3,307 research outputs found
General static spherically symmetric solutions in Horava gravity
We derive general static spherically symmetric solutions in the Horava theory
of gravity with nonzero shift field. These represent "hedgehog" versions of
black holes with radial "hair" arising from the shift field. For the case of
the standard de Witt kinetic term (lambda =1) there is an infinity of solutions
that exhibit a deformed version of reparametrization invariance away from the
general relativistic limit. Special solutions also arise in the anisotropic
conformal point lambda = 1/3.Comment: References adde
Matter instability in modified gravity
The Dolgov-Kawasaki instability discovered in the matter sector of the
modified gravity scenario incorporating a 1/R correction to Einstein gravity is
studied in general f(R) theories. A stability condition is found in the metric
version of these theories to help ruling out models that are unviable from the
theoretical point of view.Comment: 4 pages, revtex, to appear in Phys. Rev. D. In the revised version,
an error concerning the Palatini version of these theories has been corrected
and the references update
Gauss-Bonnet black holes with non-constant curvature horizons
We investigate static and dynamical n(\ge 6)-dimensional black holes in
Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an
(n-2)-dimensional Einstein space with a condition on its Weyl tensor originally
given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasi-local
mass that satisfies the unified first law, we show that most of the properties
of the quasi-local mass and the trapping horizon are shared with the case with
horizons of constant curvature. It is shown that the Dotti-Gleiser solution is
the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein
space is non-constant. The quasi-local mass becomes constant for the
Dotti-Gleiser black hole and satisfies the first law of the black-hole
thermodynamics with its Wald entropy. In the non-negative curvature case with
positive Gauss-Bonnet constant and zero cosmological constant, it is shown that
the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes
locally stable for the non-zero cosmological constant, it cannot be globally
stable for the positive cosmological constant.Comment: 15 pages, 1 figure; v2, discussion clarified and references added;
v3, published version; v4, Eqs.(4.22)-(4.24) corrected, which do not change
Eqs.(4.25)-(4.27
Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors
We consider source-free electromagnetic fields in spacetimes possessing a
non-null Killing vector field, . We assume further that the
electromagnetic field tensor, , is invariant under the action of the
isometry group induced by . It is proved that whenever the two
potentials associated with the electromagnetic field are functionally
independent the entire content of Maxwell's equations is equivalent to the
relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation
we argue that it is enough to solve merely Einstein's equation for these
electrovac spacetimes because the relevant equations of motion will be
satisfied automatically. It is also shown that for the exceptional case of
functionally related potentials \n^aT_{ab}=0 implies along with one of the
relevant equations of motion that the complementary equation concerning the
electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+
A Rigorous Derivation of Electromagnetic Self-force
During the past century, there has been considerable discussion and analysis
of the motion of a point charge, taking into account "self-force" effects due
to the particle's own electromagnetic field. We analyze the issue of "particle
motion" in classical electromagnetism in a rigorous and systematic way by
considering a one-parameter family of solutions to the coupled Maxwell and
matter equations corresponding to having a body whose charge-current density
and stress-energy tensor scale to zero size
in an asymptotically self-similar manner about a worldline as . In this limit, the charge, , and total mass, , of the body go to
zero, and goes to a well defined limit. The Maxwell field
is assumed to be the retarded solution associated with
plus a homogeneous solution (the "external field") that varies
smoothly with . We prove that the worldline must be a
solution to the Lorentz force equations of motion in the external field
. We then obtain self-force, dipole forces, and spin force
as first order perturbative corrections to the center of mass motion of the
body. We believe that this is the first rigorous derivation of the complete
first order correction to Lorentz force motion. We also address the issue of
obtaining a self-consistent perturbative equation of motion associated with our
perturbative result, and argue that the self-force equations of motion that
have previously been written down in conjunction with the "reduction of order"
procedure should provide accurate equations of motion for a sufficiently small
charged body with negligible dipole moments and spin. There is no corresponding
justification for the non-reduced-order equations.Comment: 52 pages, minor correction
Hawking radiation from dynamical horizons
In completely local settings, we establish that a dynamically evolving black
hole horizon can be assigned a Hawking temperature. Moreover, we calculate the
Hawking flux and show that the radius of the horizon shrinks.Comment: 5 Page
Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
We consider a globally hyperbolic, stationary spacetime containing a black
hole but no white hole. We assume, further, that the event horizon, \tn, of
the black hole is a Killing horizon with compact cross-sections. We prove that
if surface gravity is non-zero constant throughout the horizon one can {\it
globally} extend such a spacetime so that the image of is a proper
subset of a regular bifurcate Killing horizon in the enlarged spacetime. The
necessary and sufficient conditions are given for the extendibility of matter
fields to the enlarged spacetime. These conditions are automatically satisfied
if the spacetime is static (and, hence ``"-reflection symmetric) or
stationary-axisymmetric with ``" reflection isometry and the matter
fields respect the reflection isometry. In addition, we prove that a necessary
and sufficient condition for the constancy of the surface gravity on a Killing
horizon is that the exterior derivative of the twist of the horizon Killing
field vanish on the horizon. As a corollary of this, we recover a result of
Carter that constancy of surface gravity holds for any black hole which is
static or stationary- axisymmetric with the ``" reflection isometry. No
use of Einstein's equation is made in obtaining any of the above results. Taken
together, these results support the view that any spacetime representing the
asymptotic final state of a black hole formed by gravitational collapse may be
assumed to possess a bifurcate Killing horizon or a Killing horizon with
vanishing surface gravity.Comment: 20 pages, plain te
Black Hole Entropy is Noether Charge
We consider a general, classical theory of gravity in dimensions, arising
from a diffeomorphism invariant Lagrangian. In any such theory, to each vector
field, , on spacetime one can associate a local symmetry and, hence, a
Noether current -form, , and (for solutions to the field
equations) a Noether charge -form, . Assuming only that the
theory admits stationary black hole solutions with a bifurcate Killing horizon,
and that the canonical mass and angular momentum of solutions are well defined
at infinity, we show that the first law of black hole mechanics always holds
for perturbations to nearby stationary black hole solutions. The quantity
playing the role of black hole entropy in this formula is simply times
the integral over of the Noether charge -form associated with
the horizon Killing field, normalized so as to have unit surface gravity.
Furthermore, we show that this black hole entropy always is given by a local
geometrical expression on the horizon of the black hole. We thereby obtain a
natural candidate for the entropy of a dynamical black hole in a general theory
of gravity. Our results show that the validity of the ``second law" of black
hole mechanics in dynamical evolution from an initially stationary black hole
to a final stationary state is equivalent to the positivity of a total Noether
flux, and thus may be intimately related to the positive energy properties of
the theory. The relationship between the derivation of our formula for black
hole entropy and the derivation via ``Euclidean methods" also is explained.Comment: 16 pages, EFI 93-4
Exact dynamical AdS black holes and wormholes with a Klein-Gordon field
We present several classes of exact solutions in the Einstein-Klein-Gordon
system with a cosmological constant. The spacetime has spherical, plane, or
hyperbolic symmetry and the higher-dimensional solutions are obtained in a
closed form only in the plane symmetric case. Among them, the class-I solution
represents an asymptotically locally anti-de Sitter (AdS) dynamical black hole
or wormhole. In four and higher dimensions, the generalized Misner-Sharp
quasi-local mass blows up at AdS infinity, inferring that the spacetime is only
locally AdS. In three dimensions, the scalar field becomes trivial and the
solution reduces to the BTZ black hole.Comment: 11 pages, 2 figures, 2 tables; v2, results strengthened, argument on
trapping horizon corrected; v3, argument on locally AdS property added,
accepted for publication in Physical Review
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