Search results for "Relativity"

The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics

2000

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multidimensional relativistic hydrodynamic codes (of Godunov type) is discussed.

Stopping a slow-light soliton: an exact solution

2005

We investigate propagation of a slow-light soliton in Λ-type media such as atomic vapours and Bose–Einstein condensates. We show that the group velocity of the soliton monotonically decreases with the intensity of the controlling laser field, which decays exponentially after the laser is switched off. The shock wave of the vanishing controlling field overtakes the slow soliton and stops it, while the optical information is recorded in the medium in the form of spatially localized polarization. In the strongly nonlinear regime we find an explicit exact solution describing the whole process.

General Solution for Self-Gravitating Spherical Null Dust

1997

We find the general solution of equations of motion for self-gravitating spherical null dust as a perturbative series in powers of the outgoing matter energy-momentum tensor, with the lowest order term being the Vaidya solution for the ingoing matter. This is done by representing the null-dust model as a 2d dilaton gravity theory, and by using a symmetry of a pure 2d dilaton gravity to fix the gauge. Quantization of this solution would provide an effective metric which includes the back-reaction for a more realistic black hole evaporation model than the evaporation models studied previously.

The effect of cooling on time dependent behaviour of accretion flows around black holes

2004

We present the results of several numerical simulations of two dimensional axi-symmetric accretion flows around black holes using Smoothed Particle Hydrodynamics (SPH) in the presence of cooling effects. We consider both stellar black holes and super-massive black holes. We observe that due to {\it both radial and vertical oscillation} of shock waves in the accretion flow, the luminosity and average thermal energy content of the inner disk exhibit very interesting behaviour. When power density spectra are taken, quasi-periodic variabilities are seen at a few Hz and also occasionally at hundreds of Hz for stellar black holes. For super-massive black holes, the time scale of the oscillations …

Shock waves and QPOs in 2D rotating accretion flows around black holes

2008

We examine numerically shock waves formed in 2D rotating accretion flows around a stellar‐mass and a supermassive black holes, while taking account of the cooling and heating of the gas and the radiation transport. As the results, we obtain general properties of the shock oscillations and the luminosity behaviors as QPOs independent of the black hole masses.

Constraints on Area Variables in Regge Calculus

2000

We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.

The different fates of a low-mass X-ray binary - I. Conservative mass transfer

2003

We study the evolution of a low mass x-ray binary coupling a binary stellar evolution code with a general relativistic code that describes the behavior of the neutron star. We assume the neutron star to be low--magnetized (B~10^8 G). In the systems investigated in this paper, our computations show that during the binary evolution the companion transfers as much as 1 solar mass to the neutron star, with an accretion rate of 10^-9 solar masses/yr. This is sufficient to keep the inner rim of the accretion disc in contact with the neutron star surface, thus preventing the onset of a propeller phase capable of ejecting a significant fraction of the matter transferred by the companion. We find th…

Distance of matter inside an Einstein-Strauss vacuole

2008

Asymptotic Safety, Fractals, and Cosmology

2013

These lecture notes introduce the basic ideas of the asymptotic safety approach to quantum Einstein gravity (QEG). In particular they provide the background for recent work on the possibly multi-fractal structure of the QEG space-times. Implications of asymptotic safety for the cosmology of the early Universe are also discussed.

Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background

2021

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization metho…