Delta Institute for Theoretical Physics

We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:msub><a:mrow><a:mi>M</a:mi></a:mrow><a:mrow><a:mo stretchy="false">⊙</a:mo></a:mrow></a:msub></a:mrow></a:math> during the first and second observing runs of the advanced gravitational-wave detector network. During the first observing run (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>O</d:mi><d:mn>1</d:mn></d:math>), from September 12, 2015 to January 19, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>O</f:mi><f:mn>2</f:mn></f:math>), which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msubsup><h:mrow><h:mn>18.6</h:mn></h:mrow><h:mrow><h:mo>−</h:mo><h:mn>0.7</h:mn></h:mrow><h:mrow><h:mo>+</h:mo><h:mn>3.2</h:mn></h:mrow></h:msubsup><h:mtext> </h:mtext><h:mtext> </h:mtext><h:msub><h:mrow><h:mi>M</h:mi></h:mrow><h:mrow><h:mo stretchy="false">⊙</h:mo></h:mrow></h:msub></h:mrow></h:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mn>84.4</k:mn><k:mrow><k:mo>−</k:mo><k:mn>11.1</k:mn></k:mrow><k:mrow><k:mo>+</k:mo><k:mn>15.8</k:mn></k:mrow></k:msubsup><k:mtext> </k:mtext><k:mtext> </k:mtext><k:msub><k:mrow><k:mi>M</k:mi></k:mrow><k:mrow><k:mo stretchy="false">⊙</k:mo></k:mrow></k:msub></k:math> and range in distance between <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msubsup><n:mn>320</n:mn><n:mrow><n:mo>−</n:mo><n:mn>110</n:mn></n:mrow><n:mrow><n:mo>+</n:mo><n:mn>120</n:mn></n:mrow></n:msubsup></n:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:msubsup><p:mrow><p:mn>2840</p:mn></p:mrow><p:mrow><p:mo>−</p:mo><p:mn>1360</p:mn></p:mrow><p:mrow><p:mo>+</p:mo><p:mn>1400</p:mn></p:mrow></p:msubsup><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>Mpc</p:mi></p:mrow></p:math>. No neutron star–black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mn>110</r:mn><r:mo>−</r:mo><r:mn>3840</r:mn><r:mtext> </r:mtext><r:mtext> </r:mtext><r:msup><r:mrow><r:mi>Gpc</r:mi></r:mrow><r:mrow><r:mo>−</r:mo><r:mn>3</r:mn></r:mrow></r:msup><r:mtext> </r:mtext><r:msup><r:mrow><r:mi mathvariant="normal">y</r:mi></r:mrow><r:mrow><r:mo>−</r:mo><r:mn>1</r:mn></r:mrow></r:msup></r:mrow></r:math> for binary neutron stars and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mn>9.7</u:mn><u:mo>−</u:mo><u:mn>101</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:msup><u:mrow><u:mi>Gpc</u:mi></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>3</u:mn></u:mrow></u:msup><u:mtext> </u:mtext><u:msup><u:mrow><u:mi mathvariant="normal">y</u:mi></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>1</u:mn></u:mrow></u:msup></u:mrow></u:math> for binary black holes assuming fixed population distributions and determine a neutron star–black hole merger rate 90% upper limit of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mrow><x:mn>610</x:mn><x:mtext> </x:mtext><x:mtext> </x:mtext><x:msup><x:mrow><x:mi>Gpc</x:mi></x:mrow><x:mrow><x:mo>−</x:mo><x:mn>3</x:mn></x:mrow></x:msup><x:mtext> </x:mtext><x:msup><x:mrow><x:mi mathvariant="normal">y</x:mi></x:mrow><x:mrow><x:mo>−</x:mo><x:mn>1</x:mn></x:mrow></x:msup></x:mrow></x:math>. Published by the American Physical Society 2019

We report on gravitational-wave discoveries from compact binary coalescences detected by Advanced LIGO and Advanced Virgo in the first half of the third observing run (O3a) between 1 April 2019 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>15</a:mn><a:mo>∶</a:mo><a:mn>00</a:mn></a:mrow></a:math> UTC and 1 October 2019 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>15</c:mn><c:mo>∶</c:mo><c:mn>00</c:mn></c:mrow></c:math> UTC. By imposing a false-alarm-rate threshold of two per year in each of the four search pipelines that constitute our search, we present 39 candidate gravitational-wave events. At this threshold, we expect a contamination fraction of less than 10%. Of these, 26 candidate events were reported previously in near-real time through gamma-ray coordinates network notices and circulars; 13 are reported here for the first time. The catalog contains events whose sources are black hole binary mergers up to a redshift of approximately 0.8, as well as events whose components cannot be unambiguously identified as black holes or neutron stars. For the latter group, we are unable to determine the nature based on estimates of the component masses and spins from gravitational-wave data alone. The range of candidate event masses which are unambiguously identified as binary black holes (both objects <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>≥</e:mo><e:mn>3</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:msub><e:mi>M</e:mi><e:mo stretchy="false">⊙</e:mo></e:msub></e:math>) is increased compared to GWTC-1, with total masses from approximately <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>14</h:mn><h:mtext> </h:mtext><h:mtext> </h:mtext><h:msub><h:mi>M</h:mi><h:mo stretchy="false">⊙</h:mo></h:msub></h:math> for GW190924_021846 to approximately <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>150</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:msub><k:mi>M</k:mi><k:mo stretchy="false">⊙</k:mo></k:msub></k:math> for GW190521. For the first time, this catalog includes binary systems with significantly asymmetric mass ratios, which had not been observed in data taken before April 2019. We also find that 11 of the 39 events detected since April 2019 have positive effective inspiral spins under our default prior (at 90% credibility), while none exhibit negative effective inspiral spin. Given the increased sensitivity of Advanced LIGO and Advanced Virgo, the detection of 39 candidate events in approximately 26 weeks of data (approximately 1.5 per week) is consistent with GWTC-1. Published by the American Physical Society 2021

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.

Abstract On 2019 April 25, the LIGO Livingston detector observed a compact binary coalescence with signal-to-noise ratio 12.9. The Virgo detector was also taking data that did not contribute to detection due to a low signal-to-noise ratio, but were used for subsequent parameter estimation. The 90% credible intervals for the component masses range from to ( – if we restrict the dimensionless component spin magnitudes to be smaller than 0.05). These mass parameters are consistent with the individual binary components being neutron stars. However, both the source-frame chirp mass and the total mass of this system are significantly larger than those of any other known binary neutron star (BNS) system. The possibility that one or both binary components of the system are black holes cannot be ruled out from gravitational-wave data. We discuss possible origins of the system based on its inconsistency with the known Galactic BNS population. Under the assumption that the signal was produced by a BNS coalescence, the local rate of neutron star mergers is updated to 250–2810 .

We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light-quark and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and Z production in the forward region at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. We also include for the first time top-quark pair differential distributions and the transverse momentum of the Z bosons from ATLAS and CMS. We investigate the impact of parametrizing charm and provide evidence that the accuracy and stability of the PDFs are thereby improved. We study the impact of the new data by producing a variety of determinations based on reduced datasets. We find that both improvements have a significant impact on the PDFs, with some substantial reductions in uncertainties, but with the new PDFs generally in agreement with the previous set at the one-sigma level. The most significant changes are seen in the light-quark flavor separation, and in increased precision in the a e-mail: stefano.forte

On May 21, 2019 at 03:02:29 UTC Advanced LIGO and Advanced Virgo observed a short duration gravitational-wave signal, GW190521, with a three-detector network signal-to-noise ratio of 14.7, and an estimated false-alarm rate of 1 in 4900 yr using a search sensitive to generic transients. If GW190521 is from a quasicircular binary inspiral, then the detected signal is consistent with the merger of two black holes with masses of 85_{-14}^{+21} M_{⊙} and 66_{-18}^{+17} M_{⊙} (90% credible intervals). We infer that the primary black hole mass lies within the gap produced by (pulsational) pair-instability supernova processes, with only a 0.32% probability of being below 65 M_{⊙}. We calculate the mass of the remnant to be 142_{-16}^{+28} M_{⊙}, which can be considered an intermediate mass black hole (IMBH). The luminosity distance of the source is 5.3_{-2.6}^{+2.4} Gpc, corresponding to a redshift of 0.82_{-0.34}^{+0.28}. The inferred rate of mergers similar to GW190521 is 0.13_{-0.11}^{+0.30} Gpc^{-3} yr^{-1}.

Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gau

We show that the time dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some Hamiltonian and then evolves without dissipation according to some other Hamiltonian, may be extracted using methods of boundary critical phenomena in d + 1 dimensions. For d = 1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.

The Einstein Telescope (ET), a proposed European ground-based gravitational-wave detector of third-generation, is an evolution of second-generation detectors such as Advanced LIGO, Advanced Virgo, and KAGRA which could be operating in the mid 2030s. ET will explore the universe with gravitational waves up to cosmological distances. We discuss its main scientific objectives and its potential for discoveries in astrophysics, cosmology and fundamental physics.

The Einstein Telescope (ET), a proposed European ground-based gravitational-wave detector of third-generation, is an evolution of second-generation detectors such as Advanced LIGO, Advanced Virgo, and KAGRA which could be operating in the mid 2030s. ET will explore the universe with gravitational waves up to cosmological distances. We discuss its main scientific objectives and its potential for discoveries in astrophysics, cosmology and fundamental physics.

Abstract We report on the population of 47 compact binary mergers detected with a false-alarm rate of &lt; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi>yr</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> in the second LIGO–Virgo Gravitational-Wave Transient Catalog. We observe several characteristics of the merging binary black hole (BBH) population not discernible until now. First, the primary mass spectrum contains structure beyond a power law with a sharp high-mass cutoff; it is more consistent with a broken power law with a break at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>39.7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>9.1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>20.3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> or a power law with a Gaussian feature peaking at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>33.1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>4.0</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> (90% credible interval). While the primary mass distribution must extend to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>∼</mml:mo> <mml:mn>65</mml:mn> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> or beyond, only <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>2.9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>3.5</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>%</mml:mo> </mml:math> of systems have primary masses greater than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>45</mml:mn> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> . Second, we find that a fraction of BBH systems have component spins misaligned with the orbital angular momentum, giving rise to precession of the orbital plane. Moreover, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>12</mml:mn> </mml:math> %– <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>44</mml:mn> </mml:math> % of BBH systems have spins tilted by more than 90°, giving rise to a negative effective inspiral spin parameter, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>eff</mml:mi> </mml:mrow> </mml:msub> </mml:math> . Under the assumption that such systems can only be formed by dynamical interactions, we infer that between 25% and 93% of BBHs with nonvanishing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">∣</mml:mo> <mml:msub> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>eff</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">∣</mml:mo> <mml:mo>&gt;</mml:mo> <mml:mn>0.01</mml:mn> </mml:math> are dynamically assembled. Third, we estimate merger rates, finding <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BBH</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>23.9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>8.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>14.3</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi>Gpc</mml:mi> </mml:mrow> <mml:mro

The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low- and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with 0. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be ${m}_{g}\ensuremath{\le}4.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{eV}/{c}^{2}$ (90% credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.

Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We first establish that residuals from the best-fit waveform are consistent with detector noise, and that the low- and high-frequency parts of the signals are in agreement. We then consider parametrized modifications to the waveform by varying post-Newtonian and phenomenological coefficients, improving past constraints by factors of $\ensuremath{\sim}2$; we also find consistency with Kerr black holes when we specifically target signatures of the spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we tighten constraints on Lorentz-violating coefficients by a factor of $\ensuremath{\sim}2.6$ and bound the mass of the graviton to ${m}_{g}\ensuremath{\le}1.76\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{eV}/{c}^{2}$ with 90% credibility. We also analyze the properties of the merger remnants by measuring ringdown frequencies and damping times, constraining fractional deviations away from the Kerr frequency to $\ensuremath{\delta}{\stackrel{^}{f}}_{220}=0.0{3}_{\ensuremath{-}0.35}^{+0.38}$ for the fundamental quadrupolar mode, and $\ensuremath{\delta}{\stackrel{^}{f}}_{221}=0.0{4}_{\ensuremath{-}0.32}^{+0.27}$ for the first overtone; additionally, we find no evidence for postmerger echoes. Finally, we determine that our data are consistent with tensorial polarizations through a template-independent method. When possible, we assess the validity of general relativity based on collections of events analyzed jointly. We find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.

We report the observation of gravitational waves from a binary-black-hole coalescence during the first two weeks of LIGO’s and Virgo’s third observing run. The signal was recorded on April 12, 2019 at 05∶30∶44 UTC with a network signal-to-noise ratio of 19. The binary is different from observations during the first two observing runs most notably due to its asymmetric masses: a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo>∼</a:mo><a:mn>30</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:msub><a:mi>M</a:mi><a:mo stretchy="false">⊙</a:mo></a:msub></a:math> black hole merged with a <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mo>∼</d:mo><d:mn>8</d:mn><d:mtext> </d:mtext><d:mtext> </d:mtext><d:msub><d:mi>M</d:mi><d:mo stretchy="false">⊙</d:mo></d:msub></d:math> black hole companion. The more massive black hole rotated with a dimensionless spin magnitude between 0.22 and 0.60 (90% probability). Asymmetric systems are predicted to emit gravitational waves with stronger contributions from higher multipoles, and indeed we find strong evidence for gravitational radiation beyond the leading quadrupolar order in the observed signal. A suite of tests performed on GW190412 indicates consistency with Einstein’s general theory of relativity. While the mass ratio of this system differs from all previous detections, we show that it is consistent with the population model of stellar binary black holes inferred from the first two observing runs. Published by the American Physical Society 2020

The celebrated ``tenfold way'' provides a scheme for categorizing general topological states of matter, but it does not take into account the crystal symmetries that always exist in real materials. A new method extends this organization to allow the categorization of all topologically distinct electronic band structures in materials with only crystal symmetries for any number of physically relevant dimensions.

Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics (``ergotropy'') is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of work extraction that contrast the thermodynamic intuition are discussed, e.g. a state with larger entropy than another may produce more work, while correlations may increase or reduce the ergotropy.

Competing inhomogeneous orders are a central feature of correlated electron materials, including the high-temperature superconductors. The two-dimensional Hubbard model serves as the canonical microscopic physical model for such systems. Multiple orders have been proposed in the underdoped part of the phase diagram, which corresponds to a regime of maximum numerical difficulty. By combining the latest numerical methods in exhaustive simulations, we uncover the ordering in the underdoped ground state. We find a stripe order that has a highly compressible wavelength on an energy scale of a few kelvin, with wavelength fluctuations coupled to pairing order. The favored filled stripe order is different from that seen in real materials. Our results demonstrate the power of modern numerical methods to solve microscopic models, even in challenging settings.

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> , 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.

The Event Horizon Telescope (EHT) collaboration has recently released the first image of a black hole (BH), opening a new window onto tests of general relativity in the strong field regime. In this paper, we derive constraints on the nature of M87* (the supermassive object at the center of the galaxy M87), exploiting the fact that its shadow appears to be highly circular, and using measurements of its angular size. We first consider the simple case where M87* is assumed to be a Kerr BH. We find that the inferred circularity of M87* excludes Kerr BHs with observation angle ${\ensuremath{\theta}}_{\mathrm{obs}}\ensuremath{\gtrsim}45\ifmmode^\circ\else\textdegree\fi{}$ for dimensionless rotational parameter $0.95\ensuremath{\lesssim}{a}_{*}\ensuremath{\le}1$ whereas the observation angle is unbounded for ${a}_{*}\ensuremath{\lesssim}0.9$. We then consider the possibility that M87* might be a superspinar, i.e., an object described by the Kerr solution and spinning so fast that it violates the Kerr bound by having $|{a}_{*}|&gt;1$. We find that, within certain regions of parameter space, the inferred circularity and size of the shadow of M87* do not exclude the possibility that this object might be a superspinar.