U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, T. Hinderer, N. Yunes
We study gravitational wave emission, zoom-whirl behavior and the resulting spin of the remnant black hole in highly boosted collisions of equal-mass, non spinning black-hole binaries with generic impact parameter.
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In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.
Motion of an ultra-relativistic perfect fluid in space-time with the Kasner metrics is investigated by the Hamiltonian method. It is found that in the limit of small times a tendency takes place to formation of strong inhomogeneities in matter distribution. In the case of slow flows the effect of non-stationary anisotropy on dynamics of sound waves and behaviour of frozen-in vortices is considered. It is shown that hydrodynamics of slow vortices on the static homogeneous background is equivalent to the usual Eulerian incompressible hydrodynamics, but in the presence of an external non-stationa…
Strong gravitational lensing from black holes results in the formation of relativistic images, in particular, relativistic Einstein rings. For objects with event horizons, the radius of the unstable light ring (photon sphere) is the lowest radius at which a relativistic image might be formed. For horizonless ultracompact objects, additional relativistic images and rings can form inside this radius. In this paper, we provide an analytical approach to deal with strong gravitational lensing from such ultracompact objects, which is substantially different from the black hole cases, first reported …
We present a method of contraction that can be applied to re-construct the recent extended non-relativistic and ultra-relativistic algebras as well as corresponding action principles. The methodology involves the use of multiple copies of Poincaré algebra. Consequently, the contraction defines non-relativistic or ultra-relativistic limits of multimetric theories of gravity. In particular, we show that the non-relativistic scaling limit of bi-metric gravity corresponds to the recent formulation of an action principle for Newtonian gravity with a constant background mass density.
Working with a magnetic field periodic along $Oz$ and decaying in time, we deal with the Dirac-type equation characterizing the fermions evolving in magnetar's crust. For ultra-relativistic particles, one can employ the perturbative approach, to compute the conserved current density components. If the magnetic field is frozen and the magnetar is treated as a stationary object, the fermion's wave function is expressed in terms of the Heun's Confluent functions. Finally, we are extending some previous investigations on the linearly independent fermionic modes solutions to the Mathieu's equation …
We present a general relativistic framework for studying gravitational effects in quantum mechanical phenomena. We concentrate our attention on the case of ultra-relativistic, spin-1/2 particles propagating in Kerr spacetime. The two-component Weyl equation with general relativistic corrections is obtained in the case of a slowly rotating, weak gravitational field. Our approach is also applied to neutrino oscillations in the presence of a gravitational field. The relative phase of two different mass eigenstates is calculated in radial propagation, and the result is compared with those of previ…
In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS-Carroll type. We also present the construction of the gravity th…
The time delay between the receptions of ultra-relativistic particles emitted simultaneously is a useful observable for both fundamental physics and cosmology. The expression of the delay when the particles travel through an arbitrary spacetime has been derived recently by Fanizza et al., using a particular coordinate system and self-consistent assumptions. The present article shows that this formula enjoys a simple physical interpretation: the relative velocity between two ultra-relativistic particles is constant. This result reveals an interesting kinematical property of general relativity, …
Recent observations suggest that blobs of matter are ejected with ultra-relativistic speeds in various astrophysical phenomena such as supernova explosions, quasars, and microquasars. In this paper we analyze the gravitational radiation emitted when such an ultra-relativistic blob is ejected from a massive object. We express the gravitational wave by the metric perturbation in the transverse-traceless gauge, and calculate its amplitude and angular dependence. We find that in the ultra-relativistic limit the gravitational wave has a wide angular distribution, like $1+\cosθ$. The typical burst's…
We present an investigation of the electromagnetic instabilities which are trig gered when an ultra relativistic electron beam passes through a plasma. The linear growth rate is computed for every direction of propagation of the unstable modes, and temperatures are modelled using simple waterbag distribution functions. The ultra relativistic unstable spectrum is located around a very narrow band centered on a critical angle which value is given analytically. The growth rate of modes propagating in this direction decreases like k^(-1/3).
We point out novel consequences of general relativity involving tidal dynamics of ultrarelativistic relative motion. Specifically, we use the generalized Jacobi equation and its extension to study the force-free dynamics of relativistic flows near a massive rotating source. We show that along the rotation axis of the gravitational source, relativistic tidal effects strongly decelerate an initially ultrarelativistic flow with respect to the ambient medium, contrary to Newtonian expectations. Moreover, an initially ultrarelativistic flow perpendicular to the axis of rotation is strongly accelera…
We present results from numerical solution of the Einstein field equations describing the head-on collision of two solitons boosted to ultra relativistic energies. We show, for the first time, that at sufficiently high energies the collision leads to black hole formation, consistent with hoop conjecture arguments. This implies that the non-linear gravitational interaction between the kinetic energy of the solitons causes gravitational collapse, and that arguments for black hole formation in super-Planck scale particle collisions are robust.
Including the metric fluctuations of a realistic cosmological geometry we reconsider an earlier suggestion that measuring the relative time-of-flight of ultra-relativistic particles can provide interesting constraints on fundamental cosmological and/or particle parameters. Using convenient properties of the geodetic light-cone coordinates we first compute, to leading order in the Lorentz factor and for a generic (inhomogeneous, anisotropic) space-time, the relative arrival times of two ultra-relativistic particles as a function of their masses and energies as well as of the details of the larg…
Relativistic Stellar Oscillations from Ultralight Dark Matter
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We study the gravitational wave (GW) production in extremely strong first order phase transitions where the latent heat density dominates the plasma energy density, $α\gtrsim 1$. In such transitions, bubbles develop extremely thin and relativistic fluid configurations, resulting in strong shock waves after collisions. We first propose a strategy to understand the GW production in such a system by separating the problem into the propagation part and the collision part. Focusing on the former, we next develop an effective theory for the propagation of the relativistic fluid shells. Using this ef…
We study the gravitational self-force using the effective field theory formalism. We show that in the ultra-relativistic limit γ\to \infty, with γthe boost factor, many simplifications arise. Drawing parallels with the large N limit in quantum field theory, we introduce the parameter 1/N = 1/γ^2 and show that the effective action admits a well defined expansion in powers of λ= Nε, at each order in 1/N, where ε= E_m/M and E_m=γm is the (kinetic) energy of the small mass. Moreover, we show that diagrams with nonlinear bulk interactions first enter at O(λ^2/N^2) and only diagrams with nonlinearit…
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