In this methodological paper we consider geodesic motion of particles in a spherically symmetric black hole space-times. We develop an approach based on splitting the velocity of a freely falling particle to the flow velocity, which depends only on a metric, and deviation from it (a peculiar velocity). It applies to a wide class of spherically symmetric metrics and is exploited under the horizon of the Schwarzschild black hole. The present work generalizes previous results obtained for pure radial motion. Now, the motion is, in general, nonradial, so that an observer can have a nonzero angular momentum. This approach enables us to give simple physical interpretation of redshift (blueshift) inside the horizon including the region near the singularity and agrees with the recent results obtained by direct calculations.
We investigate the asymptotic behavior of peculiar velocities in certain physically significant time-dependent gravitational fields. Previous studies of the motion of free test particles have focused on the \emph{collapse scenario}, according to which a double-jet pattern with Lorentz factor $γ\to \infty$ develops asymptotically along the direction of complete gravitational collapse. In the present work, we identify a second \emph{wave scenario}, in which a single-jet pattern with Lorentz factor $γ\to \infty$ develops asymptotically along the direction of wave propagation. The possibility of a…
We propose the method of investigation of radial motions for charged and neutral test particles in the Reissner-Nordström field by means of mass potential. In this context we analyze special features of interaction of charges and their motions in General Relativity and construct the radial motion classification. For test particles and a central source with charges $q$ and $Q$, respectively, the conditions of attraction (when $qQ>0$) and repulsion (when $qQ<0$) are obtained. The conditions of motionless test particle states with respect to the central source are investigated and, in addition, s…
Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the stress-energy-momentum tensor. In spite of its strange nature, this solution provides with non-trivial descriptions of gravitational effects. We show that the main aspects found in the \emph{dark matter phenomena} can be satisfactorily described by this geometry. We comment on the relevance it could have to consider non-vanishing spacelike components of the stress-energ…
Peculiar velocity fields from analytic solutions of General Relativity
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学学院）
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint equations arise to maintain zero shear of the non-comoving fundamental worldlines which define a Newtonian-like frame, and these lead to the (1+3)-covariant dynamical equations, including a generalized Poisson-type equation. We investigate the relation between peculiar velocity and peculiar acceleration, finding the conditions under which they are aligned. In this c…
We consider a universe filled with perfect fluid with the constant equation of state parameter $ω$. In the theory of scalar perturbations, we study the effect of peculiar velocities on the gravitational potential. For radiation with $ω=1/3$, we obtain the expression for the gravitational potential in the integral form. Numerical calculation clearly demonstrates the modulation of the gravitational potential by acoustic oscillations due to the presence of peculiar velocities. We also show that peculiar velocities affect the gravitational potential in the case of the frustrated network of cosmic …
Large-scale peculiar motions are commonplace in our universe. Nevertheless, their origin, evolution and implications are still largely unknown. It is generally assumed that bulk motions are a relatively recent addition to the universal kinematics, triggered by the increasing inhomogeneity and anisotropy of the post-recombination epoch. In this work, we focus on the linear evolution of peculiar velocities prior to recombination, namely in the late radiation era and also during a phase of de Sitter inflation. We begin by showing/confirming that bulk motions are triggered and sustained by the non…
We consider spherically symmetric linear perturbations of static spherically symmetric spacetimes where the matter content is ellectrically counterpoised dust. We show that the evolution equation for the fluid perturbation implies that the fluid elements move with constant velocities. Therefore there are neither oscillations nor exponential departure from the background solution. We present an explicit example that shows that the perturbation could lead to the formation of a black hole.
Cosmological peculiar velocities in general relativity
Queen Mary University of London（伦敦大学玛丽女王学院）；University of the Western Cape（西开普敦大学）；National Institute for Theoretical & Computational Sciences（理论与计算科学国家研究所）
We investigate the effect of peculiar velocities of inhomogeneities and the spatial curvature of the universe on the shape of the gravitational potential. To this end, we consider scalar perturbations of the FLRW metric. The gravitational potential satisfies a Helmholtz-type equation which follows from the system of linearized Einstein equations. We obtain analytical solutions of this equation in the cases of open and closed universes, filled with cold dark matter in presence of the cosmological constant. We demonstrate that, first, peculiar velocities significantly affect the screening length…
As a study of peculiar velocities of nonlinear structure, we analyze the model of a relativistic thin-shell void in the expanding universe. (1) Adopting McVittie (MV) spacetime as a background universe, we investigate the dynamics of an uncompensated void with negative MV mass. Although the motion itself is quite different from that of a compensated void, as shown by Haines & Harris (1993), the present peculiar velocities are not affected by MV mass. (2) We discuss how precisely the formula in the linear perturbation theory applies to nonlinear relativistic voids, using the results in (1) as w…
The gravitational collapse of a spherical distribution, in a class of f(R) theories of gravity, where f(R) is power function of R, is discussed. The spacetime is assumed to admit a homothetic Killing vector. In the collapsing modes, some of the situations indeed hit a singularity, but they are all covered with an apparent horizon. Some peculiar cases are observed where the collapsing body settles to a constant radius at a given value of the radial coordinate.
We study the peculiar motion of non-relativistic matter in a fully covariant way. The exact nonlinear equations are derived and then applied to the case of pressure-free matter, moving relatively to a quasi-Newtonian Eulerian frame. Our two-frame formalism facilitates the study of the nonlinear kinematics of the matter, as the latter decouples from the background expansion and starts to ``turn around'' and collapse. Applied to second perturbative order, our equations provide a fully covariant formulation of the Zeldovich approximation, which by construction addresses the mildly nonlinear regim…
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
In dynamic spacetimes in which asymmetric gravitational collapse/expansion is taking place, the timelike geodesic equation appears to exhibit an interesting property: Relative to the collapsing configuration, free test particles undergo gravitational "acceleration" and form a double-jet configuration parallel to the axis of collapse. We illustrate this aspect of peculiar motion in simple spatially homogeneous cosmological models such as the Kasner spacetime. To estimate the effect of spatial inhomogeneities on cosmic jets, timelike geodesics in the Ricci-flat double-Kasner spacetime are studie…
In this work we investigate the systematic uncertainties that arise from the calculation of the peculiar velocity when estimating the Hubble constant ($H_0$) from gravitational wave standard sirens. We study the GW170817 event and the estimation of the peculiar velocity of its host galaxy, NGC 4993, when using Gaussian smoothing over nearby galaxies. NGC 4993 being a relatively nearby galaxy, at $\sim 40 \ {\rm Mpc}$ away, is subject to a significant effect of peculiar velocities. We demonstrate a direct dependence of the estimated peculiar velocity value on the choice of smoothing scale. We s…
Peculiar velocities change the expansion rate of any observer moving relative to the smooth Hubble flow. As a result, observers in a galaxy like our Milky Way can experience accelerated expansion within a globally decelerating universe, even when the drift velocities are small. The effect is local, but the affected scales can be large enough to give the false impression that the whole cosmos has recently entered an accelerating phase. Generally, peculiar velocities are also associated with dipole-like anisotropies, triggered by the fact that they introduce a preferred spatial direction. This i…
Recent surveys seem to support bulk peculiar velocities well in excess of those anticipated by the standard cosmological model. In view of these results, we consider here some of the theoretical implications of large-scale drift motions. We find that observers with small, but finite, peculiar velocities have generally different expansion rates than the smooth Hubble flow. In particular, it is possible for observers with larger than the average volume expansion at their location, to experience apparently accelerated expansion when the universe is actually decelerating. Analogous results have be…
We detect the correlated peculiar velocities of nearby type Ia supernovae (SNe), while highlighting an error in some of the literature. We find sigma_8=0.79 +/- 0.22 from SNe, and examine the potential of this method to constrain cosmological parameters in the future. We demonstrate that a survey of 300 low-z SNe (such as the nearby SNfactory) will underestimate the errors on w by about 35% if the coherent peculiar velocities are not included.
We consider the linear kinematics of large-scale peculiar motions in a perturbed Friedmann universe. In so doing, we take the viewpoint of the "real" observers that move along with the peculiar flow, relative to the smooth Hubble expansion. Using relativistic cosmological perturbation theory, we study the linear evolution of the peculiar velocity field, as well as the expansion/contraction, the shear and the rotation of the bulk motion. Our solutions show growth rates considerably stronger than those of the earlier treatments, which were mostly Newtonian. On scales near and beyond the Hubble r…
The problem of scattering of CMB radiation on wormholes is considered. It is shown that a static gas of wormholes does not perturb the spectrum of CMB. In the first order by $v/c$ the presence of peculiar velocities gives rise to the dipole contribution in $ΔT/T$, which corresponds to the well-known kinetic Sunyaev-Zel'dovich effect. In next orders there appears a more complicated dependence of the perturbed CMB spectrum on peculiar velocities. We also discuss some peculiar features of the scattering on a single wormhole.
We study large-scale coherent motion in our universe using the existing Type IA supernovae data. If the recently observed bulk flow is real, then some imprint must be left on supernovae motion. We run a series of Monte Carlo Markov Chain runs in various redshift bins and find a sharp contrast between the z < 0.05 and z > 0.05 data. The$z < 0.05 data are consistent with the bulk flow in the direction (l,b)=({290^{+39}_{-31}}^{\circ}, {20^{+32}_{-32}}^{\circ}) with a magnitude of v_bulk = 188^{+119}_{-103} km/s at 68% confidence. The significance of detection (compared to the null hypothesis) is…
