69 research outputs found
Particle dynamics near extreme Kerr throat and supersymmetry
The extreme Kerr throat solution is believed to be non-supersymmetric.
However, its isometry group SO(2,1) x U(1) matches precisely the bosonic
subgroup of N=2 superconformal group in one dimension. In this paper we
construct N=2 supersymmetric extension of a massive particle moving near the
horizon of the extreme Kerr black hole. Bosonic conserved charges are related
to Killing vectors in a conventional way. Geometric interpretation of
supersymmetry charges remains a challenge.Comment: V2: 10 pages; discussion in sect. 4 and 5 extended, acknowledgements
and references adde
Conformal higher-order viscoelastic fluid mechanics
We present a generally covariant formulation of conformal higher-order
viscoelastic fluid mechanics with strain allowed to take arbitrarily large
values. We give a general prescription to determine the dynamics of a
relativistic viscoelastic fluid in a way consistent with the hypothesis of
local thermodynamic equilibrium and the second law of thermodynamics. We then
elaborately study the transient time scales at which the strain almost relaxes
and becomes proportional to the gradients of velocity. We particularly show
that a conformal second-order fluid with all possible parameters in the
constitutive equations can be obtained without breaking the hypothesis of local
thermodynamic equilibrium, if the conformal fluid is defined as the long time
limit of a conformal second-order viscoelastic system. We also discuss how
local thermodynamic equilibrium could be understood in the context of the
fluid/gravity correspondence.Comment: 26 pages; v2: minor corrections; v3: minor corrections, to appear in
JHE
Some Curvature Problems in Semi-Riemannian Geometry
In this survey article we review several results on the curvature of
semi-Riemannian metrics which are motivated by the positive mass theorem. The
main themes are estimates of the Riemann tensor of an asymptotically flat
manifold and the construction of Lorentzian metrics which satisfy the dominant
energy condition.Comment: 25 pages, LaTeX, 4 figure
Counting supersymmetric branes
Maximal supergravity solutions are revisited and classified, with particular
emphasis on objects of co-dimension at most two. This class of solutions
includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We
present a group theory derivation of the counting of these objects based on the
corresponding tensor hierarchies derived from E11 and discrete T- and U-duality
transformations. This provides a rationale for the wrapping rules that were
recently discussed for \sigma<4 in the literature and extends them. Explicit
supergravity solutions that give rise to co-dimension two branes are
constructed and analysed.Comment: 1+33 pages. To the memory of Laurent Houart. v2: Published version
with added reference
Black Holes in Modified Gravity (MOG)
The field equations for Scalar-Tensor-Vector-Gravity (STVG) or modified
gravity (MOG) have a static, spherically symmetric black hole solution
determined by the mass with two horizons. The strength of the gravitational
constant is where is a parameter. A regular
singularity-free MOG solution is derived using a nonlinear field dynamics for
the repulsive gravitational field component and a reasonable physical
energy-momentum tensor. The Kruskal-Szekeres completion of the MOG black hole
solution is obtained. The Kerr-MOG black hole solution is determined by the
mass , the parameter and the spin angular momentum . The
equations of motion and the stability condition of a test particle orbiting the
MOG black hole are derived, and the radius of the black hole photosphere and
the shadows cast by the Schwarzschild-MOG and Kerr-MOG black holes are
calculated. A traversable wormhole solution is constructed with a throat
stabilized by the repulsive component of the gravitational field.Comment: 14 pages, 3 figures. Upgraded version of paper to match published
version in European Physics Journal
Generalized Geometry and M theory
We reformulate the Hamiltonian form of bosonic eleven dimensional
supergravity in terms of an object that unifies the three-form and the metric.
For the case of four spatial dimensions, the duality group is manifest and the
metric and C-field are on an equal footing even though no dimensional reduction
is required for our results to hold. One may also describe our results using
the generalized geometry that emerges from membrane duality. The relationship
between the twisted Courant algebra and the gauge symmetries of eleven
dimensional supergravity are described in detail.Comment: 29 pages of Latex, v2 References added, typos fixed, v3 corrected
kinetic term and references adde
Entropy of three-dimensional asymptotically flat cosmological solutions
The thermodynamics of three-dimensional asymptotically flat cosmological
solutions that play the same role than the BTZ black holes in the anti-de
Sitter case is derived and explained from holographic properties of flat space.
It is shown to coincide with the flat-space limit of the thermodynamics of the
inner black hole horizon on the one hand and the semi-classical approximation
to the gravitational partition function associated to the entropy of the outer
horizon on the other. This leads to the insight that it is the Massieu function
that is universal in the sense that it can be computed at either horizon.Comment: 16 pages Latex file, v2: references added, cosmetic changes, v3: 1
reference adde
Mass and Angular Momentum in General Relativity
We present an introduction to mass and angular momentum in General
Relativity. After briefly reviewing energy-momentum for matter fields, first in
the flat Minkowski case (Special Relativity) and then in curved spacetimes with
or without symmetries, we focus on the discussion of energy-momentum for the
gravitational field. We illustrate the difficulties rooted in the Equivalence
Principle for defining a local energy-momentum density for the gravitational
field. This leads to the understanding of gravitational energy-momentum and
angular momentum as non-local observables that make sense, at best, for
extended domains of spacetime. After introducing Komar quantities associated
with spacetime symmetries, it is shown how total energy-momentum can be
unambiguously defined for isolated systems, providing fundamental tests for the
internal consistency of General Relativity as well as setting the conceptual
basis for the understanding of energy loss by gravitational radiation. Finally,
several attempts to formulate quasi-local notions of mass and angular momentum
associated with extended but finite spacetime domains are presented, together
with some illustrations of the relations between total and quasi-local
quantities in the particular context of black hole spacetimes. This article is
not intended to be a rigorous and exhaustive review of the subject, but rather
an invitation to the topic for non-experts. In this sense we follow essentially
the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84,
and refer the reader interested in further developments to the existing
literature, in particular to the excellent and comprehensive review by Szabados
(2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on
Mass" (June 2008) in Orleans, France. To appear as proceedings in the book
"Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and
B. Whiting. Some comments and references added
Eisenstein series for infinite-dimensional U-duality groups
We consider Eisenstein series appearing as coefficients of curvature
corrections in the low-energy expansion of type II string theory four-graviton
scattering amplitudes. We define these Eisenstein series over all groups in the
E_n series of string duality groups, and in particular for the
infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that,
remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains
only a finite number of terms for particular choices of a parameter appearing
in the definition of the series. This resonates with the idea that the constant
term of the Eisenstein series encodes perturbative string corrections in
BPS-protected sectors allowing only a finite number of corrections. We underpin
our findings with an extensive discussion of physical degeneration limits in
D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published
in JHE
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