field equation) leads to a flat rotation curve in the halo of galaxies. In addition, for the proposed model, the light-deflection angle has been derived and drawn using some observed data.

We propose a model of gravity in which a General Relativity metric tensor and an effective metric generated from a single scalar formulated in geometric scalar gravity are mixed. We show that the model yields the exact Schwarzschild solution, along with accelerating behavior of scale factors in cosmological solutions.

We examine gravitational wave memory in the case where sources and detector are in an expanding cosmology. For simplicity, we treat the case where the cosmology is de Sitter spacetime, and discuss the possibility of generalizing our results to the case of a more realistic cosmology. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime, but with the magnitude of the effect multiplied by a redshift factor.

The Ernst formulation of the Einstein equations is generalized to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, nonlinear differential equation for a complex-valued scalar function. As a worked example, we apply the generalized Ernst equations to derive a $f(R)$ generalization of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in $f(R)$ gravity in the context of solitonlike solutions that display shock-wave behavior across the causal boundary.

We investigate theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein's equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein's equation emerges as a local equation of state from constraints on the area of a dynamical lightsheet in a fixed spacetime background. Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. This investigation points the way forward in understanding the connections between gravity and entanglement., Comment: 25 pages, 4 figures

Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum gravity theory. The gravifield sided on both locally flat noncoordinate spacetime and globally flat Minkowski spacetime is an essential ingredient for gauging global spin and scaling symmetries. The locally flat gravifield spacetime spanned by the gravifield is associated with a noncommutative geometry characterized by a gauge-type field strength of the gravifield. A coordinate-independent and gauge-invariant action for the quantum gravity is built in the gravifield basis. In the coordinate basis, we derive equations of motion for all quantum fields including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for gravifield tensor is deduced in connection directly with the total energy-momentum tensor. When the spin and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we obtain exact solutions by solving equations of motion for the background fields in a unitary basis. The massless graviton and massive spinon result as physical quantum degrees of freedom. The resulting Lorentz-invariant and conformally flat background gravifield space-time is characterized by a cosmic vector with a nonzero cosmological mass scale. The conformal size of the Universe becomes singular at the cosmological horizon and turns out to be inflationary. A mechanism for quantum inflation is demonstrated to generate the inflation of the early Universe. Two types of gravity equation result, one is as the extension to Einstein's equation of general relativity, and the other is a new one that characterizes spinon dynamics., 53 pages, PRD version

We study a spherical gravitational collapse of a small mass in higher derivative and ghost free theories of gravity. By boosting a solution of linearized equations for a static point mass in such theories we obtain in the Penrose limit the gravitational field of an ultra-relativistic particle. Taking a superposition of such solutions we construct a metric of a collapsing null shell in the linearized higher derivative and ghost free gravity. The latter allows one to find the gravitational field of a thick null shell. By analysing these solutions we demonstrate that in a wide class of the higher dimensional theories of gravity as well as for the ghost free gravity there exists a mass gap for the mini black hole production. We also found conditions when the curvature invariants remain finite at $r=0$ for the collapse of the thick null shell., 4 pages

We study the Einstein gravity and dust system in three spacetime dimensions as an example of a non-perturbative quantum gravity model with local degrees of freedom. We derive the Hamiltonian theory in the dust time gauge and show that it has a rich class of exact solutions. These include the Ba\~nados-Teitelboim-Zanelli black hole, static solutions with naked singularities and travelling wave solutions with dynamical horizons. We give a complete quantization of the wave sector of the theory, including a definition of a self-adjoint spacetime metric operator. This operator is used to demonstrate the quantization of deficit angle and the fluctuation of dynamical horizons., Comment: 14 pages

We investigate the energy-momentum balance in the perforating collision of a point particle with an infinitely thin planar domain wall within the linearized gravity in arbitrary dimensions. Since the metric of the wall increases with distance, the wall and the particle are never free, and their energy-momentum balance involves not only the instantaneous kinetic momenta, but also the non-local contribution of gravitational stresses. However, careful analysis shows that the stresses can be unambiguously divided between the colliding objects leading to definition of the gravitationally dressed momenta. These take into account for gravity in the same way as the potential energy does in the non-relativistic theory, but our treatment is fully relativistic. Another unusual feature of our problem is the non-vanishing flux of the total energy-momentum tensor through the lateral surface of the world tube. In this case the zero divergence of the energy-momentum tensor does not imply conservation of the total momentum defined as the integral over the space-like section of the tube. But one can still define the conservation low infinitesimally, passing to time derivatives of the momenta. Using this definition we establish the momentum balance in terms of the dressed particle and wall momenta., Comment: 15 pages, Revtex4. Journal version

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in two specific cases. In the first we consider a particle of mass $m$ and scalar charge $q$ moving in a background spacetime that contains a background scalar field. In the second we consider a particle of mass $m$ and electric charge $e$ moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields. It is expressed as a sum of local terms involving tensors defined in the background spacetime and evaluated at the current position of the particle, as well as tail integrals that depend on the past history of the particle. Because such an expression is rarely a useful starting point for an explicit evaluation of the self-force, we also provide covariant expressions for the singular potentials, expressed as local expansions near the world line; these can be involved in the construction of effective extended sources for the regular potentials, or in the computation of regularization parameters when the self-force is computed as a sum over spherical-harmonic modes., 20 pages, no figures

We study the gravitational collapse of a generalized Vaidya spacetime in the context of the cosmic censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed nonspacelike geodesics can terminate at the singularity in the past. Thus our result generalizes earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalized Vaidya mass functions for which the collapse terminates with a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities and there can be no extension of spacetime through them.

Known as a symmetry of vacuum Maxwell equations, the electric-magnetic duality can be lifted actually to a symmetry of an action. The Lagrangian of this action is written in terms of two vector potentials, one electric and one magnetic, and while it is manifestly invariant under duality rotations, it is not manifestly Lorentz covariant. This duality symmetry exists also in linearized gravity in four dimensions, and can be lifted off shell too. In $d$ dimensions, the link between linearized gravity and its dual can also be seen from the point of view of a parental action. This is defined by a first order Lagrangian (with the help of some auxiliary variables) that delivers both Fierz-Pauli theory and its dual. In this work we use this formalism to implement the electric-magnetic duality in the nonrelativistic deviation of Fierz-Pauli theory arising from Ho\v{r}ava-Lifshitz gravity. Because this theory breaks diffeomorphism invariance, one finds that such implementation includes some peculiarities., Comment: v1: 23 pages, 4 figures, edited with LaTeXila 2.4.0 and wxMaxima 12.04.0 for the graphics (Maxima version: 5.27.0). arXiv admin note: text overlap with arXiv:1306.1092 by other authors; v2: 24 pages, 4 figures, references added, negligence (leading to poor version management and miscommunication) rectified; v3: typos and grammar corrected, minor changes to uniformize conventions

The gravitational field of a global monopole in the context of Brans-Dicke theory of gravity is investigated. The space-time and the scalar field generated by the monopole are obtained by solving the field equations in the weak field approximation. A comparison is made with the corresponding results predicted by General Relativity., 10 pages, LaTeX; replaced with revised version Wed, 24 Sep 1997

In this paper we present a new approach to this issue which, although based on many of the standard ideas, differs from other approaches in several substantial ways. In some sense our formulation lies between the conventional and non-conventional approaches [2]. The first issue we discuss is our view towards classical general relativity (GR). At the classical level, a clear distinction can be made between GR and other field theories. Only in GR does the geometry play a dynamical role. Though often noted, this distinction has been reemphasized in a recent series of papers by presenting GR as a theory of characteristic hypersurfaces [3–5] rather than as a theory of the metric field. From this point of view the spacetime metric and associated connection are derived concepts: the basic variables are families of 3-surfaces and a scalar function (a conformal factor) from which a metric can be derived. The surfaces are automatically the characteristic surfaces of the metric and the metric automatically satisfies the Einstein field equations. This reformulation of GR has been referred to as the Null Surface Formulation of GR or simply as the NSF. It appears that no other physically relevant field theory can be stated as such a theory of surfaces. Here, we study the quantization of the linearized version of this approach. From this quantization of the NSF, we appear to be led to new ideas and results on the form a quantum theory of gravity might take. The new view essentially says that the null surfaces become operators that obey commutation relations. Furthermore, since there is a prescription for locating points of spacetime using foliations by families of null surfaces, the spacetime points themselves become operators. Roughly speaking, our formalism is a union between the Ashtekar asymptotic quantization [6] of the gravitational field and the NSF. In our formalism, the Bondi free data at future null infinity I + play a very important role. They enter as a source in the NSF field equations. Thus, for each data set, the solution to our classical equations represents a regular radiative spacetime. On the other hand, the formalism developed by Ashtekar gives a kinematic quantization of the radiative degrees of freedom of the gravitational field at I + . By promoting the classical Bondi data to quantum

Lovelock gravity is a class of higher-derivative gravitational theories whose linearized equations of motion have no more than two time derivatives. Here, it is shown that any Lovelock theory can be effectively described as Einstein gravity coupled to a p-form gauge field. This extends the known example of an f(R) theory of gravity, which can be described as Einstein gravity coupled to a scalar field., 17 pages

We calculate the explicit equations of motion for non-spinning compact objects to 2.5 post-Newtonian order, or O(v/c)^5 beyond Newtonian gravity, in a general class of scalar-tensor theories of gravity. We use the formalism of the Direct Integration of the Relaxed Einstein Equations (DIRE), adapted to scalar-tensor theory, coupled with an approach pioneered by Eardley for incorporating the internal gravity of compact, self-gravitating bodies. For the conservative part of the motion, we obtain the two-body Lagrangian and conserved energy and momentum through second post-Newtonian order. We find the 1.5 post-Newtonian and 2.5 post-Newtonian contributions to gravitational radiation reaction, the former corresponding to the effects of dipole gravitational radiation, and verify that the resulting energy loss agrees with earlier calculations of the energy flux. For binary black holes we show that the motion through 2.5 post-Newtonian order is observationally identical to that predicted by general relativity. For mixed black-hole neutron-star binary systems, the motion is identical to that in general relativity through the first post-Newtonian order, but deviates from general relativity beginning at 1.5 post-Newtonian order, in part through the onset of dipole gravitational radiation. But through 2.5 post-Newtonian order, those deviations in the motion of a mixed system are governed by a single parameter dependent only upon the scalar-tensor coupling constant and the structure of the neutron star, and are formally the same for a general class of scalar-tensor theories as they are for pure Brans-Dicke theory., 32 pages, closely matches version published in Phys. Rev. D

We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The dynamical equivalence with a non-minimally coupled bi-scalar field gravitational theory is proved. The evolution of cosmological solutions is studied using dynamical systems techniques., 11 pages, 12 figures

We analyze the cosmological perturbations valid in a broad class of generalized gravity theories in a unified manner. A complete set of perturbation equations is derived in gauge-ready forms. We present general asymptotic solutions for several different choices of the gauge conditions in unified forms. As in the case of Einstein's gravity, the uniform-curvature gauge is particularly simple for treating the scalar-type perturbations in generalized gravity theories involving the scalar field and the scalar curvature. Remarkably, considering the growing mode in the uniform-curvature gauge, the same solutions derived in Einstein's gravity remain valid in a broad class of generalized gravity theories.

The study of factorization in linearized gravity is extended to the graviton scattering processes with an electron for massive vector boson production such as {ital ge}{r_arrow}{ital Z}{ital e} and {ital ge}{r_arrow}{ital W}{nu}{sub {ital e}}. It is shown tha t every transition amplitude is completely factorized due to gravitational gauge invariance and Lorentz invariance. Also the explicit values of vector boson polarizations are obtained. {copyright} {ital 1996 The American Physical Society.}

The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with $\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air., Comment: 8 pages, 1 figure. Revised version has core unchanged but paper rewritten and expanded to clarify the reasoning and to emphasize some points. One figure added

Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry, namely to be hyperbolic, time-orientable and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics---for the general tensorial spacetime geometries satisfying the above minimum requirements---is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus the search for modified gravitational dynamics is reduced to a clear mathematical task., 47 pages, no figures, minor updates

We present a class of generally covariant nonlocal gravity models which have a flat-space general relativistic (GR) limit and also possess a stable de Sitter (dS) or Anti-de Sitter (AdS) background with an arbitrary value of its cosmological constant. The nonlocal action of the theory is formulated in the Euclidean signature spacetime and is understood as an approximation to the quantum effective action (generating functional of one-particle irreducible diagrams) originating from fundamental quantum gravity theory. Using the known relation between the Schwinger-Keldysh technique for quantum expectation values and the Euclidean quantum field theory we derive from this action the {\em causal} effective equations of motion for mean value of the metric field in the physical Lorentzian-signature spacetime. Thus we show that the (A)dS background of the theory carries as free propagating modes massless gravitons having two polarizations identical to those of the Einstein theory with a cosmological term. The on-shell action of the theory is vanishing both for the flat-space and (A)dS backgrounds which play the role of stable vacua underlying respectively the ultraviolet and infrared phases of the theory. We also obtain linearized gravitational potentials of compact matter sources and show that in the infrared (A)dS phase their effective gravitational coupling $G_{\rm eff}$ can be essentially different from the Newton gravitational constant $G_N$ of the short-distance GR phase. When $G_{\rm eff}\gg G_N$ the (A)dS phase can be regarded as a strongly coupled infrared modification of Einstein theory not only describing the dark energy mechanism of cosmic acceleration but also simulating the dark matter phenomenon by enhanced gravitational attraction at long distances., Comment: 16 pages, RevTex, final version to appear in Phys. Rev. D

We analyze detector responses of gravitational wave detectors for gravitational waves with arbitrary polarizations predicted in the metric theories of gravity. We present the general formulas for the frequency responses valid in various interferometric arrangements including Michelson, Delay-Line and Fabry-Perot detectors. We analyze the angular and frequency behavior and the sensitivity patterns of the responses for each polarization mode., 18 pages, 10 figures

We solve for the retarded Green's function for linearized gravity in a background with a negative cosmological constant, anti--de Sitter space. In this background, it is possible for a signal to reach spatial infinity in a finite time. Therefore the form of the Green's function depends on a choice of boundary condition at spatial infinity. We take as our condition that a signal which reaches infinity should be lost, not reflected back. We calculate the Green's function associated with this condition, and show that it reproduces the correct classical solution for a point mass at the origin, the anti--de Sitter--Schwarzschild solution.

Pulsar timing experiments aimed at the detection of gravitational radiation have been performed for decades now. With the forthcoming construction of large arrays capable of tracking multiple millisecond pulsars, it is very likely we will be able to make the first detection of gravitational radiation in the nano-Hertz band, and test Einstein's theory of relativity by measuring the polarization components of the detected signals. Since a gravitational wave predicted by the most general relativistic metric theory of gravity accounts for {\it six} polarization modes (the usual two Einstein's tensor polarizations as well as two vector and two scalar wave components), we have estimated the single-antenna sensitivities to these six polarizations. We find pulsar timing experiments to be significantly more sensitive, over their entire observational frequency band ($\approx 10^{-9} - 10^{-6}$ Hz), to scalar-longitudinal and vector waves than to scalar-transverse and tensor waves. At $10^{-7}$ Hz and with pulsars at a distance of $1$ kpc, for instance, we estimate an average sensitivity to scalar-longitudinal waves that is more than two orders of magnitude better than the sensitivity to tensor waves. Our results imply that a direct detection of gravitational radiation by pulsar timing will result into a test of the theory of general relativity that is more stringent than that based on monitoring the decay of the orbital period of a binary system., 11 pages, 2 figures. Submitted to Phys. Rev. D

Noncommutative geometry may be a starting point to a quantum gravity. We study the influence of the spacetime noncommutative parameter on the strong field gravitational lensing in the noncommutative Schwarzschild black-hole spacetime and obtain the angular position and magnification of the relativistic images. Supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimate the numerical values of the coefficients and observables for strong gravitational lensing. Comparing to the Reissner-Norstr\"{om} black hole, we find that the influences of the spacetime noncommutative parameter is similar to those of the charge, just these influences are much smaller. This may offer a way to distinguish a noncommutative black hole from a Reissner-Norstr\"{om} black hole, and may probe the spacetime noncommutative constant $\vartheta$ \cite{foot} by the astronomical instruments in the future., Comment: 13 pages, 4 figures, 2 tables, accepted by Phys. Rev. D

Gravitational Compton scattering process with a massive fermion is studied in the context of the linearized gravity. Gravitational gauge invariance and graviton transversality cause the transition amplitude to be factorized into that of scalar QED Compton scattering and that of fermion QED Compton scattering with an overall kinematical factor. The factorization is shown explicitly and its physical implications are discussed., Comment: 11 pages, 1 figure(not included), Revtex 3.0, SNUTP 93-24

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable., 15 pages, FTG-114-USU, Plain TeX

The direct observation of gravitational waves will provide a unique tool for probing the dynamical properties of highly compact astrophysical objects, mapping ultra-relativistic regions of space-time, and testing Einstein's general theory of relativity. LISA (Laser Interferometer Space Antenna), a joint NASA-ESA mission to be launched in the next decade, will perform these scientific tasks by detecting and studying low-frequency cosmic gravitational waves through their influence on the phases of six modulated laser beams exchanged between three remote spacecraft. By directly measuring the polarization components of the waves LISA will detect, we will be able to test Einstein's theory of relativity with good sensitivity. Since a gravitational wave signal predicted by the most general relativistic metric theory of gravity accounts for {\it six} polarization modes (the usual two Einstein's tensor polarizations as well as two vector and two scalar wave components), we have derived the LISA Time-Delay Interferometric responses and estimated their sensitivities to vector- and scalar-type waves. We find that (i) at frequencies larger than roughly the inverse of the one-way light time ($\approx 6 \times 10^{-2} $ Hz.) LISA is more than ten times sensitive to scalar-longitudinal and vector signals than to tensor and scalar-transverse waves, and (ii) in the low part of its frequency band is equally sensitive to tensor and vector waves and somewhat less sensitive to scalar signals., Comment: Paper submitted to Physical Review D. It is 20 pages long and contains 14 figures

We write down exact solutions in the collective field theory of the c=1 matrix model and in dilaton-gravity coupled to a massless scalar. Using the known correspondence between these two theories at the null boundaries of spacetime, we make a connection between scalar fields in these two theories in the bulk of spacetime. In the process, we gain insight into how a theory containing gravity can be equivalent to one without gravity. We analyze a simple time-dependent background as an example., Comment: 19 pages, 3 figures

We investigate possible modifications on the gravitational deflection of light. Two forms of deformation of the Schwarzschild spacetime are proposed. The first ansatz is a given Finslerian line element; it could be regarded as a weak quantum gravity effect on the Schwarzschild spacetime. Starting from this ansatz, we deduce the deflection angle of the light ray which passes a weak gravitational source. The second ansatz could be regarded as a quantum vacuum effect on the Schwarzschild spacetime. The deflection angle of the light ray which passes a weak gravitational source is deduced in this Riemannian spacetime. This vacuum effect may distinguish the mixed light rays in the absence of gravitational source by a ``spectroscope'' (the gravitational source). The solutions of the gravitational field equation in this Riemannian spacetime imply this issue.

In 1+3 (threading) formulation of general relativity spacetime behaves analogous to a medium with a specific index of refraction with respect to the light propagation. Accepting the reality of zero point energy, through the equivalence principle, we elevate this analogy to the case of virtual photon propagation in a quantum vacuum in a curved background spacetime. Employing this new idea one could examine the response of vacuum energy to the presence of a stationary gravitational field in its different quantum field theoretic manifestations such as Casimir effect and Lamb shift. The results are given explicitly for a Casimir apparatus in the weak field limit of a Kerr hole., 10 pages, RevTex, more typos corrected (combined with arXiv:1003.0614 published in PRD)

Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R) gravity, we consider extensions of teleparallel, or torsion scalar T, gravity to f(T) theories. The field equations are naturally second order, avoiding pathologies, and can give rise to cosmic acceleration with unique features., Comment: 7 pages, 1 figure; v2 new f(T) model without hidden cosmological constant

The loop-space representation based on Ashtekar's new variables has allowed for the first time the construction of quantum states of the gravitational field. However, all states known up to the present were associated with spacetime metrics that were everywhere degenerate. In this Letter we present a new exact solution of the constraint equations of quantum gravity that is the first quantum state of the gravitational field known to be associated with a not-everywhere-degenerate metric. The state is associated with the second coefficient of the Alexander-Conway polynomial of knot theory.

Alternative theories of gravity predict the presence of massive scalar, vector, and tensor gravitational wave modes in addition to the standard massless spin~2 graviton of general relativity. The deflection and frequency shift effects on light from distant sources propagating through a stochastic background of gravitational waves, containing such modes, differ from their counterparts in general relativity. Such effects are considered as a possible signature for alternative gravity in attempts to detect deviations from Einstein's gravity by astrophysical means., Comment: 9 pages, 1 figure

We investigate a class of theories involving a symmetric two-tensor field in Minkowski spacetime with a potential triggering spontaneous violation of Lorentz symmetry. The resulting massless Nambu-Goldstone modes are shown to obey the linearized Einstein equations in a fixed gauge. Imposing self-consistent coupling to the energy-momentum tensor constrains the potential for the Lorentz violation. The nonlinear theory generated from the self-consistent bootstrap is an alternative theory of gravity, containing kinetic and potential terms along with a matter coupling. At energies small compared to the Planck scale, the theory contains general relativity, with the Riemann-spacetime metric constructed as a combination of the two-tensor field and the Minkowski metric. At high energies, the structure of the theory is qualitatively different from general relativity. Observable effects can arise in suitable gravitational experiments., 51 pages

We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not metric, being canonically defined. The theory is obtained from general relativity (GR) in Plebanski formulation by adding to the action a certain potential. Importantly, the modification does not change the number of propagating degrees of freedom as compared to GR. We find that "small bodies" move along geodesics of a certain metric that is constructed with the help of a new potential function that appears in the matter sector. We then use the "small body" results to formulate a prescription for coupling the theory to general stress-energy tensor. In its final formulation the theory takes an entirely standard form, with matter propagating in a metric background and only the matter-gravity coupling and the gravitational dynamics being modified. This completes the construction of the theory and opens way to an analysis of its physical predictions., Comment: (v1) 23 pages (v2) 24 pages, references and a comment on Urbantke metric added

A nontrivial redundancy relation, due to the differential structure of the gravitational Bianchi identity as well as the symmetry of the Friedmann-Robertson-Walker metric, in the gravitational field equation is clarified. A generalized Friedmann-Robertson-Walker metric is introduced in order to properly define a one-dimensional reduced problem which offers an alternative approach to obtain the gravitational field equations on Friedmann-Robertson-Walker spaces.