Starting from first principles and general assumptions we present a heuristic argument that shows that Newton’s law of gravitation naturally arises in a theory in which space emerges through a ...holographic scenario. Gravity is identified with an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton’s law of inertia needs to be explained. The equivalence principle auggests that it is actually the law of inertia whose origin is entropic.
Recent theoretical progress indicates that spacetime and gravity
emerge together from the entanglement structure of an underlying
microscopic theory. These ideas are best understood in Anti-de Sitter
...space, where they rely on the area law for entanglement entropy. The
extension to de Sitter space requires taking into account the entropy
and temperature associated with the cosmological horizon. Using insights
from string theory, black hole physics and quantum information theory we
argue that the positive dark energy leads to a thermal volume law
contribution to the entropy that overtakes the area law precisely at the
cosmological horizon. Due to the competition between area and volume law
entanglement the microscopic de Sitter states do not thermalise at
sub-Hubble scales: they exhibit memory effects in the form of an entropy
displacement caused by matter. The emergent laws of gravity contain an
additional ‘dark’ gravitational force describing the ‘elastic’ response
due to the entropy displacement. We derive an estimate of the strength
of this extra force in terms of the baryonic mass, Newton’s constant and
the Hubble acceleration scale
a_0 =cH_0
a
0
=
c
H
0
,
and provide evidence for the fact that this additional ‘dark
gravity force’ explains the observed phenomena in galaxies and clusters
currently attributed to dark matter.
A
bstract
We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS
3
in Poincaré coordinates leads to an ...extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.
A
bstract
We study the semi-classical thermodynamics of two-dimensional de Sitter space (dS
2
) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter. We extend the quasi-local formalism of ...Brown and York to dS
2
, where a timelike boundary is introduced in the static patch to uniquely define conserved charges, including quasi-local energy. The boundary divides the static patch into two systems, a cosmological system and a black hole system, the former being unstable under thermal fluctuations while the latter is stable. A semi-classical quasi-local first law is derived, where the Gibbons–Hawking entropy is replaced by the generalized entropy. In the microcanonical ensemble the generalized entropy is stationary. Further, we show the on-shell Euclidean microcanonical action of a causal diamond in semi-classical JT gravity equals minus the generalized entropy of the diamond, hence extremization of the entropy follows from minimizing the action. Thus, we provide a first principles derivation of the island rule for U(1) symmetric dS
2
backgrounds, without invoking the replica trick. We discuss the implications of our findings for static patch de Sitter holography.
Spacetime fluctuations in AdS/CFT Verlinde, Erik; Zurek, Kathryn M.
The journal of high energy physics,
04/2020, Letnik:
2020, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A
bstract
We compute fluctuations in the modular energy of the vacuum associated with a Rindler-wedge in AdS spacetime in the context of AdS/CFT. We discuss the possible effect of these energy ...fluctuations on the spacetime geometry, and on the traversal time of a light beam propagating from the boundary to the bulk and back.
A universe field theory for JT gravity Post, Boris; van der Heijden, Jeremy; Verlinde, Erik
The journal of high energy physics,
05/2022, Letnik:
2022, Številka:
5
Journal Article
Recenzirano
Odprti dostop
A
bstract
We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean Jackiw-Teitelboim (JT) gravity. We show how the gravitational path ...integral, defined as a sum over topologies, can be reproduced from the perturbative expansion of a Kodaira-Spencer (KS) field theory for the complex structure deformations of the spectral curve. We use that the Schwinger-Dyson equations for the KS theory can be mapped to the topological recursion relations. We refer to this dual description of JT gravity as a ‘universe field theory’. By introducing non-compact D-branes in the target space geometry, we can probe non-perturbative aspects of JT gravity. The relevant operators are obtained through a modification of the JT path integral with Neumann boundary conditions. The KS/JT identification suggests that the ensemble average for JT gravity can be understood in terms of a more standard open/closed duality in topological string theory.
No Page curves for the de Sitter horizon Kames-King, Joshua; Verheijden, Evita M. H.; Verlinde, Erik P.
The journal of high energy physics,
03/2022, Letnik:
2022, Številka:
3
Journal Article
Recenzirano
Odprti dostop
A
bstract
We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies ...an auxiliary system acting as a heat bath both at
I
+
and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the past cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at
I
+
naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer will see unitary evaporation.
We consider the uncertainty in the arm length of an interferometer due to metric fluctuations from the quantum nature of gravity, proposing a concrete microscopic model of energy fluctuations in ...holographic degrees of freedom on the surface bounding a causally connected region of spacetime. In our model, fluctuations longitudinal to the beam direction accumulate in the infrared and feature strong long distance correlation in the transverse direction. This leads to a signal that could be observed in a gravitational wave interferometer. We connect the positional uncertainty principle arising from our calculations to the 't Hooft gravitational S-matrix.
A
bstract
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
AdS
3
×
S
q
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.
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