86 research outputs found
From qubits to black holes: entropy, entanglement and all that
Entropy plays a crucial role in characterization of information and
entanglement, but it is not a scalar quantity and for many systems it is
different for different relativistic observers. Loop quantum gravity predicts
the Bekenstein-Hawking term for black hole entropy and logarithmic correction
to it. The latter originates in the entanglement between the pieces of spin
networks that describe black hole horizon. Entanglement between gravity and
matter may restore the unitarity in the black hole evaporation process. If the
collapsing matter is assumed to be initially in a pure state, then entropy of
the Hawking radiation is exactly the created entanglement between matter and
gravity.Comment: Honorable Mention in the 2005 Gravity Research Foundation Essay
Competitio
Ground state entanglement and geometric entropy in the Kitaev's model
We study the entanglement properties of the ground state in Kitaev's model.
This is a two-dimensional spin system with a torus topology and nontrivial
four-body interactions between its spins. For a generic partition of
the lattice we calculate analytically the von Neumann entropy of the reduced
density matrix in the ground state. We prove that the geometric
entropy associated with a region is linear in the length of its boundary.
Moreover, we argue that entanglement can probe the topology of the system and
reveal topological order. Finally, no partition has zero entanglement and we
find the partition that maximizes the entanglement in the given ground state.Comment: 4 pages, one fig, ReVTeX 4; updated to the published versio
Statistical Origin of Black Hole Entropy in Matrix Theory
The statistical entropy of black holes in M-theory is considered. Assuming
Matrix theory is the discretized light-cone quantization of a theory with
eleven-dimensional Lorentz invariance, we map the counting problem onto the
original Gibbons-Hawking calculation of the thermodynamic entropy.Comment: 9 pages, harvmac, (v2 References added, typo fixed), (v3 Some
clarifying comments added.
Soliton Induced Singularities in 2 d Gravity and their Evaporation
Positive energy singularities induced by Sine-Gordon solitons in 1+1
dimensional dilaton gravity with positive and negative cosmological constant
are considered. When the cosmological constant is positive, the singularities
combine a white hole, a timelike singularity and a black hole joined smoothly
near the soliton center. When the cosmological constant is negative, the
solutions describe two timelike singularities joined smoothly near the soliton
center. We describe these spacetimes and examine their evaporation in the one
loop approximation.Comment: 15 pages (37.7 kb), PHYZZX. Figures available from authors
Entropy in the RST Model
The RST Model is given boundary term and Z-field so that it is well-posed and
local. The Euclidean method is described for general theory and used to
calculate the RST intrinsic entropy. The evolution of this entropy for the
shockwave solutions is found and obeys a second law.Comment: 10 pages, minor revisions, published version in Late
A Proof of the Generalized Second Law for Two-Dimensional Black Holes
We investigate the generalized second law for two-dimensional black holes in
equilibrium (Hartle-Hawking) and nonequilibrium (Unruh) with the heat bath
surrounding the black holes. We obtain a simple expression for the change of
total entropy in terms of covariant thermodynamic variables, which is valid not
only for the Hartle-Hawking state but also for the Unruh state up to leading
order, without assuming a quasi-stationary evolution of the black holes. Using
this expression, it is shown that the rate of local entropy production is
non-negative in the two-dimensional black hole systems.Comment: 15 pages, boundary condition of static black hole is added to clarify
the situation, abstract and section 4 (concluding remarks) is rewritten, and
minor corrections, references adde
Unruh Radiation, Holography and Boundary Cosmology
A uniformly acclerated observer in anti-deSitter space-time is known to
detect thermal radiation when the acceleration exceeds a critical value. We
investigate the holographic interpretation of this phenomenon. For uniformly
accelerated trajectories transverse to the boundary of the AdS space, the
hologram is a blob which expands along the boundary. Observers on the boundary
co-moving with the hologram become observers in cosmological space-times. For
supercritical accelerations one gets a Milne universe when the holographic
screen is the boundary in Poincare coordinates, while for the boundary in
hyperspherical coordinates one gets deSitter spacetimes. The presence or
absence of thermality is then interpreted in terms of specific classes of
observers in these cosmologies.Comment: LaTeX, 35 pages, 3 figures. A reference is added and typos are
correcte
Hawking Radiation and Unitary evolution
We find a family of exact solutions to the semi-classical equations
(including back-reaction) of two-dimensional dilaton gravity, describing
infalling null matter that becomes outgoing and returns to infinity without
forming a black hole. When a black hole almost forms, the radiation reaching
infinity in advance of the original outgoing null matter has the properties of
Hawking radiation. The radiation reaching infinity after the null matter
consists of a brief burst of negative energy that preserves unitarity and
transfers information faster than the theoretical bound for positive energy.Comment: LaTex file + uuencoded ps version including 4 figure
Degrees of freedom in two dimensional string theory
We discuss two issues regarding the question of degrees of freedom in two
dimensional string theory. The first issue relates to the classical limit of
quantum string theory. In the classical theory one requires an infinite number
of fields in addition to the collective field to describe ``folds'' on the
fermi surface. We argue that in the quantum theory these are not additional
degrees of freedom. Rather they represent quantum dispersions of the collective
field which are {\em not} suppressed when whenever a fold
is present, thus leading to a nontrivial classical limit. The second issue
relates to the ultraviolet properties of the geometric entropy. We argue that
the geometric entropy is finite in the ultraviolet due to {\em nonperturbative}
effects. This indicates that the true degrees of freedom of the two dimensional
string at high energies is much smaller than what one naively expects.
(Based on talks at Spring Workshop on String theory and Quantum Gravity,
ICTP, Trieste, March 1995 and VIIth Regional Conference on Mathematical
Physics, Bandar-Anzali, October 1995.)Comment: 18 pages, LaTe
Does the generalized second law hold in the form of time derivative expression?
We investigate whether the generalized second law is valid, using two
dimensional black hole spacetime, irrespective of models. A time derivative
form of the generalized second law is formulated and it is shown that the law
might become invalid. The way to resolve this difficulty is also presented and
discussed.Comment: 12 pages, 3 figures, revte
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