33 research outputs found
Gravitational Thermodynamics of Causal Diamonds in (A)dS
The static patch of de Sitter spacetime and the Rindler wedge of Minkowski
spacetime are causal diamonds admitting a true Killing field, and they behave
as thermodynamic equilibrium states under gravitational perturbations. We
explore the extension of this gravitational thermodynamics to all causal
diamonds in maximally symmetric spacetimes. Although such diamonds generally
admit only a conformal Killing vector, that seems in all respects to be
sufficient. We establish a Smarr formula for such diamonds and a "first law"
for variations to nearby solutions. The latter relates the variations of the
bounding area, spatial volume of the maximal slice, cosmological constant, and
matter Hamiltonian. The total Hamiltonian is the generator of evolution along
the conformal Killing vector that preserves the diamond. To interpret the first
law as a thermodynamic relation, it appears necessary to attribute a negative
temperature to the diamond, as has been previously suggested for the special
case of the static patch of de Sitter spacetime. With quantum corrections
included, for small diamonds we recover the "entanglement equilibrium" result
that the generalized entropy is stationary at the maximally symmetric vacuum at
fixed volume, and we reformulate this as the stationarity of free conformal
energy with the volume not fixed.Comment: v3: 64 pages, 6 appendices, 8 figures; matches published versio
Hints towards the Emergent Nature of Gravity
A possible way out of the conundrum of quantum gravity is the proposal that
general relativity (GR) is not a fundamental theory but emerges from an
underlying microscopic description. Despite recent interest in the emergent
gravity program within the physics as well as the philosophy community, an
assessment of the theoretical evidence for this idea is lacking at the moment.
We intend to fill this gap in the literature by discussing the main arguments
in favour of the hypothesis that the metric field and its dynamics are
emergent. First, we distinguish between microstructure inspired from GR, such
as through quantization or discretization, and microstructure that is not
directly motivated from GR, such as strings, quantum bits or condensed matter
fields. The emergent gravity approach can then be defined as the view that the
metric field and its dynamics are derivable from the latter type of
microstructure. Subsequently, we assess in how far the following properties of
(semi-classical) GR are suggestive of underlying microstructure: (1) the
metric's universal coupling to matter fields, (2) perturbative
non-renormalizability, (3) black hole thermodynamics, and (4) the holographic
principle. In the conclusion we formalize the general structure of the
plausibility arguments put forward.Comment: 36 pages, v2: minor additions, references added. Journal version in
Studies in History and Philosophy of Modern Physic
Holographic Thermodynamics Requires a Chemical Potential for Color
The thermodynamic Euler equation for high-energy states of large- gauge
theories is derived from the dependence of the extensive quantities on the
number of colors . This Euler equation relates the energy of the state to
the temperature, entropy, number of degrees of freedom and its chemical
potential, but not to the volume or pressure. In the context of the
gauge/gravity duality we show that the Euler equation is dual to the
generalized Smarr formula for black holes in the presence of a negative
cosmological constant. We also match the fundamental variational equation of
thermodynamics to the first law of black hole mechanics, when extended to
include variations of the cosmological constant and Newton's constant.Comment: 9 pages, v2: corrected reference to Karch-Robinson, clarified regime
of validity of holographic Euler equation, and fixed typos; v3: reorganized
and rewritten, added a brief discussion about Lifshitz black holes and a new
section on comparison with previous literatur
Entropy of causal diamond ensembles
We define a canonical ensemble for a gravitational causal diamond by
introducing an artificial York boundary inside the diamond with a fixed induced
metric and temperature, and evaluate the partition function using a saddle
point approximation. For Einstein gravity with zero cosmological constant there
is no exact saddle with a horizon, however the portion of the Euclidean diamond
enclosed by the boundary arises as an approximate saddle in the
high-temperature limit, in which the saddle horizon approaches the boundary.
This high-temperature partition function provides a statistical interpretation
of the recent calculation of Banks, Draper and Farkas, in which the entropy of
causal diamonds is recovered from a boundary term in the on-shell Euclidean
action. In contrast, with a positive cosmological constant, as well as in
Jackiw-Teitelboim gravity with or without a cosmological constant, an exact
saddle exists with a finite boundary temperature, but in these cases the causal
diamond is determined by the saddle rather than being selected a priori.Comment: 15 pages, 3 figures, v3: added references and edited introductio
Partition function for a volume of space
We consider the quantum gravity partition function that counts the dimension
of the Hilbert space of a spatial region with topology of a ball and fixed
proper volume, and evaluate it in the leading order saddle point approximation.
The result is the exponential of the Bekenstein-Hawking entropy associated with
the area of the saddle ball boundary, and is reliable within effective field
theory provided the mild curvature singularity at the ball boundary is
regulated by higher curvature terms. This generalizes the classic
Gibbons-Hawking computation of the de Sitter entropy for the case of positive
cosmological constant and unconstrained volume, and hence exhibits the
holographic nature of nonperturbative quantum gravity in generic finite volumes
of space.Comment: 10 pages plus appendices, 2 figures, v2: added figure and improved
presentatio
Towards non-AdS Holography via the Long String Phenomenon
The microscopic description of AdS space obeys the holographic principle in
the sense that the number of microscopic degrees of freedom is given by the
area of the holographic boundary. We assume the same applies to the microscopic
holographic theories for non-AdS spacetimes, specifically for Minkowski, de
Sitter, and AdS below its curvature radius. By taking general lessons from
AdS/CFT we derive the cut-off energy of the holographic theories for these
non-AdS geometries. Contrary to AdS/CFT, the excitation energy decreases
towards the IR in the bulk, which is related to the negative specific heat of
black holes. We construct a conformal mapping between the non-AdS geometries
and spacetimes, and relate the microscopic properties
of the holographic theories for non-AdS spaces to those of symmetric product
CFTs. We find that the mechanism responsible for the inversion of the
energy-distance relation corresponds to the long string phenomenon. This same
mechanism naturally explains the negative specific heat for non-AdS black holes
and the value of the vacuum energy in (A)dS spacetimes.Comment: 38+3 pages, 5 figures. v2: typos corrected, references added. v3:
added refs and clarifications in the conclusion; matches published versio
Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
Quantum extremal surfaces (QES), codimension-2 spacelike regions which extremize the generalized entropy of a gravity-matter system, play a key role in the study of the black hole information problem. The thermodynamics of QESs, however, has been largely unexplored, as a proper interpretation requires a detailed understanding of backreaction due to quantum fields. We investigate this problem in semi-classical Jackiw-Teitelboim (JT) gravity, where the spacetime is the eternal two-dimensional Anti-de Sitter (AdS2) black hole, Hawking radiation is described by a conformal field theory with central charge c, and backreaction effects may be analyzed exactly. We show the Wald entropy of the semi-classical JT theory entirely encapsulates the generalized entropy β including time-dependent von Neumann entropy contributions β whose extremization leads to a QES lying just outside of the black hole horizon. Consequently, the QES defines a Rindler wedge nested inside the enveloping black hole. We use covariant phase space techniques on a time-reflection symmetric slice to derive a Smarr relation and first law of nested Rindler wedge thermodynamics, regularized using local counterterms, and intrinsically including semi-classical effects. Moreover, in the microcanonical ensemble the semi-classical first law implies the generalized entropy of the QES is stationary at fixed energy. Thus, the thermodynamics of the nested Rindler wedge is equivalent to the thermodynamics of the QES in the microcanonical ensemble