4,015 research outputs found
Lagrangian perfect fluids and black hole mechanics
The first law of black hole mechanics (in the form derived by Wald), is
expressed in terms of integrals over surfaces, at the horizon and spatial
infinity, of a stationary, axisymmetric black hole, in a diffeomorphism
invariant Lagrangian theory of gravity. The original statement of the first law
given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system
contained, in addition, volume integrals of the fluid fields, over a spacelike
slice stretching between these two surfaces. When applied to the
Einstein-perfect fluid system, however, Wald's methods yield restricted
results. The reason is that the fluid fields in the Lagrangian of a gravitating
perfect fluid are typically nonstationary. We therefore first derive a first
law-like relation for an arbitrary Lagrangian metric theory of gravity coupled
to arbitrary Lagrangian matter fields, requiring only that the metric field be
stationary. This relation includes a volume integral of matter fields over a
spacelike slice between the black hole horizon and spatial infinity, and
reduces to the first law originally derived by Bardeen, Carter and Hawking when
the theory is general relativity coupled to a perfect fluid. We also consider a
specific Lagrangian formulation for an isentropic perfect fluid given by
Carter, and directly apply Wald's analysis. The resulting first law contains
only surface integrals at the black hole horizon and spatial infinity, but this
relation is much more restrictive in its allowed fluid configurations and
perturbations than that given by Bardeen, Carter and Hawking. In the Appendix,
we use the symplectic structure of the Einstein-perfect fluid system to derive
a conserved current for perturbations of this system: this current reduces to
one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2
The Frenet Serret Description of Gyroscopic Precession
The phenomenon of gyroscopic precession is studied within the framework of
Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to
the congruence vorticity is highlighted with particular reference to the
irrotational congruence admitted by the stationary, axisymmetric spacetime.
General precession formulae are obtained for circular orbits with arbitrary
constant angular speeds. By successive reduction, different types of
precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime
family. The phenomenon is studied in the case of other interesting spacetimes,
such as the De Sitter and G\"{o}del universes as well as the general
stationary, cylindrical, vacuum spacetimes.Comment: 37 pages, Paper in Late
Entropy of Constant Curvature Black Holes in General Relativity
We consider the thermodynamic properties of the constant curvature black hole
solution recently found by Banados. We show that it is possible to compute the
entropy and the quasilocal thermodynamics of the spacetime using the
Einstein-Hilbert action of General Relativity. The constant curvature black
hole has some unusual properties which have not been seen in other black hole
spacetimes. The entropy of the black hole is not associated with the event
horizon; rather it is associated with the region between the event horizon and
the observer. Further, surfaces of constant internal energy are not isotherms
so the first law of thermodynamics exists only in an integral form. These
properties arise from the unusual topology of the Euclidean black hole
instanton.Comment: 4 pages LaTeX2e (RevTeX), 2 PostScript figures. Small corrections in
the text and the reference
Asymmetric Light Bending in the Equatorial Kerr Metric
The observation of the bending of light by mass, now known as gravitational
lensing, was key in establishing general relativity as one of the pillars of
modern physics. In the past couple of decades, there has been increasing
interest in using gravitational lensing to test general relativity beyond the
weak deflection limit. Black holes and neutron stars produce the strong
gravitational fields needed for such tests. For a rotating compact object, the
distinction between prograde and retrograde photon trajectories becomes
important. In this paper, we explore subtleties that arise in interpreting the
bending angle in this context and address the origin of seemingly contradictory
results in the literature. We argue that analogies that cannot be precisely
quantified present a source of confusion
Decay of charged scalar field around a black hole: quasinormal modes of R-N, R-N-AdS and dilaton black holes
It is well known that the charged scalar perturbations of the
Reissner-Nordstrom metric will decay slower at very late times than the neutral
ones, thereby dominating in the late time signal. We show that at the stage of
quasinormal ringing, on the contrary, the neutral perturbations will decay
slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly
extreme RN black hole have the same imaginary parts (damping times) for charged
and neutral perturbations. An explanation of this fact is not clear but,
possibly, is connected with the Choptuik scaling.Comment: 10 pages, LaTeX, 4 figures, considerable changes made and wrong
interpretation of computations correcte
String Theory and Water Waves
We uncover a remarkable role that an infinite hierarchy of non-linear
differential equations plays in organizing and connecting certain {hat c}<1
string theories non-perturbatively. We are able to embed the type 0A and 0B
(A,A) minimal string theories into this single framework. The string theories
arise as special limits of a rich system of equations underpinned by an
integrable system known as the dispersive water wave hierarchy. We observe that
there are several other string-like limits of the system, and conjecture that
some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain
how these and several string-like special points arise and are connected. In
some cases, the framework endows the theories with a non-perturbative
definition for the first time. Notably, we discover that the Painleve IV
equation plays a key role in organizing the string theory physics, joining its
siblings, Painleve I and II, whose roles have previously been identified in
this minimal string context.Comment: 49 pages, 4 figure
Non-magnetic left-handed material
We develop a new approach to build a material with negative refraction index.
In contrast to conventional designs which make use of a resonant behavior to
achieve a non-zero magnetic response, our material is intrinsically
non-magnetic and relies on an anisotropic dielectric constant to provide a
left-handed response in waveguide geometry. We demonstrate that the proposed
material can support surface (polariton) waves, and show the connection between
polaritons and the enhancement of evanescent fields, also referred to as
super-lensing
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