34 research outputs found

### Null cone evolution of axisymmetric vacuum spacetimes

We present the details of an algorithm for the global evolution of
asymptotically flat, axisymmetric spacetimes, based upon a characteristic
initial value formulation using null cones as evolution hypersurfaces. We
identify a new static solution of the vacuum field equations which provides an
important test bed for characteristic evolution codes. We also show how
linearized solutions of the Bondi equations can be generated by solutions of
the scalar wave equation, thus providing a complete set of test beds in the
weak field regime. These tools are used to establish that the algorithm is
second order accurate and stable, subject to a Courant-Friedrichs-Lewy
condition. In addition, the numerical versions of the Bondi mass and news
function, calculated at scri on a compactified grid, are shown to satisfy the
Bondi mass loss equation to second order accuracy. This verifies that numerical
evolution preserves the Bianchi identities. Results of numerical evolution
confirm the theorem of Christodoulou and Klainerman that in vacuum, weak
initial data evolve to a flat spacetime. For the class of asymptotically flat,
axisymmetric vacuum spacetimes, for which no nonsingular analytic solutions are
known, the algorithm provides highly accurate solutions throughout the regime
in which neither caustics nor horizons form.Comment: 25 pages, 6 figure

### Black holes on the brane

We consider exact solutions for static black holes localized on a three-brane
in five-dimensional gravity in the Randall-Sundrum scenario. We show that the
Reissner-Nordstrom metric is an exact solution of the effective Einstein
equations on the brane, re-interpreted as a black hole without electric charge,
but with instead a tidal 'charge' arising via gravitational effects from the
fifth dimension. The tidal correction to the Schwarzschild potential is
negative, which is impossible in general relativity, and in this case only one
horizon is admitted, located outside the Schwarzschild horizon. The solution
satisfies a closed system of equations on the brane, and describes the
strong-gravity regime. Current observations do not strongly constrain the tidal
charge, and significant tidal corrections could in principle arise in the
strong-gravity regime and for primordial black holes.Comment: 5 pages Revtex. v2: Expanded discussion, minor corrections,
additional references. v3: Improved discussion of black hole properties.
Version to appear in Phys. Lett.

### Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Kerr black hole

In our program of studying numerically the so-called Bondi-Hoyle accretion in
the fully relativistic regime, we present here first results concerning the
evolution of matter accreting supersonically onto a rotating (Kerr) black hole.
These computations generalize previous results where the non-rotating
(Schwarzschild) case was extensively considered. We parametrize our initial
data by the asymptotic conditions for the fluid and explore the dependence of
the solution on the angular momentum of the black hole. Towards quantifying the
robustness of our numerical results, we use two different geometrical
foliations of the black hole spacetime, the standard form of the Kerr metric in
Boyer-Lindquist coordinates as well as its Kerr-Schild form, which is free of
coordinate singularities at the black hole horizon. We demonstrate some
important advantages of using such horizon adapted coordinate systems.
Our numerical study indicates that regardless of the value of the black hole
spin the final accretion pattern is always stable, leading to constant
accretion rates of mass and momentum. The flow is characterized by a strong
tail shock, which, unlike the Schwarzschild case, is increasingly wrapped
around the central black hole as the hole angular momentum increases. The
rotation induced asymmetry in the pressure field implies that besides the well
known drag, the black hole will experience also a lift normal to the flow
direction. This situation exhibits some analogies with the Magnus effect of
classical fluid dynamics.Comment: 33 pages, 20 figures, submited to MNRA

### Dynamics of Scalar Fields in the Background of Rotating Black Holes

A numerical study of the evolution of a massless scalar field in the
background of rotating black holes is presented. First, solutions to the wave
equation are obtained for slowly rotating black holes. In this approximation,
the background geometry is treated as a perturbed Schwarzschild spacetime with
the angular momentum per unit mass playing the role of a perturbative
parameter. To first order in the angular momentum of the black hole, the scalar
wave equation yields two coupled one-dimensional evolution equations for a
function representing the scalar field in the Schwarzschild background and a
second field that accounts for the rotation. Solutions to the wave equation are
also obtained for rapidly rotating black holes. In this case, the wave equation
does not admit complete separation of variables and yields a two-dimensional
evolution equation. The study shows that, for rotating black holes, the late
time dynamics of a massless scalar field exhibit the same power-law behavior as
in the case of a Schwarzschild background independently of the angular momentum
of the black hole.Comment: 14 pages, RevTex, 6 Figure

### A "horizon adapted" approach to the study of relativistic accretion flows onto rotating black holes

We present a new geometrical approach to the study of accretion flows onto
rotating (Kerr) black holes. Instead of Boyer-Lindquist coordinates, the
standard choice in all existing numerical simulations in the literature, we
employ the simplest example of a horizon adapted coordinate system, the
Kerr-Schild coordinates. This choice eliminates boundary ambiguities and
unphysical divergent behavior at the event horizon. Computations of Bondi-Hoyle
accretion onto extreme Kerr black holes, performed here for the first time,
demonstrate the key advantages of this procedure. We argue it offers the best
approach to the numerical study of the, observationally, increasingly more
accesible relativistic inner region around black holes.Comment: 15 pages, 2 figures, aasms4.sty, major changes regarding section
names and style, accepted in ApJ Letter

### Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems: The Black Hole Regime

The Cauchy+characteristic matching (CCM) problem for the scalar wave equation
is investigated in the background geometry of a Schwarzschild black hole.
Previously reported work developed the CCM framework for the coupled
Einstein-Klein-Gordon system of equations, assuming a regular center of
symmetry. Here, the time evolution after the formation of a black hole is
pursued, using a CCM formulation of the governing equations perturbed around
the Schwarzschild background. An extension of the matching scheme allows for
arbitrary matching boundary motion across the coordinate grid. As a proof of
concept, the late time behavior of the dynamics of the scalar field is
explored. The power-law tails in both the time-like and null infinity limits
are verified.Comment: To appear in Phys. Rev. D, 9 pages, revtex, 5 figures available at
http://www.astro.psu.edu/users/nr/preprints.htm