257 research outputs found
BMS invariance and the membrane paradigm
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry
group of asymptotically flat spacetime. It is infinite dimensional and entails
an infinite number of conservation laws. According to the black hole membrane
paradigm, null infinity (in asymptotically flat spacetime) and black hole event
horizons behave like fluid membranes. The fluid dynamics of the membrane is
governed by an infinite set of symmetries and conservation laws. Our main
result is to point out that the infinite set of symmetries and conserved
charges of the BMS group and the membrane paradigm are the same. This
relationship has several consequences. First, it sheds light on the physical
interpretation of BMS conservation laws. Second, it generalizes the BMS
conservation laws to arbitrary subregions of arbitrary null surfaces. Third, it
clarifies the identification of the superrotation subgroup of the BMS group. We
briefly comment on the black hole information problem.Comment: 16 pages, 1 figur
Black hole Meissner effect and entanglement
Extremal black holes tend to expel magnetic and electric fields. Fields are
unable to reach the horizon because the length of the black hole throat blows
up in the extremal limit. The length of the throat is related to the amount of
entanglement between modes on either side of the horizon. So it is natural to
try to relate the black hole Meissner effect to entanglement. We derive the
black hole Meissner effect directly from the low temperature limit of two-point
functions in the Hartle-Hawking vacuum. Then we discuss several new examples of
the black hole Meissner effect, its applications to astrophysics, and its
relationship to gauge invariance
Energy extraction from boosted black holes: Penrose process, jets, and the membrane at infinity
Numerical simulations indicate that black holes carrying linear momentum
and/or orbital momentum can power jets. The jets extract the kinetic energy
stored in the black hole's motion. This could provide an important
electromagnetic counterpart to gravitational wave searches. We develop the
theory underlying these jets. In particular, we derive the analogues of the
Penrose process and the Blandford-Znajek jet power prediction for boosted black
holes. The jet power we find is , where is the
hole's velocity, is its mass, and is the magnetic flux. We show that
energy extraction from boosted black holes is conceptually similar to energy
extraction from spinning black holes. However, we highlight two key technical
differences: in the boosted case, jet power is no longer defined with respect
to a Killing vector, and the relevant notion of black hole mass is observer
dependent. We derive a new version of the membrane paradigm in which the
membrane lives at infinity rather than the horizon and we show that this is
useful for interpreting jets from boosted black holes. Our jet power prediction
and the assumptions behind it can be tested with future numerical simulations.Comment: 14 pages, 5 figures, updated to match Phys. Rev. D versio
Black hole jet power from impedance matching
Black hole jet power depends on the angular velocity of magnetic field lines,
. Force-free black hole magnetospheres typically have
, where is the angular velocity of
the horizon. We give a streamlined proof of this result using an extension of
the classical black hole membrane paradigm. The proof is based on an
impedance-matching argument between membranes at the horizon and infinity. Then
we consider a general relativistic magnetohydrodynamic simulation of an
accreting, spinning black hole and jet. We find that the theory correctly
describes the simulation in the jet region. However, the field lines threading
the horizon near the equator have much smaller because the
force-free approximation breaks down in the accretion flow.Comment: 8 pages, 8 figures, updated to match Phys. Rev. D versio
Are entangled particles connected by wormholes? Support for the ER=EPR conjecture from entropy inequalities
If spacetime is built out of quantum bits, does the shape of space depend on
how the bits are entangled? The ER=EPR conjecture relates the entanglement
entropy of a collection of black holes to the cross sectional area of
Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the
geometrical entropy of classical ER bridges satisfies the subadditivity,
triangle, strong subadditivity, and CLW inequalities. These are nontrivial
properties of entanglement entropy, so this is evidence for ER=EPR. We further
show that the entanglement entropy associated to classical ER bridges has
nonpositive interaction information. This is not a property of entanglement
entropy, in general. For example, the entangled four qubit pure state
|GHZ_4>=(|0000>+|1111>)/\sqrt{2} has positive interaction information, so this
state cannot be described by a classical ER bridge. Large black holes with
massive amounts of entanglement between them can fail to have a classical ER
bridge if they are built out of |GHZ_4> states. States with nonpositive
interaction information are called monogamous. We conclude that classical ER
bridges require monogamous EPR correlations.Comment: 11 pages, 4 figure
Asymptotic symmetries of three dimensional gravity and the membrane paradigm
The asymptotic symmetry group of three-dimensional (anti) de Sitter space is
the two dimensional conformal group with central charge . Usually
the asymptotic charge algebra is derived using the symplectic structure of the
bulk Einstein equations. Here, we derive the asymptotic charge algebra by a
different route. First, we formulate the dynamics of the boundary as a
1+1-dimensional dynamical system. Then we realize the boundary equations of
motion as a Hamiltonian system on the dual Lie algebra, , of
the two-dimensional conformal group. Finally, we use the Lie-Poisson bracket on
to compute the asymptotic charge algebra. This streamlines the
derivation of the asymptotic charge algebra because the Lie-Poisson bracket on
the boundary is significantly simpler than the symplectic structure derived
from the bulk Einstein equations. It also clarifies the analogy between the
infinite dimensional symmetries of gravity and fluid dynamics.Comment: 15 page
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