172 research outputs found
Phase Structure of Black Holes and Strings on Cylinders
We use the (M,n) phase diagram recently introduced in hep-th/0309116 to
investigate the phase structure of black holes and strings on cylinders. We
first prove that any static neutral black object on a cylinder can be put into
an ansatz for the metric originally proposed in hep-th/0204047, generalizing a
result of Wiseman. Using the ansatz, we then show that all branches of
solutions obey the first law of thermodynamics and that any solution has an
infinite number of copies. The consequences of these two results are analyzed.
Based on the new insights and the known branches of solutions, we finally
present an extensive discussion of the possible scenarios for the
Gregory-Laflamme instability and the black hole/string transition.Comment: 26 pages, 10 figures, v2: refs. added, minor corrections and
addition
From Black Strings to Black Holes
Using recently developed numerical methods, we examine neutral compactified
non-uniform black strings which connect to the Gregory-Laflamme critical point.
By studying the geometry of the horizon we give evidence that this branch of
solutions may connect to the black hole solutions, as conjectured by Kol. We
find the geometry of the topology changing solution is likely to be nakedly
singular at the point where the horizon radius is zero. We show that these
solutions can all be expressed in the coordinate system discussed by Harmark
and Obers.Comment: 6 pages, 5 figures, RevTe
Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings
We describe new numerical methods to solve the static axisymmetric vacuum
Einstein equations in more than four dimensions. As an illustration, we study
the compactified non-uniform black string phase connected to the uniform
strings at the Gregory-Laflamme critical point. We compute solutions with a
ratio of maximum to minimum horizon radius up to nine. For a fixed
compactification radius, the mass of these solutions is larger than the mass of
the classically unstable uniform strings. Thus they cannot be the end state of
the instability.Comment: 48 pages, 13 colour figures; v2: references correcte
Axisymmetric metrics in arbitrary dimensions
We consider axially symmetric static metrics in arbitrary dimension, both
with and without a cosmological constant. The most obvious such solutions have
an SO(n) group of Killing vectors representing the axial symmetry, although one
can also consider abelian groups which represent a flat `internal space'. We
relate such metrics to lower dimensional dilatonic cosmological metrics with a
Liouville potential. We also develop a duality relation between vacuum
solutions with internal curvature and those with zero internal curvature but a
cosmological constant. This duality relation gives a solution generating
technique permitting the mapping of different spacetimes. We give a large class
of solutions to the vacuum or cosmological constant spacetimes. We comment on
the extension of the C-metric to higher dimensions and provide a novel solution
for a braneworld black hole.Comment: 36 pages, LaTeX (JHEP), 4 figures, section added (published version
Relativistic Stars in Randall-Sundrum Gravity
The non-linear behaviour of Randall-Sundrum gravity with one brane is
examined. Due to the non-compact extra dimension, the perturbation spectrum has
no mass gap, and the long wavelength effective theory is only understood
perturbatively. The full 5-dimensional Einstein equations are solved
numerically for static, spherically symmetric matter localized on the brane,
yielding regular geometries in the bulk with axial symmetry. An elliptic
relaxation method is used, allowing both the brane and asymptotic radiation
boundary conditions to be simultaneously imposed. The same data that specifies
stars in 4-dimensional gravity, uniquely constructs a 5-dimensional solution.
The algorithm performs best for small stars (radius less than the AdS length)
yielding highly non-linear solutions. An upper mass limit is observed for these
small stars, and the geometry shows no global pathologies. The geometric
perturbation is shown to remain localized near the brane at high densities, the
confinement interestingly increasing for both small and large stars as the
upper mass limit is approached. Furthermore, the static spatial sections are
found to be approximately conformal to those of AdS. We show that the intrinsic
geometry of large stars, with radius several times the AdS length, is described
by 4-dimensional General Relativity far past the perturbative regime. This
indicates that the non-linear long wavelength effective action remains local,
even though the perturbation spectrum has no mass gap. The implication is that
Randall-Sundrum gravity, with localized brane matter, reproduces relativistic
astrophysical solutions, such as neutron stars and massive black holes,
consistent with observation.Comment: 57 pages, 26 (colour) figures; minor typos corrected, references
added and introduction condense
New Phase Diagram for Black Holes and Strings on Cylinders
We introduce a novel type of phase diagram for black holes and black strings
on cylinders. The phase diagram involves a new asymptotic quantity called the
relative binding energy. We plot the uniform string and the non-uniform string
solutions in this new phase diagram using data of Wiseman. Intersection rules
for branches of solutions in the phase diagram are deduced from a new Smarr
formula that we derive.Comment: 19 pages, 6 figures, v2: typos corrected, v3: refs. added, comment on
bounds on the relative binding energy n added in end of section
Small localized black holes in a braneworld: Formulation and numerical method
No realistic black holes localized on a 3-brane in the Randall-Sundrum
infinite braneworld have been found so far. The problem of finding a static
black hole solution is reduced to a boundary value problem. We solve it by
means of a numerical method, and show numerical examples of a localized black
hole whose horizon radius is small compared to the bulk curvature scale. The
sequence of small localized black holes exhibits a smooth transition from a
five-dimensional Schwarzschild black hole, which is a solution in the limit of
small horizon radius. The localized black hole tends to flatten as its horizon
radius increases. However, it becomes difficult to find black hole solutions as
its horizon radius increases.Comment: RevTeX, 13 pages, 6 figures, references corrected, typos corrected;
to appear in Phys.Rev.
Naked shell singularities on the brane
By utilizing non-standard slicings of 5-dimensional Schwarzschild and
Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static
and spherically symmetric braneworld spacetimes containing shell-like naked
null singularities. For planar slicings, we find that the brane-matter sourcing
the solution is a perfect fluid with an exotic equation of state and a pressure
singularity where the brane crosses the bulk horizon. From a relativistic point
of view, such a singularity is required to maintain matter infinitesimally
above the surface of a black hole. From the point of view of the AdS/CFT
conjecture, the singular horizon can be seen as one possible quantum correction
to a classical black hole geometry. Various generalizations of planar slicings
are also considered for a Ricci-flat bulk, and we find that singular horizons
and exotic matter distributions are common features.Comment: REVTeX4, 13 pages, 6 figures, references and comments adde
Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes
We construct and analyze a large class of exact five- and six-dimensional
regular and static solutions of the vacuum Einstein equations. These solutions
describe sequences of Kaluza-Klein bubbles and black holes, placed alternately
so that the black holes are held apart by the bubbles. Asymptotically the
solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they
are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In
particular, they occupy a hitherto unexplored region of the phase diagram,
since their relative tension exceeds that of the uniform black string. The
solutions contain bubbles and black holes of various topologies, including
six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology
S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against
gravitational collapse. We find two maps between solutions, one that relates
five- and six-dimensional solutions, and another that relates solutions in the
same dimension by interchanging bubbles and black holes. To illustrate the
richness of the phase structure and the non-uniqueness in the (\mu,n) phase
diagram, we consider in detail particular examples of the general class of
solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.
Compactification, topology change and surgery theory
We study the process of compactification as a topology change. It is shown
how the mediating spacetime topology, or cobordism, may be simplified through
surgery. Within the causal Lorentzian approach to quantum gravity, it is shown
that any topology change in dimensions may be achieved via a causally
continuous cobordism. This extends the known result for 4 dimensions.
Therefore, there is no selection rule for compactification at the level of
causal continuity. Theorems from surgery theory and handle theory are seen to
be very relevant for understanding topology change in higher dimensions.
Compactification via parallelisable cobordisms is particularly amenable to
study with these tools.Comment: 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected
case adde
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