Einstein's General Relativity Research Articles

Growth factor in f(T) gravity

We derive the evolution equation of growth factor forthe matter over-dense perturbation in f(T) gravity. For instance,we investigate its behavior in power law model at small redshift andcompare it to the prediction of ΛCDM and dark energy withthe same equation of state in the framework of Einstein generalrelativity. We find that the perturbation in f(T) gravity growsslower than that in Einstein general relativity if ∂f/∂T > 0 dueto the effectively weakened gravity.

Twisting of light around rotating black holes

Kerr black holes are among the most intriguing predictions of Einstein's general relativity theory. These rotating massive astrophysical objects drag and intermix their surrounding space and time, deflecting and phase-modifying light emitted nearby them. We have found that this leads to a new relativistic effect that imposes orbital angular momentum onto such light. Numerical experiments, based on the integration of the null geodesic equations of light from orbiting point-like sources in the Kerr black hole equatorial plane to an asymptotic observer, indeed identify the phase change and wavefront warping and predict the associated light-beam orbital angular momentum spectra. Setting up the best existing telescopes properly, it should be possible to detect and measure this twisted light, thus allowing a direct observational demonstration of the existence of rotating black holes. Since non-rotating objects are more an exception than a rule in the Universe, our findings are of fundamental importance.

Hawking Tunneling Radiation of Black Holes in Deformed Hŏrava—Lifshitz Gravity

Tunneling of scalar particles and Dirac particles from a black hole in the deformed Hŏrava—Lifshitz gravity is discussed in this paper. We consider the case that the dynamical coupling constant λ = 1, when it reduces to Einstein's General Relativity at large scales and the black hole behaves like the Reissner—Nordström black hole. The result shows that though the black hole entropy bears logarithmic correction, the tunneling probability is still related to its differences for the scalar particles and Dirac particles.

HOMOGENEOUS SOLUTIONS OF QUADRATIC GRAVITY

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3 + 1 decomposition for the zero vorticity case for arbitrary spatially homogenous spaces. We specialize for the particular Bianchi I diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi I case is a limiting case where this potential is negligible to the dynamics. The spirit should be analogous, in some sense to the BKL solution. In this sense, a better understanding of the Bianchi I case could shed some light into the general Bianchi case.

Past, present and future of the Resonant-Mass gravitational wave detectors

Resonant-mass gravitational wave detectors are reviewed from the concept of gravitational waves and its mathematical derivation, using Einstein's general relativity, to the present status of bars and spherical detectors, and their prospects for the future, which include dual detectors and spheres with non-resonant transducers. The review not only covers technical aspects of detectors and sciences that will be done, but also analyzes the subject in a historical perspective, covering the various detection efforts over four decades, starting from Weber's pioneering work.

GRAVITATIONAL FIELD SHIELDING AND SUPERNOVA EXPLOSIONS

A new mechanism for supernova explosions called gravitational field shielding is proposed, in accord with a five-dimensional fully covariant Kaluza-Klein theory with a scalar field that unifies the four-dimensional Einsteinian general relativity and Maxwellian electromagnetic theory. It is shown that a dense compact collapsing core of a star will suddenly turn off or completely shield its gravitational field when the core collapses to a critical density, which is inversely proportional to the square of mass of the core. As the core suddenly turns off its gravity, the extremely large pressure immediately stops the core collapse and pushes the mantle material of supernova moving outward. The work done by the pressure in the expansion can be the order of energy released in a supernova explosion. The gravity will resume and stop the core from a further expansion when the core density becomes less than the critical density. Therefore, the gravitational field shielding leads a supernova to impulsively explode and form a compact object such as a neutron star as a remnant. It works such that a compressed spring will shoot the oscillator out when the compressed force is suddenly removed.

The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe in the light of the general relativity, quantum mechanics, and observations

Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.

Horava–Lifshitz cosmology and quark–hadron phase transition

Recently, Horava proposed a non-relativistic renormalisable theory of gravitation which reduces to Einstein general relativity at large distances but violate Lorentz invariance at small distances. In this paper, we consider the quark–hadron phase transition in Horava–Lifshitz cosmology within an effective model of quantum chromodynamics. We study the evolution of the physical quantities relevant to the physical description of the early universe, namely, the energy density, temperature and the scale factor before, during, and after the phase transition and investigate the effects of the dynamical coupling constant λ and the 1/a4 term on the cosmological phase transition.

Unifying exact scalar field cosmologies

We present a mechanism that generates the exact solutions of scalar field cosmologies in an unified way. This applies both to standard and phantom scalar fields in the framework of Einsteins General Relativity, and also to extended scenarios based on generalized gravity theories such as Scalar-Tensor theories. We provide a classification of the solutions in terms a single generating function. The existence of form-invariant dualities between the solutions is also discussed.

Stationary axisymmetric solutions and their energy contents in teleparallel equivalent of Einstein theory

We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general relativity and Møller’s tetrad theory of gravitation.

TIMELIKE GEODESIC MOTION IN HORAVA–LIFSHITZ SPACE–TIME

Recently a nonrelativistic renormalizable theory of gravitation has been proposed by P. Horava. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory is expected to flow to the relativistic value λ = 1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. In this paper under allowing the lapse function to depend on the spatial coordinates xias well as t, we obtain the spherically symmetric solutions. And then by analyzing the behavior of the effective potential for the particle, we investigate the timelike geodesic motion of particle in the Horava–Lifshitz space–time. We find that the nonradial particle falls from a finite distance to the center along the timelike geodesics when its energy is in an appropriate range. However, we find that it is complexity for radial particle along the timelike geodesics. There are three different cases due to the energy of radial particle: (i) when the energy of radial particle is higher than a critical value EC, the particle will fall directly from infinity to the singularity; (ii) when the energy of radial particle equals to the critical value EC, the particle orbit at r = rCis unstable, i.e. the particle will escape from r = rCto the infinity or to the singularity, depending on the initial conditions of the particle; (iii) when the energy of radial particle is in a proper range, the particle will rebound to the infinity or plunge to the singularity from a infinite distance, depending on the initial conditions of the particle.

FRW universe in Hor̃ava gravity

Recently, a field theoretic model for a UV complete theory of gravity has been proposed by Ho\~{r}ava. This theory is a non-relativistic renormalizable gravity theory which coincides with Einstein's general relativity at large distances. Subsequently L\"{u} et al have formulated the modified Friedmann equations and have presented a solution in vacuum. In the present work, we rewrite the modified FRW equations in the form of usual FRW equations in Einstein gravity and consequences has been analyzed. Also the thermodynamics of the FRW universe has been studied.

Static spherically symmetric solutions to modified Hořava-Lifshitz gravity with a projectability condition

In this paper we seek static spherically symmetric solutions of Horava-Lifshitz-like gravity with projectability condition. We consider the most general form of gravity action without detailed balance, and require the spacetime metric to respect the projectability condition. We find that for any value of $\lambda$, it may exists the solutions of topology $R\times M_3$, where $R$ is the time direction and $M_3$ is a three-dimensional maximally symmetric space depending on the value of cosmological constant and the potential of the action. Besides, in the UV region where $\lambda\neq 1$, we find Minkowski or de-Sitter space-time as the solution, while in the IR region where $\lambda=1$, we prove that (dS-)Schwarzschild solution is the only nontrivial solution. We also notice that the other static spherically symmetric solutions found in the literature do not satisfy the projectability condition and are not the solutions we get. Our study shows that in Horava-Lifshitz gravity with projectability condition, there is no novel correction to Einstein's general relativity in solar system tests.

BEND IT LIKE EINSTEIN: GRAVITATIONAL DEFLECTION OF CLASSICAL, QUANTUM AND EXOTIC LIGHT

Gravitational bending of light is a spectacular prediction of Einstein's general relativity, tested and observed in numerous situations. We examine the fine structure of gravitational bending in new light to obtain insights pertaining to some deep links between gravity and quantum mechanics. The new results include quantum-theoretical interpretation of part of the light bending, making a good case for gravity encompassing wave–particle duality, perhaps a new insight for quantum gravity itself. We reiterate the mutual compatibility of the equivalence principle and quantum dynamics in a simple proof. Finally, we address certain unresolved issues regarding the gravitational bending of ultraslow light and tunneling photons in the context of experiments that might pose fresh challenges for the interface of the two century-old theories.

INTERFEROMETRIC DETECTION OF GRAVITATIONAL WAVES: THE DEFINITIVE TEST FOR GENERAL RELATIVITY

Even though Einstein's general relativity has achieved great success and passed a lot of experimental tests, it has also shown some shortcomings and flaws which today prompt theorists to ask if it is the definitive theory of gravity. In this essay we show that if advanced projects on the detection of gravitational waves (GWs) improve their sensitivity, allowing us to perform a GW astronomy then accurate angle- and frequency-dependent response functions of interferometers for GWs arising from various theories of gravity, i.e. general relativity and extended theories of gravity, will be the definitive test for general relativity. The papers mentioned in this essay were the world's most-cited in 2007 of the Astroparticle Publication Review of ASPERA with 13 citations.

Bernhard Riemann's Conceptual Mathematics and the Idea of Space

This essay explores the power and fertility of mathematical imagination, as they are manifest in the thought of a nineteenth-century German mathematician Bernhard Riemann (1826–1866), one of the greatest and most imaginative mathematicians who ever lived. Riemann introduced radically new ideas in every main field of modern mathematics: algebra, analysis, geometry, and topology. These ideas transformed each of these fields and played major roles in making mathematics into what it is now. The essay considers in particular two interrelated aspects of Riemann's work: the first is his concept of "manifold(ness)," which transformed our mathematical, physical, and philosophical understanding of spatiality; and the second is the conceptual character of Riemann's mathematical thinking as responsible for the radical nature of his ideas, such as those concerning spatiality and/as manifoldness. The essay also addresses, in closing, some of the implications of Riemann's ideas for modern physics, most especially for Albert Einstein's general relativity—his non-Newtonian theory of gravitation.

Homopolar artificial gravity generator based on frame-dragging

Space exploration is linked in many ways to the generation and challenges of artificial gravity. Space stations and drag-free satellite platforms are used to provide microgravity environments for scientific experiments. On the other hand, microgravity or reduced gravity environments such as on Moon and Mars are known to put limits for long-term human presence. Large centrifuges in space may provide Earth-like gravity environments during long-term travels, however, such technology certainly has its limits to provide similar environments for human outposts on other moons and planets. One can imagine a different technology using a prediction out of Einstein's general relativity theory which is called frame-dragging. In principle, frame-dragging might be used to generate artificial gravitational fields similar to electric fields generated by time-varying or moving magnetic fields. We will show that it is also possible to generate constant artificial gravitational fields that could provide microgravity or artificial gravity environments. Although such technology is possible in principle, the field strengths calculated from Einstein's theory are too small to be useful so far. However, recently detected anomalies around low-temperature spinning matter as well as fly-by anomalies point to possible enhancement mechanisms that might make an artificial gravity generator based on frame-dragging a reality in the future.

Creativity in Einstein's and Hilbert's General Relativity

In the same days in which Albert Einstein was completing his formulation of the theory of general relativity, David Hilbert arrived to the same field equations following a different path and different mathematical procedures. In this article, both ways to get to the same formal result will be analyzed, together with the exchange of letters between the two scientists, underlining the two different, but extremely sharp, creativities.

THE AMPLITUDE OF THE DE BROGLIE GRAVITATIONAL WAVES

We calculate the amplitude of the de Broglie gravitational waves using the standard Einstein General Relativity. We find that these waves disappear in the limit ℏ→0 and when their source has a large mass and volume. From the experimental point of view, the knowledge of the amplitude allows to estimate the magnitude of the effect of the wave on a sphere of test particles. We propose also to measure a very special shift angle that does not change with time.

New Agegraphic Dark Energy in Brans–Dicke Theory

In this paper, we investigate the new agegraphic dark energy model in the framework of Brans–Dicke theory, which is a natural extension of the Einstein's general relativity. In this framework the form of the new agegraphic dark energy density takes as ρq = 3n2 Φ(t)η−2, where η is the conformal age of the universe and Φ(t) is the Brans–Dicke scalar field representing the inverse of the time-variable Newton's constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans–Dicke theory. It is very interesting to find that in the Brans–Dicke theory the agegraphic dark energy realizes quintom-like behavior, i.e., its equation of state crosses the phantom divide w = –1 during the evolution. We also compare the situation of the agegraphic dark energy model in the Brans–Dicke theory with that in the Einstein's theory. In addition, we discuss the new agegraphic dark energy model with interaction in the framework of the Brans–Dicke theory.