14 research outputs found

### Second law from the Noether current on null hypersurfaces

I study the balance law equation of surface charges in the presence of
background fields. The construction allows a unified description of Noether's
theorem for both global and local symmetries. From the balance law associated
with some of these symmetries, I will discuss generalizations of Wald's Noether
entropy formula and general entropy balance laws on null hypersurfaces based on
the null energy conditions, interpreted as an entropy creation term. The
entropy is generally the so-called improved Noether charge, a quantity that has
recently been investigated by many authors, associated to null future-pointing
diffeomorphisms. These local and dynamical definitions of entropy on the black
hole horizon differ from the Bekenstein-Hawking entropy through terms
proportional to the first derivative of the area along the null geodesics. Two
different definitions of the dynamical entropy are identified, deduced from
gravity symplectic potentials providing a suitable notion of gravitational flux
which vanish on non-expanding horizons. The first one is proposed as a
definition of the entropy for dynamical black holes by Wald and Zhang, and it
satisfies the physical process first law locally. The second one vanishes on
any cross section of Minkowski's light cone. I study general properties of its
balance law. In particular, I look at first order perturbations around a non
expanding horizon. Furthermore, I show that the dynamical entropy increases on
the event horizon formed by a spherical symmetric collapse between the two
stationary states of vanishing flux, i.e the initial flat light cone and the
final stationary black hole. I compare this process to a phase transition, in
which the symmetry group of the stationary black hole phase is enlarged by the
supertranslations.Comment: Accepted in Phys.Rev.D. Clarifications added, some parts have been
cleaned u

### A note on the physical process first law of black hole mechanics

I give a simple proof of the physical process first law of black hole
thermodynamics including charged black holes, in which all perturbations are
computed on the horizon.Comment: v2, 7 pages, 1 figure, minor modifications with respect to v

### Black to white transition of a charged black hole

We present an exact solution of the Maxwell-Einstein equations, which
describes the exterior of a charged spherical mass collapsing into its own
trapping horizon and then bouncing back from an anti-trapping horizon at the
same space location of the same asymptotic region. The solution is locally but
not globally isometric to the maximally extended Reissner-Nordstr\"{o}m metric
and depends on seven parameters. It is regular, and defined everywhere except
for a small region, where quantum tunnelling is expected. This region lies
outside the mass: the mass-bounce and its near exterior are governed by
classical general relativity. We discuss the relevance of this result for the
fate of realistic black holes. We comment on possible effects of the classical
instabilities and the Hawking radiation.Comment: 12 pages, 13 figure

### Covariance and symmetry algebras

In general relativity as well as gauge theories, non-trivial symmetries can
appear at boundaries. In the presence of radiation some of the symmetries are
not Hamiltonian vector fields, hence the definition of charges for the
symmetries becomes delicate. It can lead to the problem of field-dependent
2-cocycles in the charge algebra, as opposed to the central extensions allowed
in standard classical mechanics. We show that if the Wald-Zoupas prescription
is implemented, its covariance requirement guarantees that the algebra of
Noether currents is free of field-dependent 2-cocycles, and its stationarity
requirement further removes central extensions. Therefore the charge algebra
admits at most a time-independent field-dependent 2-cocycle, whose existence
depends on the boundary conditions. We report on new results for asymptotic
symmetries at future null infinity that can be derived with this approach.Comment: 10 page

### General gravitational charges on null hypersurfaces

We perform a detailed study of the covariance properties of the symplectic
potential of general relativity on a null hypersurface, and of the different
polarizations that can be used to study conservative as well as leaky boundary
conditions. This allows us to identify a one-parameter family of covariant
symplectic potentials. We compute the charges and fluxes for the most general
phase space with arbitrary variations. We study five symmetry groups that arise
when different restrictions on the variations are included, two of which are
new. Requiring stationarity as in the original Wald-Zoupas prescription selects
a unique member of the family of symplectic potentials, the one of
Chandrasekaran, Flanagan and Prabhu. The associated charges are all conserved
on non-expanding horizons, but not on flat spacetime. We show that it is
possible to require a weaker notion of stationarity which selects another
symplectic potential, again in a unique way, and whose charges are conserved on
both non-expanding horizons and flat light-cones. Furthermore, the flux of
future-pointing diffeomorphisms at leading-order around an outgoing flat
light-cone is positive and reproduces a tidal heating plus a memory term. We
also study the conformal conservative boundary conditions suggested by the
alternative polarization and identify under which conditions they define a
non-ambiguous variational principle. Our results have applications for
dynamical notions of entropy, and are useful to clarify the interplay between
different boundary conditions, charge prescriptions, and symmetry groups that
can be associated with a null boundary.Comment: 54 pages. v2: Improved text, minor corrections, references adde

### Wald-Zoupas prescription with (soft) anomalies

We show that the Wald-Zoupas prescription for gravitational charges is valid
in the presence of anomalies and field-dependent diffeomorphism, but only if
these are related to one another in a specific way. The geometric
interpretation of the allowed anomalies is exposed looking at the example of
BMS symmetries: They correspond to soft terms in the charges. We determine if
the Wald-Zoupas prescription coincides with an improved Noether charge. The
necessary condition is a certain differential equation, and when it is
satisfied, the boundary Lagrangian of the resulting improved Noether charge
contains in general a non-trivial corner term that can be identified a priori
from a condition of anomaly-freeness. Our results explain why the Wald-Zoupas
prescription works in spite of the anomalous behaviour of BMS transformations,
and should be helpful to relate different branches of the literature on surface
charges.Comment: 19 pages plus Appendix. V2: many improvements to the text,
clarifications added, improved comparison with the results in the literature.
More general analysis of the WZ covariance requirement, leading to a simpler
discussion of some results at future null infinity. V3: minor amendments,
matches published versio

### Thermodynamics of precision in quantum nanomachines

Fluctuations strongly affect the dynamics and functionality of nanoscale thermal machines. Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations. These relations imply that increasing the reliability or precision of an engine's power output comes at a greater thermodynamic cost. Here we study the thermodynamics of precision for small thermal machines in the quantum regime. In particular, we derive exact relations between the power, power fluctuations, and entropy production rate for several models of few-qubit engines (both autonomous and cyclic) that perform work on a quantized load. Depending on the context, we find that quantum coherence can either help or hinder where power fluctuations are concerned. We discuss design principles for reducing such fluctuations in quantum nanomachines and propose an autonomous three-qubit engine whose power output for a given entropy production is more reliable than would be allowed by any classical Markovian model

### Second law from the Noether current on null hypersurfaces

International audienceI study the balance law equation of surface charges in the presence of background fields. The construction allows a unified description of Noether's theorem for both global and local symmetries. From the balance law associated with some of these symmetries, I will discuss generalizations of Wald's Noether entropy formula and general entropy balance laws on null hypersurfaces based on the null energy conditions, interpreted as an entropy creation term. The entropy is generally the so-called improved Noether charge, a quantity that has recently been investigated by many authors, associated to null future-pointing diffeomorphisms. These local and dynamical definitions of entropy on the black hole horizon differ from the Bekenstein-Hawking entropy through terms proportional to the first derivative of the area along the null geodesics. Two different definitions of the dynamical entropy are identified, deduced from gravity symplectic potentials providing a suitable notion of gravitational flux which vanish on non-expanding horizons. The first one is proposed as a definition of the entropy for dynamical black holes by Wald and Zhang, and it satisfies the physical process first law locally. The second one vanishes on any cross section of Minkowski's light cone. I study general properties of its balance law. In particular, I look at first order perturbations around a non expanding horizon. Furthermore, I show that the dynamical entropy increases on the event horizon formed by a spherical symmetric collapse between the two stationary states of vanishing flux, i.e the initial flat light cone and the final stationary black hole. I compare this process to a phase transition, in which the symmetry group of the stationary black hole phase is enlarged by the supertranslations

### Wald-Zoupas prescription with (soft) anomalies

We show that the Wald-Zoupas prescription for gravitational charges is valid in the presence of anomalies and field-dependent diffeomorphism, but only if these are related to one another in a specific way. The geometric interpretation of the allowed anomalies is exposed looking at the example of BMS symmetries: They correspond to soft terms in the charges. We determine if the Wald-Zoupas prescription coincides with an improved Noether charge. The necessary condition is a certain differential equation, and when it is satisfied, the boundary Lagrangian of the resulting improved Noether charge contains in general a non-trivial corner term that can be identified a priori from a condition of anomaly-freeness. Our results explain why the Wald-Zoupas prescription works in spite of the anomalous behaviour of BMS transformations, and should be helpful to relate different branches of the literature on surface charges