72 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
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
Thermodynamics of the two-dimensional black hole in the Teitelboim-Jackiw theory
The two-dimensional theory of Teitelboim and Jackiw has constant and negative
curvature. In spite of this, the theory admits a black hole solution with no
singularities. In this work we study the thermodynamics of this black hole
using York's formalism.Comment: 16 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
The information paradox and the locality bound
Hawking's argument for information loss in black hole evaporation rests on
the assumption of independent Hilbert spaces for the interior and exterior of a
black hole. We argue that such independence cannot be established without
incorporating strong gravitational effects that undermine locality and
invalidate the use of quantum field theory in a semiclassical background
geometry. These considerations should also play a role in a deeper
understanding of horizon complementarity.Comment: 21 pages, harvmac; v2-3. minor corrections, references adde
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
Solving the Simplest Theory of Quantum Gravity
We solve what is quite likely the simplest model of quantum gravity, the
worldsheet theory of an infinitely long, free bosonic string in Minkowski
space. Contrary to naive expectations, this theory is non-trivial. We
illustrate this by constructing its exact factorizable S-matrix. Despite its
simplicity, the theory exhibits many of the salient features expected from more
mature quantum gravity models, including the absence of local off-shell
observables, a minimal length, a maximum achievable (Hagedorn) temperature, as
well as (integrable relatives of) black holes. All these properties follow from
the exact S-matrix. We show that the complete finite volume spectrum can be
reconstructed analytically from this S-matrix with the help of the
thermodynamic Bethe Ansatz. We argue that considered as a UV complete
relativistic two-dimensional quantum field theory the model exhibits a new type
of renormalization group flow behavior, "asymptotic fragility". Asymptotically
fragile flows do not originate from a UV fixed point.Comment: 32+4 pages, 1 figure, v2: typos fixed, published versio
Non-zero entropy density in the XY chain out of equilibrium
The von Neumann entropy density of a block of n spins is proved to be
non-zero for large n in the non-equilibrium steady state of the XY chain
constructed by coupling a finite cutout of the chain to the two infinite parts
to its left and right which act as thermal reservoirs at different
temperatures. Moreover, the non-equilibrium density is shown to be strictly
greater than the density in thermal equilibrium
Geometric Entropy of Nonrelativistic Fermions and Two Dimensional Strings
We consider the geometric entropy of free nonrelativistic fermions in two
dimensions and show that it is ultraviolet finite for finite fermi energies,
but divergent in the infrared. In terms of the corresponding collective field
theory this is a {\em nonperturbative} effect and is related to the soft
behaviour of the usual thermodynamic entropy at high temperatures. We then show
that thermodynamic entropy of the singlet sector of the one dimensional matrix
model at high temperatures is governed by nonperturbative effects of the
underlying string theory. In the high temperature limit the ``exact''
expression for the entropy is regular but leads to a negative specific heat,
thus implying an instability. We speculate that in a properly defined two
dimensional string theory, the thermodynamic entropy could approach a constant
at high temperatures and lead to a geometric entropy which is finite in the
ultraviolet.Comment: LaTex, 19 pages, no figures. Some references adde
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