On Gravitational Radiation Graviton Number Density: Application to a Nambu String

A formalism is developed to compute the number density of gravitons, of specified energies, produced by an arbitrary external energy-momentum tensor source at any temperature. The formalism is applied to a simple Nambu string without making the usual assumption of a long wavelength approximation (L.W.A.). This exact result is also compared to the L.W.A.     

Letter: Cosmic Rays and Large Extra Dimensions

We have proposed that the cosmic ray spectrum knee, the steepening of the cosmic ray spectrum at energy E 10^15.5 eV, is due to new physics, namely new interactions at TeV cm energies which produce particles undetected by the experimental apparatus. In this letter we examine specifically the possibility that this interaction is low scale gravity. We consider that the graviton propagates, besides the usual four dimensions, into an additional , compactified, large dimensions and we estimate the graviton production in pp collisions in the high energy approximation where graviton emission is factorized. We find that the cross section for graviton production rises as fast as ( /M _f)²⁺, where M _f is the fundamental scale of gravity in 4 + dimensions, and that the distribution of radiating a fraction y of the initial particle's energy into gravitational energy (which goes undetected) behaves as y ^{– 1}. The missing energy leads to an underestimate of the true energy and generates a break in the inferred cosmic ray spectrum (the knee). By fitting the cosmic ray spectrum data we deduce that the favorite values for the parameters of the theory are M _f 8 TeV and = 4.     

Equation of Motion of a Spinning Test Particle in Gravitational Field

Based on the coupfing between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.     

Letter: Gravitational Thermodynamics of a Vaidya Black Hole

The path integral approach is applied to the statistical thermodynamics of a radiating Vaidya black hole. The entropy still satisfies the Bekenstein-Hawking formula, except for a negligible term. The entropy production, as a measurement of the irreversibility, is also obtained.     

Letter: The Gravitational Energy of a Black Hole

An exact energy expression for a physical black hole is derived by considering the escape of a photon from the black hole. The mass of the black hole within its horizon is found to be twice its mass as observed at infinity. This result is important in understanding gravitational waves in black hole collisions.     

Letter: Gravitational Entropy of Constrained Instanton

The seeds for quantum creations of universes areconstrained gravitational instantons. For all compactconstrained instantons with a U(1) isometry, the period of the group parameter is identifiedas the reciprocal of the temperature. If remains a free parameter under the constraints, then theEuclidean action becomes the negative of the entropy. Asexamples, we perform the calculations forthe Taub-nut and Taub-Bolt-type models andstudy the quantum creation of the Taub-nutuniverse.     

Letter: Bounds on the Deficit Solid Angle Parameter from Solar System Tests

We analyze the Mercury perihelion precession, the bending of starlight, and the radar echo delay in the Schwarzschild field modified by the presence of a solid angle deficit. By using the experimental data we obtain that the parameter characterizing the solid angle deficit is less than 10^–9, 10^–8 and 10^–9, respectively, on the length scales associated with such phenomena. In particular, if the solid angle deficit is generated by a global monopole, it is shown that within the length scales associated with such phenomena, the observational data available constrain the monopole energy scale to lower bounds which are in considerable agreement with the limits derived from grand unified theory and cosmology.     

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.     

Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge*

The exact metric of a Schwarzschild black hole in the true radiation gauge was recently reported.In this work, we base on this gravity and calculate the gravitational deflection of relativistic massive particles up to the fourth post-Minkowskian order. It is found that the result is consistent with the previous formulations for both the case of dropping the fourth-order contribution and the case of light deflection. Our result might be helpful for future high-accuracy observations.     

Letter: Gravitational Waves in the Generalized Chaplygin Gas Model

The consequences of taking the generalized Chaplygin gas as the dark energy constituent of the Universe on the gravitational waves are studied and the spectrum obtained from this model, for the flat case, is analyzed. Besides its importance for the study of the primordial Universe, the gravitational waves represent an additional perspective (besides the CMB temperature and polarization anisotropies) to evaluate the consistence of the different dark energy models and establish better constraints to their parameters. The analysis presented here takes this fact into consideration to open one more perspective of verification of the generalized Chaplygin gas model applicability. Nine particular cases are compared: one where no dark energy is present; two that simulate the -CDM model; two where the gas acts like the traditional Chaplygin gas; and four where the dark energy is the generalized Chaplygin gas. The different spectra permit to distinguish the -CDM and the Chaplygin gas scenarios.     

The Gravitational Deflection of Light in f(R)-Gravity

Gravitation deflects light, which has been confirmed by a large number of observation data. f(R)-gravity is modification of Einstein’s gravity. According to the field equations obtained by the action of the f(R) form, a similar Schwarzschild metric is obtained. According to the condition that four-dimension momenta of the photon return to zero and conservation of covariant momenta, we obtain an equation of photon motion in a specific form of f(R)-gravity. We solve the equation to get gravitational deflection angle of light that grazes surface of sun and the calculation result is consistent with the experimental observation data.     

Letter: Gravitational Potential in the Palatini Formulation of Modified Gravity

General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We argue that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity are very small for a slowly moving source.     

Gravitational Corrections to Energy-Levels of a Hydrogen Atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Letter: Wave Equations for the Perturbations of a Charged Black Hole

A pair of simple wave equations is presented for the symmetric gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled, and the other has a source term given by the solution of the first equation. The derivation is presented in full detail for either axially symmetric or stationary perturbations, and is quite straightforward. This result is expected to have important applications in astrophysical models.     

Letter: A Reassessment of the Systematic Gravitational Error in the LARES Mission

In this letter we reexamine the evaluation of the error due to the even zonal harmonics of the geopotential in some proposed tests of relativistic gravitomagnetism with existing and proposed laser–ranged LAGEOS–like satellites in the gravitational field of the Earth. It is particularly important because the error due to the even zonal harmonics of the geopotential is one of the major sources of systematic errors in this kind of measurements. A conservative, although maybe pessimistic, approach is followed by using the diagonal part only of the covariance matrix of the EGM96 Earth's gravity model up to degree l = 20. It turns out that, within this context and according to the present level of knowledge of the terrestrial gravitational field, the best choice would be the use of a recently proposed combination which involves the nodes of LAGEOS, LAGEOS II and LARES and the perigees of LAGEOS II and LARES. Indeed, it turns out that the unavoidable orbital injection errors in the inclination of LARES would not affect the gravitational error which would also be insensitive to the correlations among the even zonal harmonics of geopotential.     

整体单极子黑洞引力场中的加速效应

给出了含有整体单极子的黑洞的引力场中试验粒子加速度的表达式, 讨论了整体单极子对加速效应的贡献. 结果表明, 由于整体单极子的存在, 产生了斥力效应; 当速度趋近于光速时, 中性粒子在引力场中受到了斥力作用. 这是牛顿力学中所没有的.     

Letter: Parametrization of the Kerr-NUT Solution

The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere.     

Gravitational collapse of dissipative fluid as a source of gravitational waves

Gravitational collapse of cylindrical anisotropic fluid has been considered in analogy with the work of Misner and Sharp. Using Darmois matching conditions, the interior cylindrical dissipative fluid (in the form of shear viscosity and heat flux) is matched to an exterior vacuum Einstein–Rosen space–time. It is found that on the bounding 3-surface the radial pressure of the anisotropic perfect fluid is linearly related to the shear viscosity and the heat flux of the dissipative fluid on the boundary. This non-zero radial pressure on the bounding surface may be considered as the source of gravitational waves outside the collapsing matter distribution.