Gravity In Spacetime Research Articles

The detection of quasinormal mode witha/M= 0.95 would prove a sphere 99% soaking in the ergoregion of the Kerr space-time

Recent numerical relativity simulations of mergers of binary black holes suggest that the maximum final value of $a/M$ is $\sim 0.95$ for the coalescence of two equal mass black holes with aligned spins of the same magnitude $a/M=0.994$ which is close to the upper limit $a/M=0.998$ of accretion spin-up shown by Thorne. Using the WKB method, we suggest that if quasinormal modes with $a/M \sim 0.95$ are detected by the second generation gravitational wave detectors, we could confirm the strong gravity space-time based on Einstein's general relativity up to $1.33M$ which is only $\sim 1.014$ times the event horizon radius and within the ergoregion. One more message about black hole geometry is expected here. If the quasinormal mode is different from that of general relativity, we need to find the true theory of gravity which deviates from general relativity only near the black hole horizon.

G超统一论—G引力规范理论

本文提出G超统一群及粒子，揭示时空的起源。其直积群表示为U(1) XSU(2) XSU(3) XU(4)，也可用单群U(20)表示。该文指出：随着宇宙温度的逐渐降低，宇宙第一次破缺，生成了U(4) XU(5)群，此时引力分离出来，用U(4) (G粒子) (引力时空)群表示。之后，引力破缺成轻子和夸克群，即U(2) XU(2)。轻子和夸克群相互作用生成了我们现在的三维反对称空间和一维全对称时间；宇宙第二次破缺时，强相互作用分离出来，第三次破缺，弱作用分离出来，剩余的一维U(1)群，形成了电磁相互作用，即SU(3) XSU(2) XU(1)。 This thesis puts forth G super-unified group and particle, and reveals the source for space and time. The direct product group is expressed as U(1) XSU(2) XSU(3) XU(4) which can also be expressed as single group U(20). This thesis points out that: with the gradual fall of temperature of the universe, the universe will break for the first time and generate U(4) XU(5) group to cause gravity separation expressed as U(4) (G particle) (gravity space-time) group. Afterwards, the gravity will break into lepton and quark group, i.e. U(2) XU(2). The interaction of lepton and quark group will generate the present three-dimensional antisymmetric space and one-dimensional full symmetric time. When the universe breaks for the second time, the strong interaction is separated. When it breaks for the third time, weak interaction is separated; the remaining one-dimensional U(1) group will form electromagnetic interaction, i.e. SU(3) XSU(2) XU(1).

Quantum transitions between classical histories

In a quantum theory of gravity spacetime behaves classically when quantum probabilities are high for histories of geometry and field that are correlated in time by the Einstein equation. Probabilities follow from the quantum state. This quantum perspective on classicality has important implications: (a) Classical histories are generally available only in limited patches of the configuration space on which the state lives. (b) In a given patch states generally predict relative probabilities for an ensemble of possible classical histories. (c) In between patches classical predictability breaks down and is replaced by quantum evolution connecting classical histories in different patches. (d) Classical predictability can break down on scales well below the Planck scale, and with no breakdown in the classical equations of motion. We support and illustrate (a)-(d) by calculating the quantum transition across the de Sitter like throat connecting asymptotically classical, inflating histories in the no-boundary quantum state. This supplies probabilities for how a classical history on one side transitions and branches into a range of classical histories on the opposite side. We also comment on the implications of (a)-(d) for the dynamics of black holes and eternal inflation.

Einstein relatively simple: our universe revealed in everyday language

Special Relativity: The Newton - Maxwell Conflict Einstein's Light and Relativity Postulates How Time Slows and Space Shrinks with Motion Simultaneity The Equivalence of Mass and Energy Per E=mc2 The Unification of Space and Time in the Spacetime Interval The Twins Paradox General Relativity: The Equivalence Principle Gravitational Time Dilation Ehrenfest's Paradox The Warping of Time and Space Time Travel Local and Global Gravity Spacetime Curvature The Einstein Equation Black Holes Gravitational Lensing Gravity Waves Frame Dragging Wormholes The Expansion of the Universe The Big Bang Cosmic Inflation Dark Matter Dark Energy The Future of the Universe.

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.

Approximate waveforms for extreme-mass-ratio inspirals in modified gravity spacetimes

Extreme mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole, are prime candidates for detection with space-borne milliHertz gravitational wave detectors, similar to the Laser Interferometer Space Antenna. The gravitational waves generated during such inspirals encode information about the background in which the small object is moving, providing a tracer of the spacetime geometry and a probe of strong-field physics. In this paper, we construct approximate, ``analytic-kludge'' waveforms for such inspirals with parametrized post-Einsteinian corrections that allow for generic, model-independent deformations of the supermassive black hole background away from the Kerr metric. These approximate waveforms include all of the qualitative features of true waveforms for generic inspirals, including orbital eccentricity and relativistic precession. The deformations of the Kerr metric are modeled using a recently proposed, modified gravity bumpy metric, which parametrically deforms the Kerr spacetime while ensuring that three approximate constants of the motion remain for geodesic orbits: a conserved energy, azimuthal angular momentum and Carter constant. The deformations represent modified gravity effects and have been analytically mapped to several modified gravity black hole solutions in four dimensions. In the analytic kludge waveforms, the conservative motion is modeled by a post-Newtonian expansion of the geodesic equations in the deformed spacetimes, which in turn induce modifications to the radiation-reaction force. These analytic-kludge waveforms serve as a first step toward complete and model-independent tests of general relativity with extreme mass-ratio inspirals.

6D conformal gravity

In the framework of an ordinary-derivative approach, conformal gravity in spacetime of dimension 6 is studied. The field content, in addition to conformal graviton field, includes two auxiliary rank-2 symmetric tensor fields, two Stueckelberg vector fields and one Stueckelberg scalar field. The gauge invariant Lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained. One of the rank-2 tensor fields and the scalar field have a canonical conformal dimension. With respect to these fields, the Lagrangian contains, in addition to other terms, a cubic potential. Gauging away the Stueckelberg fields and excluding the auxiliary fields via equations of motion, the higher derivative Lagrangian of 6D conformal gravity is obtained. The higher derivative Lagrangian involves quadratic and cubic curvature terms. This higher derivative Lagrangian coincides with the simplest Weyl invariant density discussed in the earlier literature. Generalization of de Donder gauge conditions to 6D conformal fields is also obtained.

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

Quantum singularities considered in the 3D BTZ spacetime by Pitelli and Letelier (Phys. Rev. D77: 124030, 2008) is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and non-linear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analysed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields; the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying Klein-Gordon equation but nonsingular for fermions obeying Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes do not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.

A quantum Goldman bracket in (2 + 1) quantum gravity**Dedicated to John Charap, in gratitude for his inspiration and vision.

In the context of quantum gravity for spacetimes of dimension (2 + 1), we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in (representing loops on the spatial manifold, i.e. the torus) and a quantum connection with noncommuting components, we review how holonomies and Wilson loops for two homotopic paths are related by phases in terms of the signed area between them. Paths rerouted at intersection points with other paths occur on the rhs of the Goldman bracket. To better understand their nature we introduce the concept of integer points inside the parallelogram spanned by two intersecting paths, and show that the rerouted paths must necessarily pass through these integer points.

The standard model physical degrees of freedom interpretation of the electromagnetic fine structure coupling [formula omitted

The present short note gives for the first time a derivation of the inverse electromagnetic fine structure constant from the elementary particles content of the standard model plus graviton and the Higgs. It is the first derivation ever to interpret α ¯ o = 137 as the familiar N f = (2)(48) = 96 Fermions and N B = (2)(15) = 30 Bosons of the standard model plus the eleven dimensions D = 11 of super gravity spacetime N f + N B + D = α ¯ o . The exact theoretical value 137.082039325 and the accurate experimental results are also given clear mathematical derivation showing that all of the 137 and not only the 96 + 30 = 126 may be interpreted as physical particles so that in a sense elementary particles create and span spacetime.

Geometrical (2+1)-Gravity and the Chern-Simons Formulation: Grafting, Dehn Twists, Wilson Loop Observables and the Cosmological Constant

We relate the geometrical and the Chern-Simons description of (2+1)-dimensional gravity for spacetimes of topology \({\mathbb{R}}\times S_g\) , where Sg is an oriented two-surface of genus g > 1, for Lorentzian signature and general cosmological constant and the Euclidean case with negative cosmological constant. We show how the variables parametrising the phase space in the Chern-Simons formalism are obtained from the geometrical description and how the geometrical construction of (2+1)-spacetimes via grafting along closed, simple geodesics gives rise to transformations on the phase space. We demonstrate that these transformations are generated via the Poisson bracket by one of the two canonical Wilson loop observables associated to the geodesic, while the other acts as the Hamiltonian for infinitesimal Dehn twists. For spacetimes with Lorentzian signature, we discuss the role of the cosmological constant as a deformation parameter in the geometrical and the Chern-Simons formulation of the theory. In particular, we show that the Lie algebras of the Chern-Simons gauge groups can be identified with the (2+1)-dimensional Lorentz algebra over a commutative ring, characterised by a formal parameter ΘΛ whose square is minus the cosmological constant. In this framework, the Wilson loop observables that generate grafting and Dehn twists are obtained as the real and the ΘΛ-component of a Wilson loop observable with values in the ring, and the grafting transformations can be viewed as infinitesimal Dehn twists with the parameter ΘΛ.

Solution generating in 5D Einstein-Maxwell-dilaton gravity and derivation of dipole black ring solutions

We consider 5D Einstein-Maxwell-dilaton (EMd) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors, one of which is hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EMd equations are completely integrable. We also develop a solution generating method for explicit construction of exact EMd solutions from known exact solutions of 5D vacuum Einstein equations with considered symmetries. We derive explicitly the rotating dipole black ring solutions as a particular application of the solution generating method.

Completely integrable sector in 5D Einstein-Maxwell gravity and derivation of the dipole black ring solutions

We consider 5D Einstein-Maxwell (EM) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors one of them being hypersurface orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EM equations are completely integrable by deriving a Lax-pair presentation. We also develop a solution generating method for explicit construction of exact EM solutions with considered symmetries. We also derive explicitly a new rotating six parametric 5D EM solution which includes the dipole black ring solution as a particular case.

Worldline approach to vector and antisymmetric tensor fields

The N=2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a one-dimensional torus of the N=2 spinning particle coupled to spacetime gravity. The action has a local N=2 worldline supersymmetry with a gauged U(1) symmetry that includes a Chern-Simons coupling. Its quantization on the torus produces the one-loop effective action for a single antisymmetric tensor. We use this worldline representation to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side results we obtain the correct trace anomaly of a spin 1 particle in four dimensions as well as exact duality relations between differential form gauge fields. This approach yields a drastic simplification over standard heat-kernel methods. It contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Worldline methods are generically simpler and more efficient in perturbative computations then standard QFT Feynman rules. This is particularly evident when the coupling to gravity is considered.

Don't panic! closed string tachyons in ALE spacetimes

We consider closed string tachyons localized at the fixed points of noncompact nonsupersymmetric orbifolds. We argue that tachyon condensation drives these orbifolds to flat space or supersymmetric ALE spaces. The decay proceeds via an expanding shell of dilaton gradients and curvature which interpolates between two regions of distinct angular geometry. The string coupling remains weak throughout. For small tachyon VEVs, evidence comes from quiver theories on D-branes probes, in which deformations by twisted couplings smoothly connect non-supersymmetric orbifolds to supersymmetric orbifolds of reduced order. For large tachyon VEVs, evidence comes from worldsheet RG flow and spacetime gravity. For $\IC^2/\IZ_n$, we exhibit infinite sequences of transitions producing SUSY ALE spaces via twisted closed string condensation from non-supersymmetric ALE spaces. In a $T$-dual description this provides a mechanism for creating NS5-branes via {\it closed} string tachyon condensation similar to the creation of D-branes via {\it open} string tachyon condensation. We also apply our results to recent duality conjectures involving fluxbranes and the type 0 string.

Conserved charges for gravity with locally anti-de sitter asymptotics

A new formula for the conserved charges in 3+1 gravity for spacetimes with local anti-de Sitter asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the Lambda = 0 limit.

Discrete-state moduli of string theory from the c = 1 matrix model

We propose a new formulation of the space-time interpretation of the c = 1 matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the Fermi vacuum on both sides of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree-level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black-hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent non-perturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.

QUANTUM THEORY OF SPACE-TIMES WITH ONE KILLING FIELD

We describe the canonical quantization of Einstein gravity for space-times with one killing vector field. We use the new canonical variables introduced by Ashtekar. Both the connection and loop space representations for the quantum theory are considered. We find that the physical state space has a characterization in terms of equivalence classes of Eulerian graphs.