12,156 research outputs found
Dynamics of critical collapse
Critical collapse of a massless scalar field in spherical symmetry is
systematically studied. We combine numerical simulations and asymptotic
analysis, and synthesize critical collapse, spacetime singularities, and
complex science. First set of approximate analytic expressions near the center
are obtained. We observe that, near the center, the spacetime is nearly
conformally flat, the dynamics is not described by the Kasner solution, and the
Kreschmann scalar is proportional to r^(-5.30), where r is the areal radius.
These features are significantly different from those in black hole
singularities. It is speculated that the scalar field in critical collapse may
be a special standing wave.Comment: Title changed. 11 pages, 8 figures, 1 tabl
Interior dynamics of neutral and charged black holes in f(R) gravity
In this paper, we explore the interior dynamics of neutral and charged black
holes in gravity. We transform gravity from the Jordan frame into
the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and
Reissner-Nordstr\"om geometries. In simulating scalar collapses in
Schwarzschild and Reissner-Nordstr\"om geometries, Kruskal and Kruskal-like
coordinates are used, respectively, with the presence of and a physical
scalar field being taken into account. The dynamics in the vicinities of the
central singularity of a Schwarzschild black hole and of the inner horizon of a
Reissner-Nordstr\"om black hole is examined. Approximate analytic solutions for
different types of collapses are partially obtained. The scalar degree of
freedom , transformed from , plays a similar role as a physical
scalar field in general relativity. Regarding the physical scalar field in
case, when is negative (positive), the physical scalar field
is suppressed (magnified) by , where is the coordinate time. For dark
energy gravity, inside black holes, gravity can easily push to .
Consequently, the Ricci scalar becomes singular, and the numerical
simulation breaks down. This singularity problem can be avoided by adding an
term to the original function, in which case an infinite Ricci
scalar is pushed to regions where is also infinite. On the other hand, in
collapse for this combined model, a black hole, including a central
singularity, can be formed. Moreover, under certain initial conditions,
and can be pushed to infinity as the central singularity is approached.
Therefore, the classical singularity problem, which is present in general
relativity, remains in collapse for this combined model.Comment: 35 pages, 22 figures. (Special Issue. Modified Gravity Cosmology:
From Inflation to Dark Energy). Minor change. arXiv admin note: substantial
text overlap with arXiv:1507.0180
BPS -branes in Dual to Loop Operators
In this paper, we first compute the Killing spinors of and its certain orbifolds. Based on this, two classes of -brane
solutions are found. The first class of solutions includes -branes dual to
Wilson loops in the fundamental representation as special cases. The second
class includes the candidates of the holographic description of vortex loops in
the dual field theories.Comment: v6, typoes fixed, 14 pages, no figure
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