1,752 research outputs found

### Geometric Analysis of Particular Compactly Constructed Time Machine Spacetimes

We formulate the concept of time machine structure for spacetimes exhibiting
a compactely constructed region with closed timelike curves. After reviewing
essential properties of the pseudo Schwarzschild spacetime introduced by A.
Ori, we present an analysis of its geodesics analogous to the one conducted in
the case of the Schwarzschild spacetime. We conclude that the pseudo
Schwarzschild spacetime is geodesically incomplete and not extendible to a
complete spacetime. We then introduce a rotating generalization of the pseudo
Schwarzschild metric, which we call the the pseudo Kerr spacetime. We establish
its time machine structure and analyze its global properties.Comment: 14 pages, 3 figure

### Radiation-reaction-induced evolution of circular orbits of particles around Kerr Black Holes

It is demonstrated that, in the adiabatic approximation, non-Equatorial
circular orbits of particles in the Kerr metric (i.e. orbits of constant
Boyer-Lindquist radius) remain circular under the influence of gravitational
radiation reaction. A brief discussion is given of conditions for breakdown of
adiabaticity and of whether slightly non-circular orbits are stable against the
growth of eccentricity.Comment: 23 pages. Revtex 3.0. Inquiries to [email protected]

### Are naked singularites forbidden by the second law of thermodynamics?

By now, many examples of naked singularities in classical general relativity
are known. It may however be that a physical principle over and above the
general theory prevents the occurrence of such singularities in nature.
Assuming the validity of the Weyl curvature hypothesis, we propose that naked
singularities are forbidden by the second law of thermodynamics.Comment: 6 pages, Latex file. This essay was selected for honorable mention by
the Gravity Research Foundatio

### Survival of the black hole's Cauchy horizon under non-compact perturbations

We study numerically the evolution of spactime, and in particular of a
spacetime singularity, inside a black hole under a class of perturbations of
non-compact support. We use a very simplified toy model of a spherical charged
black hole which is perturbed nonlinearly by a self-gravitating, spherical
scalar field. The latter grows logarithmically with advanced time along an
outgoing characteristic hypersurface. We find that for that class of
perturbations a portion of the Cauchy horizon survives as a non-central, null
singularity.Comment: 5 pages, 4 figure

### The late-time singularity inside non-spherical black holes

It was long believed that the singularity inside a realistic, rotating black
hole must be spacelike. However, studies of the internal geometry of black
holes indicate a more complicated structure is typical. While it seems likely
that an observer falling into a black hole with the collapsing star encounters
a crushing spacelike singularity, an observer falling in at late times
generally reaches a null singularity which is vastly different in character to
the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity.
In the spirit of the classic work of BKL we present an asymptotic analysis of
the null singularity inside a realistic black hole. Motivated by current
understanding of spherical models, we argue that the Einstein equations reduce
to a simple form in the neighborhood of the null singularity. The main results
arising from this approach are demonstrated using an almost plane symmetric
model. The analysis shows that the null singularity results from the blueshift
of the late-time gravitational wave tail; the amplitude of these gravitational
waves is taken to decay as an inverse power of advanced time as suggested by
perturbation theory. The divergence of the Weyl curvature at the null
singularity is dominated by the propagating modes of the gravitational field.
The null singularity is weak in the sense that tidal distortion remains bounded
along timelike geodesics crossing the Cauchy horizon. These results are in
agreement with previous analyses of black hole interiors. We briefly discuss
some outstanding problems which must be resolved before the picture of the
generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi

### Are physical objects necessarily burnt up by the blue sheet inside a black hole?

The electromagnetic radiation that falls into a Reissner-Nordstrom black hole
develops a ``blue sheet'' of infinite energy density at the Cauchy horizon. We
consider classical electromagnetic fields (that were produced during the
collapse and then backscattered into the black hole), and investigate the
blue-sheet effects of these fields on infalling objects within a simplified
model. These effects are found to be finite and even negligible for typical
parameters.Comment: 13 pages, ordinary LaTex. Accepted for Physical Review Letters

### Critical phenomena in Newtonian gravity

We investigate the stability of self-similar solutions for a gravitationally
collapsing isothermal sphere in Newtonian gravity by means of a normal mode
analysis. It is found that the Hunter series of solutions are highly unstable,
while neither the Larson-Penston solution nor the homogeneous collapse one have
an analytic unstable mode. Since the homogeneous collapse solution is known to
suffer the kink instability, the present result and recent numerical
simulations strongly support a proposition that the Larson-Penston solution
will be realized in astrophysical situations. It is also found that the Hunter
(A) solution has a single unstable mode, which implies that it is a critical
solution associated with some critical phenomena which are analogous to those
in general relativity. The critical exponent $\gamma$ is calculated as
$\gamma\simeq 0.10567$. In contrast to the general relativistic case, the order
parameter will be the collapsed mass. In order to obtain a complete picture of
the Newtonian critical phenomena, full numerical simulations will be needed.Comment: 25 pages, 7 figures, accepted for publication in Physical Review

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