6,631 research outputs found
Stability of naked singularities and algebraically special modes
We show that algebraically special modes lead to the instability of naked
singularity spacetimes with negative mass. Four-dimensional negative-mass
Schwarzschild and Schwarzschild-de Sitter spacetimes are unstable. Stability of
the Schwarzschild-anti-de Sitter spacetime depends on boundary conditions. We
briefly discuss the generalization of these results to charged and rotating
singularities.Comment: 6 pages. ReVTeX4. v2: Minor improvements and extended discussion on
boundary conditions. Version to appear in Phys. Rev.
New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation
We discuss a numerical method to compute the homogeneous solutions of the
Teukolsky equation which is the basic equation of the black hole perturbation
method. We use the formalism developed by Mano, Suzuki and Takasugi, in which
the homogeneous solutions of the radial Teukolsky equation are expressed in
terms of two kinds of series of special functions, and the formulas for the
asymptotic amplitudes are derived explicitly.Although the application of this
method was previously limited to the analytical evaluation of the homogeneous
solutions, we find that it is also useful for numerical computation. We also
find that so-called "renormalized angular momentum parameter", , can be
found only in the limited region of for each if we assume
is real (here, is the angular frequency, and and are degree
and order of the spin-weighted spheroidal harmonics respectively). We also
compute the flux of the gravitational waves induced by a compact star in a
circular orbit on the equatorial plane around a rotating black hole. We find
that the relative error of the energy flux is about which is much
smaller than the one obtained by usual numerical integration methods.Comment: 36 pages,7 figure
Electrodynamics in Friedmann-Robertson-Walker Universe: Maxwell and Dirac fields in Newman-Penrose formalism
Maxwell and Dirac fields in Friedmann-Robertson-Walker spacetime is
investigated using the Newman-Penrose method. The variables are all separable,
with the angular dependence given by the spin-weighted spherical harmonics. All
the radial parts reduce to the barrier penetration problem, with mostly
repulsive potentials representing the centrifugal energies. Both the helicity
states of the photon field see the same potential, but that of the Dirac field
see different ones; one component even sees attractive potential in the open
universe. The massless fields have the usual exponential time dependencies;
that of the massive Dirac field is coupled to the evolution of the cosmic scale
factor . The case of the radiation filled flat universe is solved in terms
of the Whittaker function. A formal series solution, valid in any FRW universe,
is also presented. The energy density of the Maxwell field is explicitly shown
to scale as . The co-moving particle number density of the massless
Dirac field is found to be conserved, but that of the massive one is not.
Particles flow out of certain regions, and into others, creating regions that
are depleted of certain linear and angular momenta states, and others with
excess. Such current of charged particles would constitute an electric current
that could generate a cosmic magnetic field. In contrast, the energy density of
these massive particles still scales as .Comment: 18 pages including 9 figure
Radiative interactions in chemically reacting supersonic internal flows
The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation for hydrogen-air systems. The chemistry source terms in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a ten-degree compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assure nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species and that this can have a significant influence on the flowfield
Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics
of a dynamical Lorentz gas, by which we mean an ensemble of particles moving
through a -dimensional array of fixed soft scatterers that each possess an
internal harmonic or anharmonic degree of freedom to which moving particles
locally couple. We establish that the momentum distribution of the moving
particles approaches a Maxwell-Boltzmann distribution at a certain temperature
, provided that they are initially fast and the scatterers are in a
sufficiently energetic but otherwise arbitrary stationary state of their free
dynamics--they need not be in a state of thermal equilibrium. The temperature
to which the particles equilibrate obeys a generalized equipartition
relation, in which the associated thermal energy is equal to
an appropriately defined average of the scatterers' kinetic energy. In the
equilibrated state, particle motion is diffusive
Does certification work in emerging markets? evidence from the Indian IPO market
There is inconclusive evidence regarding the economic value of certification in the context of IPOs in developed markets. Using a natural experiment of regulator mandated IPO grading requirement, we examine the effects of third-party certification in the Indian IPO market. We summarize our empirical results below. First, underpricing is unaffected by the grading process. Second, stock price informativeness as proxied by idiosyncratic volatility increases significantly due to IPO grading process. Third, retail and institutional subscription levels are significantly positively associated with IPO grades after controlling for other certification mechanisms such as underwriter reputation, group affiliation, analyst recommendation and venture capital backing. Finally, using a pseudo grading process we conclude that IPO grades are not mechanically derivable from publicly available information. In a nutshell, we use our unique setting to examine the usefulness of certification in emerging markets with institutional voids
Outgoing gravitational shock-wave at the inner horizon: The late-time limit of black hole interiors
We investigate the interiors of 3+1 dimensional asymptotically flat charged
and rotating black holes as described by observers who fall into the black
holes at late times, long after any perturbations of the exterior region have
decayed. In the strict limit of late infall times, the initial experiences of
such observers are precisely described by the region of the limiting stationary
geometry to the past of its inner horizon. However, we argue that late
infall-time observers encounter a null shockwave at the location of the
would-be outgoing inner horizon. In particular, for spherically symmetric black
hole spacetimes we demonstrate that freely-falling observers experience a
metric discontinuity across this shock, that is, a gravitational shock-wave.
Furthermore, the magnitude of this shock is at least of order unity. A similar
phenomenon of metric discontinuity appears to take place at the inner horizon
of a generically-perturbed spinning black hole. We compare the properties of
this null shockwave singularity with those of the null weak singularity that
forms at the Cauchy horizon.Comment: 23 pages, 4 figures, minor change
Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix
Under the dissipative effects of gravitational radiation, black hole binaries
will transition from an inspiral to a plunge. The separatrix between bound and
plunging orbits features prominently in the transition. For equatorial Kerr
orbits, we show that the separatrix is a homoclinic orbit in one-to-one
correspondence with an energetically-bound, unstable circular orbit. After
providing a definition of homoclinic orbits, we exploit their correspondence
with circular orbits and derive exact solutions for them. This paper focuses on
homoclinic behavior in physical space, while in a companion paper we paint the
complementary phase space portrait. The exact results for the Kerr separatrix
could be useful for analytic or numerical studies of the transition from
inspiral to plunge.Comment: 21 pages, some figure
On the Superradiance of Spin-1 Waves in an Equatorial Wedge around a Kerr Hole
Recently Van Putten has suggested that superradiance of magnetosonic waves in
a toroidal magnetosphere around a Kerr black hole may play a role in the
central engine of gamma-ray bursts. In this context, he computed (in the WKB
approximation) the superradiant amplification of scalar waves confined to a
thin equatorial wedge around a Kerr hole and found that the superradiance is
higher than for radiation incident over all angles. This paper presents
calculations of both spin-0 (scalar) superradiance (integrating the radial
equation rather than using the WKB method) and and spin-1
(electromagnetic/magnetosonic) superradiance, in Van Putten's wedge geometry.
In contrast to the scalar case, spin-1 superradiance decreases in the wedge
geometry, decreasing the likelihood of its astrophysical importance.Comment: Submitted to The Astrophysical Journal Letter
On the stable configuration of ultra-relativistic material spheres. The solution for the extremely hot gas
During the last stage of collapse of a compact object into the horizon of
events, the potential energy of its surface layer decreases to a negative value
below all limits. The energy-conservation law requires an appearance of a
positive-valued energy to balance the decrease. We derive the internal-state
properties of the ideal gas situated in an extremely strong, ultra-relativistic
gravitational field and suggest to apply our result to a compact object with
the radius which is slightly larger than or equal to the Schwarzschild's
gravitational radius. On the surface of the object, we find that the extreme
attractivity of the gravity is accompanied with an extremely high internal,
heat energy. This internal energy implies a correspondingly high pressure, the
gradient of which has such a behavior that it can compete with the gravity. In
a more detail, we find the equation of state in the case when the magnitude of
the potential-type energy of constituting gas particles is much larger than
their rest energy. This equation appears to be identical with the
general-relativity condition of the equilibrium between the gravity and
pressure gradient. The consequences of the identity are discussed.Comment: 12 pages (no figure, no table) Changes in 3-rd version: added an
estimate of neutrino cooling and relative time-scale of the final stage of
URMS collaps
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