Deriving relativistic momentum and energy. II. Three-dimensional case

We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.Comment: 7 page

Variation of the speed of light with temperature of the expanding universe

From an extended relativistic dynamics for a particle moving in a cosmic background field with temperature T, we aim to obtain the speed of light with an explicit dependence on the background temperature of the universe. Although finding the speed of light in the early universe much larger than its current value, our approach does not violate the postulate of special relativity. Moreover, it is shown that the high value of the speed of light in the early universe was drastically decreased before the beginning of the inflationary period. So we are led to conclude that the theory of varying speed of light should be questioned as a possible solution of the horizon problem.Comment: 3 pages and 1 figure; Phys. Rev. D86, 027703 (2012

The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited

We study the effect of the cosmological constant $\Lambda$ on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account, $\Lambda$ does indeed contribute to the bending.Comment: 5 pages, 2 figure

The Gravitational Horizon for a Universe with Phantom Energy

The Universe has a gravitational horizon, coincident with the Hubble sphere, that plays an important role in how we interpret the cosmological data. Recently, however, its significance as a true horizon has been called into question, even for cosmologies with an equation-of-state w = p/rho > -1, where p and rho are the total pressure and energy density, respectively. The claim behind this argument is that its radius R_h does not constitute a limit to our observability when the Universe contains phantom energy, i.e., when w < -1, as if somehow that mitigates the relevance of R_h to the observations when w > -1. In this paper, we reaffirm the role of R_h as the limit to how far we can see sources in the cosmos, regardless of the Universe's equation of state, and point out that claims to the contrary are simply based on an improper interpretation of the null geodesics.Comment: 9 pages, 1 figure. Slight revisions in refereed version. Accepted for publication in JCAP. arXiv admin note: text overlap with arXiv:1112.477

Local and Global Light Bending in Einstein's and Other Gravitational Theories

To remedy a certain confusion in the literature, we stress the distinction between local and global light bending. Local bending is a purely kinematic effect between mutually accelerating reference frames tracking the same signal, and applies via Einstein's equivalence principle exactly and equally in Newton's, Einstein's, Nordström's and other gravitational theories, independently of all field equations. Global bending, on the other hand, arises as an integral of local bending and depends critically on the conformal spacetime structure and thus on the specific field equations of a given theory

A gravitationally induced (machian) magnetic field

The magnetic field induced by a rotating mass-shell having at its center a stationary charged sphere is calculated in the framework of linearized general relativity

Successive Schwarzschild spheres and other rigidity frontiers in spherically symmetric dust-plus-vacuum spacetimes

Just outside a Schwarzschild sphere concentric rigid test matter spheres can persist while just inside they cannot. We construct spacetimes containing successive Schwarzschild spheres and show that there exist similar but moving rigidity frontiers between them. Some of our solutions exemplify inextensible nonempty spacetimes with Kruskal-like topology having two asymptotically flat ends of possibly different Schwarzschild (≡ADM) mass

A covariant formalism of spin precession with respect to a reference congruence

We derive an effectively three-dimensional relativistic spin precession formalism. The formalism is applicable to any spacetime where an arbitrary timelike reference congruence of worldlines is specified. We employ what we call a stopped spin vector which is the spin vector that we would get if we momentarily make a pure boost of the spin vector to stop it relative to the congruence. Starting from the Fermi transport equation for the standard spin vector we derive a corresponding transport equation for the stopped spin vector. Employing a spacetime transport equation for a vector along a worldline, corresponding to spatial parallel transport with respect to the congruence, we can write down a precession formula for a gyroscope relative to the local spatial geometry defined by the congruence. This general approach has already been pursued by Jantzen et. al. (see e.g. Jantzen, Carini and Bini, Ann. Phys. 215 (1997) 1), but the algebraic form of our respective expressions differ. We are also applying the formalism to a novel type of spatial parallel transport introduced in Jonsson (Class. Quantum Grav. 23 (2006) 1), as well as verifying the validity of the intuitive approach of a forthcoming paper (Jonsson, Am. Journ. Phys. 75 (2007) 463) where gyroscope precession is explained entirely as a double Thomas type of effect. We also present the resulting formalism in explicit three-dimensional form (using the boldface vector notation), and give examples of applications.Comment: 27 pages, 8 figure

General relativity and cosmology derived from principle of maximum power or force

The field equations of general relativity are shown to derive from the existence of a limit force or of a limit power in nature. The limits have the value of c^4/4G and c^5/4G. The proof makes use of a result by Jacobson. All known experimental data is consistent with the limits. Applied to the universe, the limits predict its darkness at night and the observed scale factor. Some experimental tests of the limits are proposed. The main counter-arguments and paradoxes are discussed, such as the transformation under boosts, the force felt at a black hole horizon, the mountain problem, and the contrast to scalar--tensor theories of gravitation. The resolution of the paradoxes also clarifies why the maximum force and the maximum power have remained hidden for so long. The derivation of the field equations shows that the maximum force or power plays the same role for general relativity as the maximum speed plays for special relativity.Comment: 24 pages, 1 figure, LaTeX, published versio

Comments on the tethered galaxy problem

In a recent paper Davis et al. make the counter intuitive assertion that a galaxy held `tethered' at a fixed distance from our own could emit blueshifted light. Moreover, this effect may be derived from the simplest Friedmann-Robertson-Walker spacetimes and the (0.3,0.7) case which is believed to be a good late time model of our own universe. In this paper we recover the previous authors' results in a more transparent form. We show how their results rely on a choice of cosmological distance scale and revise the calculations in terms of observable quantities which are coordinate independent. By this method we see that, although such a tethering would reduce the redshift of a receding object, it would not do so sufficiently to cause the proposed blueshift. The effect is also demonstrated to be much smaller than conjectured below the largest intergalactic scales. We also discuss some important issues, raised by this scenario, relating to the interpretation of redshift and distance in relativistic cosmology.Comment: 6 pages, 3 figures, submitted to Am.J.Phy