We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit solutions. We use generalized Fermi-Walker transport to parallel transport the Frenet basis along the trajectory. In flat spacetime, we obtain velocity and acceleration transformations from a uniformly accelerated system to an inertial system. We obtain the time dilation between accelerated clocks. We apply our acceleration transformations to the motion of a charged particle in a constant electromagnetic field and recover the Lorentz-Abraham-Dirac equation.
Einstein's relativity theory demands that all meaningful physical objects should be defined covariantly, i.e. in a coordinate independent way. Concepts of relative velocity, acceleration, gravity acceleration and gravity potential are fundamental in Newton's theory and they are imprinted in everyone's physical intuition. Unfortunately, relativistic definitions of them are not commonly known or appreciated. Every now and then some confused authors use wrong, non-covariant, definitions of velocity, acceleration and gravity, based on their vague Newtonian intuitions and hidden in a superficial, o…
Analytical and numerical solutions for the integral curves of the velocity field (streamlines) of a steady-state flow of an ideal fluid with $p = ρ$ equation of state are presented. The streamlines associated with an accelerate black hole and a rigid sphere are studied in some detail, as well as, the velocity fields of a black hole and a rigid sphere in an external dipolar field (constant acceleration field). In the latter case the dipole field is produced by an axially symmetric halo or shell of matter. For each case the fluid density is studied using contour lines. We found that the presence…
When introducing special relativity, an elegant connection to familiar rules governing Galilean constant acceleration can be made, by describing first the discovery at high speeds that the clocks (as well as odometers) of different travelers may proceed at different rates. One may then show how to parameterize any given interval of constant acceleration with {\em either}: Newtonian (low-velocity approximation) time, inertial relativistic (unaccelerated observer) time, or traveler proper (accelerated observer) time, by defining separate velocities for each of these three kinematics as well. Kin…
The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates; both in the cases of uniform and arbitrary accelerations. In the first case, explicit formulae for the transformation of coordinates have been derived and, in both cases, we have also obtained the infinitesimal generators and their commutation relations. The outcome has been an extension of the Poincaré algebra (in 1+1 dimensions), which is infinite dimensional in the case of general acceleration. This extension turns out to be trivial, in the sense that it is Abelian.
The basic principles of General Theory of Relativity historically have been tested in gedanken experiments in rotating frame of references. One of the key issues, which still evokes a lot of controversy, is the centrifugal acceleration. Machabeli & Rogava (1994) argued that centrifugal acceleration reverse direction for particles moving radially with relativistic velocities within a "bead on a wire" approximation. We show that this result is frame-dependent and reflects a special relativistic dilution of time (as correctly argued by de Felice (1995)) and is analogous to freezing of motion on t…
We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.
An exact solution of Einstein's field equations for a static spherically symmetric medium with a radially boost invariant energy-momentum tensor is presented. In the limit of an equation of state corresponding to a distribution of radially directed strings there is a $1/r$ correction to Newton's force law. At large distances and small accelerations this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. The present model explaines why the critical acceleration of Milgrom is of the same …
Equations of motion, in cylindrical co-ordinates, for the observed rotation of gases within the gravitational potential of spiral galaxies have been derived from Carmeli's Cosmological General Relativity theory. A Tully-Fisher type relation results and rotation curves are reproduced without the need for non-baryonic halo dark matter. Two acceleration regimes are discovered that are separated by a critical accleration $\approx 4.75 \times 10^{-10}$ $m.s^{-2}$. For accelerations larger than the critical value the Newtonian force law applies, but for accelerations less than the critical value the…
The widely accepted description of the present cosmic acceleration and the neutrino oscillations in terms of a cosmological constant and neutrino masses, respectively, seems conceptually not very satisfactory. From a phenomenological perspective, the possibility that those phenomena are instead the first windows to new physics at very low energies is explored.
An exact solution of Einstein's field equations for a point mass surrounded by a static, spherically symmetric fluid of strings is presented. The solution is singular at the origin. Near the string cloud limit there is a $1/r$ correction to Newton's force law. It is noted that at large distances and small accelerations, this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. When interpreted in the context of a cosmological model with a string fluid, the new solution naturally explains …
It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and its calculation in terms of the proper acceleration history of the timelike curve would provide an important tool for the autonomous spacetime navigation of non-inertial observers. I give a solution in 3+1 dimensions which holds whenever the acceleration is decomposed with respect to a lightlike transported frame (lightlike transport will be defined), the a…
We introduce a modified divergence law for the energy-momentum tensor in the theory of unimodular relativity. Consequently, an additional equation for the measure field follows from the divergence of the field equations. The equations of motion are derived and the weak-field, low-velocity limit is investigated. It is found that the gravitational acceleration acquires a term that is proportional to the gradient of the mass density. We show that this term can provide the additional acceleration observed on astrophysical scales without the need for dark matter.
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions.
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (1/c^6 beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO-type experiments.
Electron accelerations of the order of $10^{21} g$ obtained by laser fields open up the possibility of experimentally testing one of the cornerstones of general relativity, the weak equivalence principle, which states that the local effects of a gravitational field are indistinguishable from those sensed by a properly accelerated observer in flat space-time. We illustrate how this can be done by solving the Einstein equations in vacuum and integrating the geodesic equations of motion for a uniformly accelerated particle.
General Very Special Relativity (GVSR) is the curved space-time of Very Special Relativity (VSR) proposed by Cohen and Glashow. The geometry of GVSR possesses a line element of Finsler Geometry proposed by Bogoslovsky. We calculate the Einstein field equations and derive a modified FRW cosmology, for an osculating Riemannian space. The Friedman equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial spurionic vector field introduced into the metric, gives back an estimation of t…
We show that in the realm of general relativity a non minimal coupling between the electromagnetic and the gravitational fields may produce an era of accelerated expansion.
Federal University of Campina Grande（坎皮纳格兰德联邦大学）；Federal University of Paraíba（帕拉伊巴联邦大学）；Center for Theoretical Physics, Khazar University（阿塞拜疆汗沙尔大学理论物理中心）；Universidade Federal do Carirí（卡里里联邦大学）
We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen fro…
The limiting mass of cold white dwarfs was first calculated by E. Stoner in an approximate model of a uniform star and was soon reduced by ~20% in papers by S. Chandrasekhar and L. D. Landau based on an exact solution of the equations for the stellar equilibrium. Here we examine uniform models of white dwarfs taking general relativity effects and the influence of finite temperature into account. Solutions are obtained in the form of finite analytic formulas and, for masses differing by no more than ~20% from the exact solutions, found by numerical integration of the differential equations for …
We present a formalism to obtain equilibrium configurations of uniformly rotating fluid in the second post-Newtonian approximation of general relativity. In our formalism, we need to solve 29 Poisson equations, but their source terms decrease rapidly enough at the external region of the matter(i.e., at worst $O(r^{-4})$). Hence these Poisson equations can be solved accurately as the boundary value problem using standard numerical methods.This formalism will be useful to obtain nonaxisymmetric uniformly rotating equilibrium configurations such as synchronized binary neutron stars just before me…
We present a convenient null gauge for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connexion between the field equation and the balanced equations of motion. We present the balanced equations of motion in second order of the acceleration. We solve the required components of the field equation at their respective required orders, $G^2$ and $G^3$. We indicate how this approach can be extended to higher orders.
To test the role of large-scale magnetic fields in accretion processes, we study dynamics of charged test particles in vicinity of a black hole immersed into an asymptotically uniform magnetic field. Using the Hamiltonian formalism of charged particle dynamics, we examine chaotic scattering in the effective potential related to the black hole gravitational field combined with the uniform magnetic field. Energy interchange between the translational and oscillatory modes od the charged particle dynamics provides mechanism for charged particle acceleration along the magnetic field lines. This ene…
The Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) is a multi-purpose relativity mission concept. ASTROD's scientific goals are the measurement of relativistic and solar system parameters to unprecedented precision, and the detection and observation of low-frequency gravitational waves to frequencies down to $5\times10^{-6}$ Hz. To accomplish its goals, ASTROD will employ a constellation of drag-free satellites, aiming for a residual acceleration noise of (0.3-1)$\times$ 10$^{-15}$ m s$^{-2}$ Hz$^{-1/2}$ at 0.1 mHz. Noise sources and strategies for improving present acc…
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into general relativity through a splitting of spacetime into space-plus-time associated with a family of test observers, one may further split the local rest space of those observers with respect to the direction of relative motion of a test particle world line in order to define longitudinal and transverse accelerations as well. The intrinsic covariant derivative (…
We review some quantum electrodynamical effects related to the uniform acceleration of atoms in vacuum. After discussing the energy level shifts of a uniformly accelerated atom in vacuum, we investigate the atom-wall Casimir-Polder force for accelerated atoms, and the van der Waals/Casimir-Polder interaction between two accelerated atoms. The possibility of detecting the Unruh effect through these phenomena is also discussed in detail.
Moving cavities promise to be a suitable system for relativistic quantum information processing. It has been shown that an inertial and a uniformly accelerated one-dimensional cavity can become entangled by letting an atom emit an excitation while it passes through the cavities, but the acceleration degrades the ability to generate entanglement. We show that in the two-dimensional case the entanglement generated is affected not only by the cavity's acceleration but also by its transverse dimension which plays the role of an effective mass.
This work generalizes the treatment of flat spin connections in the teleparallel equivalent of general relativity. It is shown that a general flat spin connection form a subspace in the affine space of spin connections which is dynamically decoupled from the tetrad and the matter fields. A translation in the affine subspace introduces a torsion term without changing the tetrad. Instead, the change in the torsion is related to the introduction of a global acceleration field term that introduces Lorentz inertial effects in the reference frame. The dynamics of the gravitationally coupled matter f…
Theoretical approaches to explaining the observed acceleration of the universe are reviewed. We briefly discuss the evidence for cosmic acceleration, and the implications for standard General Relativity coupled to conventional sources of energy-momentum. We then address three broad methods of addressing an accelerating universe: the introduction of a cosmological constant, its problems and origins; the possibility of dark energy, and the associated challenges for fundamental physics; and the option that an infrared modification of general relativity may be responsible for the large-scale behav…
The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. This locality postulate is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties in general cannot be measured instantaneously. The problem is corrected in nonlocal relativity by supplementing the locality postulate with a certain…
The discovery that the cosmic expansion is accelerating has been followed by an intense theoretical and experimental response in physics and astronomy. The discovery implies that our most basic notions about how gravity work are violated on cosmological distance scales. One simple fix is the introduction of a cosmological constant into the field equations for general relativity. However, the extremely small value of the cosmological constant, relative to theoretical expectations, has led theorists to explore a wide variety of alternative explanations that involve the introduction of an exotic …
A web of interlocking observations has established that the expansion of the Universe is speeding up and not slowing, revealing the presence of some form of repulsive gravity. Within the context of general relativity the cause of cosmic acceleration is a highly elastic (p\sim -rho), very smooth form of energy called ``dark energy'' accounting for about 75% of the Universe. The ``simplest'' explanation for dark energy is the zero-point energy density associated with the quantum vacuum; however, all estimates for its value are many orders-of-magnitude too large. Other ideas for dark energy inclu…
Employing a Mathematica symbolic computer algebra package called xTensor, we present $(1+3)$-covariant special case proofs of the shear-free perfect fluid conjecture in General Relativity. We first present the case where the pressure is constant, and where the acceleration is parallel to the vorticity vector. These cases were first presented in their covariant form by Senovilla et. al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the…
We deduce from energy conservation a lower bound on the mass of any system capable of imparting a constant acceleration to a charged body. We also point out a connection between this bound and the so called dominant energy condition of general relativity.
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.
We consider a recently proposed nonlinear Schroedinger equation exhibiting soliton-like solutions of the power-law form $e_q^{i(kx-wt)}$, involving the $q$-exponential function which naturally emerges within nonextensive thermostatistics [$e_q^z \equiv [1+(1-q)z]^{1/(1-q)}$, with $e_1^z=e^z$]. Since these basic solutions behave like free particles, obeying $p=\hbar k$, $E=\hbar ω$ and $E=p^2/2m$ ($1 \le q<2$), it is relevant to investigate how they change under the effect of uniform acceleration, thus providing the first steps towards the application of the aforementioned nonlinear equation to…
Deviations from general relativity, such as could be responsible for the cosmic acceleration, would influence the growth of large scale structure and the deflection of light by that structure. We clarify the relations between several different model independent approaches to deviations from general relativity appearing in the literature, devising a translation table. We examine current constraints on such deviations, using weak gravitational lensing data of the CFHTLS and COSMOS surveys, cosmic microwave background radiation data of WMAP5, and supernova distance data of Union2. Markov Chain Mo…
We study the acceleration of an electric current-carrying and axially-symmetric string loop initially oscillating in the vicinity of a Schwarzschild black hole embedded in an external asymptotically uniform magnetic field. The plane of the string loop is orthogonal to the magnetic field lines and the acceleration of the string loop occurs due to the transmutation effect turning in the deep gravitational field the internal energy of the oscillating strings to the energy of their translational motion along the axis given by the symmetry of the black hole spacetime and the magnetic field. We rest…
The Weyssenhoff fluid is a perfect fluid with spin where the spin of the matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov and Korotky showed that this fluid can be described as an effective fluid with spin in general relativity. A dynamical analysis of such a fluid is performed in a gauge invariant manner using the 1+3 covariant approach. This yields the propagation and constraint equations for the set of dynamical variables. A verification of these equations is performed for the special case of irrotational flow with zero peculiar acceleration by evolving the co…
The analysis of the data from the distant supernovae (A.Riess et al, Astron.J. {\bf 116}, 1009, (1988)) for acceleration of the expending Universe from the viewpoint of the gravitation equations proposed by one of the authors (Phys.Lett. {\bf 156}, 404 (1991)) is given. It is shown that the result from the above data that the deceleration parameter $q_{0}$ is negative is a natural consequence of the property of the gravitation force which follows from the above gravitation equations . It is an alternative explanation to general relativity where a nonzero cosmological constant is used to explai…
Accelerating black holes, connected to cosmic strings could evolve to supermassive black holes. However, if they are going to take part in structure formation and resides at the center of galaxies, their acceleration should be small. This slow acceleration does not change the shadow or image position in gravitational lensing effect significantly. However we show that the time delay associated to these images change significantly. This is in contrast with when the theory governing the strong gravitational field around the black hole is different from general relativity, where not only the diffe…
We discuss the classical tests of general relativity in the presence of Rindler acceleration. Among these tests the perihelion shifts give the tightest constraints and indicate that the Pioneer anomaly cannot be caused by a universal solar system Rindler acceleration. We address potential caveats for massive test-objects. Our tightest bound on Rindler acceleration that comes with no caveats is derived from radar echo delay and yields |a|<3nm/s^2.
In addition to nonzero forces and nontrivial metrics, here I show that a nonconstant Higgs expectation value, which endows elementary particles with their masses, also leads to apparent universal particle accelerations and photon frequency shifts. When effects of the Higgs is attributed to spacetime curvatures, a spurious stress-energy tensor is required in Einstein's equation. On cosmological scales, the spurious density coincides with the observed dark energy density. On smaller scales, effects of the Standard Model Higgs gradients are unlikely observable except near compact astrophysical bo…
Using the theory of optimal rocket trajectories in general relativity, recently developed in arXiv:1105.5235, we show that the "obvious" manoeuvre of using a tangential instantaneous acceleration to escape a stable circular orbit in the Schwarzschild spacetime satisfies the optimality conditions if and only if the magnitude of the acceleration is smaller than a certain bound.
A geometric framework for metrics of maximal acceleration which is applicable to large proper accelerations is discussed, including a theory of connections associated with the geometry of maximal acceleration. In such a framework it is shown that the uniform bound on the proper maximal acceleration implies an uniform bound for certain bilinear combinations of the Riemannian curvature components in the domain of the spacetime where curvature is finite.
We use Generalized Fermi-Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame $K'$ to an inertial frame $K$. The spacetime transformations between two uniformly accelerated frames with the same acceleration are L…
We consider the interatomic van der Waals interaction energy between two neutral ground-state atoms moving in the vacuum space with the same uniform acceleration. We assume the acceleration orthogonal to their separation, so that their mutual distance remains constant. Using a model for the van der Waals dispersion interaction based on the interaction between the instantaneous atomic dipole moments, which are induced and correlated by the zero-point field fluctuations, we evaluate the interaction energy between the two accelerating atoms in terms of quantities expressed in the laboratory refer…
Recent observations provide strong evidence that the universe is accelerating. This confronts theory with a severe challenge. Explanations of the acceleration within the framework of general relativity are plagued by difficulties. General relativistic models require a "dark energy" field with effectively negative pressure. An alternative to dark energy is that gravity itself may behave differently from general relativity on the largest scales, in such a way as to produce acceleration. The alternative approach of modified gravity also faces severe difficulties, but does provide a new angle on t…
We derive the radial acceleration of stars in galaxies by using basic features of thermodynamics, statistical mechanics and general relativity. We assume that the "dark" component of the radial acceleration is originated from the reaction of dark energy to the presence of baryonic matter. It can be also explained as the macroscopic manifestation of a huge number of extremely soft bosonic excitations of the dark energy medium with wavelength larger than the size of the cosmological horizon, in thermal equilibrium with de Sitter spacetime. Our formula agrees with the phenomenological relation pr…
