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Universe, Volume 5, Issue 7 (July 2019) – 19 articles

Cover Story (view full-size image): The Highly Eccentric Relativity Orbiter (HERO) is a space-based mission concept which aims to perform several tests of post-Newtonian (pN) gravity with a preferably drag-free spacecraft in a highly elliptical orbit. HERO may detect, for the first time, the pN linear trend of the semimajor axis a induced by the Earth's quadrupole, amounting to ≃4–12 cm yr−1 for certain orbital configurations. The secular decay of a of a geodetic satellite was recently measured with an error of 0.7 cm yr−1. Also, the pN Lense-Thirring and Schwarzschild effects could be accurately tested, depending on the drag-free apparatus. Moreover, the large orbital eccentricity would allow one to constrain several modified models of gravity and to measure the gravitational redshift with improved accuracy as well. View this paper.
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Open AccessReview
A Model-Independent Characterisation of Strong Gravitational Lensing by Observables
Universe 2019, 5(7), 177; https://doi.org/10.3390/universe5070177 - 23 Jul 2019
Cited by 6 | Viewed by 908
Abstract
When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie in its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly distorted images [...] Read more.
When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie in its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly distorted images of the source are observed. This strong gravitational lensing effect has so far been treated as a model-fitting problem. Using the observed multiple images as constraints yields a self-consistent model of the deflecting mass density and the source object. As several models meet the constraints equally well, we develop a lens characterisation that separates data-based information from model assumptions. The observed multiple images allow us to determine local properties of the deflecting mass distribution on any mass scale from one simple set of equations. Their solution is unique and free of model-dependent degeneracies. The reconstruction of source objects can be performed completely model-independently, enabling us to study galaxy evolution without a lens-model bias. Our approach reduces the lens and source description to its data-based evidence that all models agree upon, simplifies an automated treatment of large datasets, and allows for an extrapolation to a global description resembling model-based descriptions. Full article
(This article belongs to the Special Issue Observing Gravitational Lenses: Present and Future)
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Open AccessReview
The String Theory Landscape
Universe 2019, 5(7), 176; https://doi.org/10.3390/universe5070176 - 20 Jul 2019
Cited by 4 | Viewed by 1958
Abstract
String/M theory is formulated in 10 and 11 space-time dimensions; in order to describe our universe, we must postulate that six or seven of the spatial dimensions form a small compact manifold. In 1985, Candelas et al. showed that by taking the extra [...] Read more.
String/M theory is formulated in 10 and 11 space-time dimensions; in order to describe our universe, we must postulate that six or seven of the spatial dimensions form a small compact manifold. In 1985, Candelas et al. showed that by taking the extra dimensions to be a Calabi–Yau manifold, one could obtain the grand unified theories which had previously been postulated as extensions of the Standard Model of particle physics. Over the years since, many more such compactifications were found. In the early 2000s, progress in nonperturbative string theory enabled computing the approximate effective potential for many compactifications, and it was found that they have metastable local minima with small cosmological constant. Thus, string/M theory appears to have many vacuum configurations which could describe our universe. By combining results on these vacua with a measure factor derived using the theory of eternal inflation, one gets a theoretical framework which realizes earlier ideas about the multiverse, including the anthropic solution to the cosmological constant problem. We review these arguments and some of the criticisms, with their implications for the prediction of low energy supersymmetry and hidden matter sectors, as well as recent work on a variation on eternal inflation theory motivated by computational complexity considerations. Full article
(This article belongs to the Special Issue The Multiverse)
Open AccessArticle
Multiverse Predictions for Habitability: Fraction of Life That Develops Intelligence
Universe 2019, 5(7), 175; https://doi.org/10.3390/universe5070175 - 17 Jul 2019
Cited by 5 | Viewed by 941
Abstract
Do mass extinctions affect the development of intelligence? If so, we may expect to be in a universe that is exceptionally placid. We consider the effects of impacts, supervolcanoes, global glaciations, and nearby gamma ray bursts, and how their rates depend on fundamental [...] Read more.
Do mass extinctions affect the development of intelligence? If so, we may expect to be in a universe that is exceptionally placid. We consider the effects of impacts, supervolcanoes, global glaciations, and nearby gamma ray bursts, and how their rates depend on fundamental constants. It is interesting that despite the very disparate nature of these processes, each occurs on timescales of 100 Myr-Gyr. We argue that this is due to a selection effect that favors both tranquil locales within our universe, as well as tranquil universes. Taking gamma ray bursts to be the sole driver of mass extinctions is disfavored in multiverse scenarios, as the rate is much lower for different values of the fundamental constants. In contrast, geological causes of extinction are very compatible with the multiverse. Various frameworks for the effects of extinctions are investigated, and the intermediate disturbance hypothesis is found to be most compatible with the multiverse. Full article
(This article belongs to the Special Issue The Multiverse)
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Open AccessCommunication
Compact Star Properties from an Extended Linear Sigma Model
Universe 2019, 5(7), 174; https://doi.org/10.3390/universe5070174 - 15 Jul 2019
Cited by 1 | Viewed by 992
Abstract
The equation of state provided by effective models of strongly interacting matter should comply with the restrictions imposed by current astrophysical observations of compact stars. Using the equation of state given by the (axial-)vector meson extended linear sigma model, we determine the mass–radius [...] Read more.
The equation of state provided by effective models of strongly interacting matter should comply with the restrictions imposed by current astrophysical observations of compact stars. Using the equation of state given by the (axial-)vector meson extended linear sigma model, we determine the mass–radius relation and study whether these restrictions are satisfied under the assumption that most of the star is filled with quark matter. We also compare the mass–radius sequence with those given by the equations of state of somewhat simpler models. Full article
(This article belongs to the Special Issue The Zimányi School and Analytic Hydrodynamics in High Energy Physics)
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Open AccessEditor’s ChoiceArticle
The Geometrical Trinity of Gravity
Universe 2019, 5(7), 173; https://doi.org/10.3390/universe5070173 - 15 Jul 2019
Cited by 85 | Viewed by 1869
Abstract
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. [...] Read more.
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. However, this is not the only possibility. In these notes, we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrelated representations of the same underlying theory. Based on these three alternative formulations of General Relativity, we then discuss some extensions. Full article
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Open AccessReview
Anthropic Selection of Physical Constants, Quantum Entanglement, and the Multiverse Falsifiability
Universe 2019, 5(7), 172; https://doi.org/10.3390/universe5070172 - 14 Jul 2019
Cited by 3 | Viewed by 1389
Abstract
This paper evaluates some important aspects of the multiverse concept. Firstly, the most realistic opportunity for it which is the spacetime variability of the physical constants and may deliver worlds with different physics, hopefully fulfilling the conditions of the anthropic principles. Then, more [...] Read more.
This paper evaluates some important aspects of the multiverse concept. Firstly, the most realistic opportunity for it which is the spacetime variability of the physical constants and may deliver worlds with different physics, hopefully fulfilling the conditions of the anthropic principles. Then, more esoteric versions of the multiverse being the realisation of some abstract mathematics or even logic (cf. paper by M. Heller in this volume). Finally, it evaluates the big challenge of getting any signal from “other universes” using recent achievements of the quantum theory. Full article
(This article belongs to the Special Issue The Multiverse)
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Open AccessArticle
Multiverse Predictions for Habitability: Fraction of Planets that Develop Life
Universe 2019, 5(7), 171; https://doi.org/10.3390/universe5070171 - 14 Jul 2019
Cited by 5 | Viewed by 1031
Abstract
In a multiverse context, determining the probability of being in our particular universe depends on estimating its overall habitability compared to other universes with different values of the fundamental constants. One of the most important factors in determining this is the fraction of [...] Read more.
In a multiverse context, determining the probability of being in our particular universe depends on estimating its overall habitability compared to other universes with different values of the fundamental constants. One of the most important factors in determining this is the fraction of planets that actually develop life, and how this depends on planetary conditions. Many proposed possibilities for this are incompatible with the multiverse: if the emergence of life depends on the lifetime of its host star, the size of the habitable planet, or the amount of material processed, the chances of being in our universe would be very low. If the emergence of life depends on the entropy absorbed by the planet, however, our position in this universe is very natural. Several proposed models for the subsequent development of life, including the hard step model and several planetary oxygenation models, are also shown to be incompatible with the multiverse. If any of these are observed to play a large role in determining the distribution of life throughout our universe, the multiverse hypothesis will be ruled out to high significance. Full article
(This article belongs to the Special Issue The Multiverse)
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Open AccessArticle
Dynamical Properties of the Mukhanov-Sasaki Hamiltonian in the Context of Adiabatic Vacua and the Lewis-Riesenfeld Invariant
Universe 2019, 5(7), 170; https://doi.org/10.3390/universe5070170 - 13 Jul 2019
Cited by 4 | Viewed by 1099
Abstract
We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context of inflation considering a quasi-de Sitter spacetime. Our main [...] Read more.
We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context of inflation considering a quasi-de Sitter spacetime. Our main interest lies in the question of to which extent these already well-established methods at the classical and quantum level for finitely many degrees of freedom can be generalized to field theory. As our results show, a straightforward generalization does in general not lead to a unitary operator on Fock space that implements the corresponding time-dependent canonical transformation associated with the Lewis-Riesenfeld invariant. The action of this operator can be rewritten as a time-dependent Bogoliubov transformation, where we also compare our results to already existing ones in the literature. We show that its generalization to Fock space has to be chosen appropriately in order to not violate the Shale-Stinespring condition. Furthermore, our analysis relates the Ermakov differential equation that plays the role of an auxiliary equation, whose solution is necessary to construct the Lewis-Riesenfeld invariant, as well as the corresponding time-dependent canonical transformation, to the defining differential equation for adiabatic vacua. Therefore, a given solution of the Ermakov equation directly yields a full solution of the differential equation for adiabatic vacua involving no truncation at some adiabatic order. As a consequence, we can interpret our result obtained here as a kind of non-squeezed Bunch-Davies mode, where the term non-squeezed refers to a possible residual squeezing that can be involved in the unitary operator for certain choices of the Bogoliubov map. Full article
(This article belongs to the Special Issue Progress in Group Field Theory and Related Quantum Gravity Formalisms)
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Open AccessArticle
Phases of Hadron-Quark Matter in (Proto) Neutron Stars
Universe 2019, 5(7), 169; https://doi.org/10.3390/universe5070169 - 11 Jul 2019
Cited by 6 | Viewed by 941
Abstract
In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. [...] Read more.
In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size of this phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu–Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. Part two of the paper deals with the quark-hadron composition of hot (proto) neutron star matter. To this end we use a local three-flavor Polyakov–Nambu–Jona-Lasinio model which includes the ’t Hooft (quark flavor mixing) term. It is found that this term leads to non-negligible changes in the particle composition of (proto) neutron stars made of hadron-quark matter. Full article
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Open AccessCommunication
The General Linear Cartan Khronon
Universe 2019, 5(7), 168; https://doi.org/10.3390/universe5070168 - 08 Jul 2019
Cited by 6 | Viewed by 869
Abstract
A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space that—in the symmetry-broken phase—reproduces the predictions of [...] Read more.
A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space that—in the symmetry-broken phase—reproduces the predictions of General Relativity in the presence of dark matter. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
Open AccessArticle
Disformal Transformations in Scalar–Torsion Gravity
Universe 2019, 5(7), 167; https://doi.org/10.3390/universe5070167 - 07 Jul 2019
Cited by 13 | Viewed by 811
Abstract
We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, [...] Read more.
We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
Open AccessArticle
The Dynamical Origin of the Graviton Mass in the Non-Linear Theory of Massive Gravity
Universe 2019, 5(7), 166; https://doi.org/10.3390/universe5070166 - 06 Jul 2019
Cited by 1 | Viewed by 799
Abstract
We compare the standard Higgs mechanism corresponding to the scalar field, with the dynamical origin of the graviton mass inside the scenario of the dRGT theory of massive gravity. We demonstrate that the effective mass perceived locally by different observers depends on how [...] Read more.
We compare the standard Higgs mechanism corresponding to the scalar field, with the dynamical origin of the graviton mass inside the scenario of the dRGT theory of massive gravity. We demonstrate that the effective mass perceived locally by different observers depends on how they define the local time with respect to the preferred notion of time defined by the Stückelberg function T 0 ( r , t ) . Full article
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Open AccessEditor’s ChoiceArticle
A HERO for General Relativity
Universe 2019, 5(7), 165; https://doi.org/10.3390/universe5070165 - 05 Jul 2019
Cited by 2 | Viewed by 1471
Abstract
HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We [...] Read more.
HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of 10 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
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Open AccessArticle
Gravitational Radiation, Vorticity And Super–Energy: A Conspicuous Threesome
Universe 2019, 5(7), 164; https://doi.org/10.3390/universe5070164 - 04 Jul 2019
Cited by 2 | Viewed by 852
Abstract
We elaborate on the link relating gravitational radiation, vorticity and a flux of super–energy on the plane orthogonal to the vorticity vector. We examine the vorticity appearing in the congruence of observers at the outside of the source, as well as the vorticity [...] Read more.
We elaborate on the link relating gravitational radiation, vorticity and a flux of super–energy on the plane orthogonal to the vorticity vector. We examine the vorticity appearing in the congruence of observers at the outside of the source, as well as the vorticity of the fluid distribution, the source of the gravitational radiation is made of. The information provided by the study of the physical aspects of the source poses new questions which could, in principle, be solved by the observational evidence. Besides the study of the theoretical issues associated to such relationship, we also stress the new observational possibilities to detect gravitational radiation, appearing as consequence of the above mentioned link. The high degree of development achieved in the gyroscope technology, as well as recent proposals to detect rotations by means of ring lasers, atom interferometers, atom lasers and anomalous spin–precession experiments, lead us to believe that an alternative to the laser interferometers used so far to detect gravitational waves, may be implemented based on the detection of the vorticity associated with gravitational radiation. Additionally, this kind of detectors might be able to elucidate the open question about the physical properties of the tail of the waves appearing as the consequence of the violation of the Huygens’s principle in general relativity. Full article
(This article belongs to the Special Issue Rotation Effects in Relativity)
Open AccessArticle
Identification of a Regular Black Hole by Its Shadow
Universe 2019, 5(7), 163; https://doi.org/10.3390/universe5070163 - 03 Jul 2019
Cited by 11 | Viewed by 1025
Abstract
We study shadows of regular rotating black holes described by the axially symmetric solutions asymptotically Kerr for a distant observer, obtained from regular spherical solutions of the Kerr–Schild class specified by T t t = T r r ( p r = ε ) . All regular solutions obtained with the Newman–Janis algorithm belong to this class. Their basic generic feature is the de Sitter vacuum interior. Information about the interior content of a regular rotating de Sitter-Kerr black hole can be in principle extracted from observation of its shadow. We present the general formulae for description of shadows for this class of regular black holes, and numerical analysis for two particular regular black hole solutions. We show that the shadow of a de Sitter-Kerr black hole is typically smaller than that for the Kerr black hole, and the difference depends essentially on the interior density and on the pace of its decreasing. Full article
(This article belongs to the Collection Open Questions in Black Hole Physics)
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Open AccessArticle
Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors
Universe 2019, 5(7), 162; https://doi.org/10.3390/universe5070162 - 02 Jul 2019
Cited by 2 | Viewed by 872
Abstract
A new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis of Grassmann variables, which [...] Read more.
A new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis of Grassmann variables, which we call gamma operators. Various field theory constructions are defined with use of these structures. We derive formulas for the vacuum state vector. Five operator analogs of five Dirac gamma matrices exist in the superalgebraic approach as well as two additional operator analogs of gamma matrices, which are absent in the theory of Dirac spinors. We prove that there is a relationship between gamma operators and the most important physical operators of the second quantization method: number of particles, energy–momentum and electric charge operators. In addition to them, a series of similar operators are constructed from the creation and annihilation operators, which are Lorentz-invariant analogs of Dirac matrices. However, their physical meaning is not yet clear. We prove that the condition for the existence of spinor vacuum imposes restrictions on possible variants of the signature of the four-dimensional spacetime. It can only be (1, 1 , 1 , 1 ), and there are two additional axes corresponding to the inner space of the spinor, with a signature ( 1 , 1 ). Developed mathematical formalism allows one to obtain the second quantization operators in a natural way. Gauge transformations arise due to existence of internal degrees of freedom of superalgebraic spinors. These degrees of freedom lead to existence of nontrivial affine connections. Proposed approach opens perspectives for constructing a theory in which the properties of spacetime have the same algebraic nature as the momentum, electromagnetic field and other quantum fields. Full article
Open AccessArticle
Magnification Cross Sections for the Elliptic Umbilic Caustic Surface
Universe 2019, 5(7), 161; https://doi.org/10.3390/universe5070161 - 02 Jul 2019
Cited by 2 | Viewed by 886
Abstract
In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as μ 2 for fold caustics and μ 2.5 for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as μ 2.5 in the two-image region and μ 2 in the four-image region, where μ is the total unsigned magnification. In both cases our results are supported both numerically and analytically. Full article
(This article belongs to the Special Issue Gravitational Lensing and Optical Geometry: A Centennial Perspective)
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Open AccessReview
Higgs and BSM Studies at the LHC
Universe 2019, 5(7), 160; https://doi.org/10.3390/universe5070160 - 02 Jul 2019
Viewed by 1052
Abstract
The discovery and study of the Higgs boson at the Large Hadron Collider of CERN has proven the validity of the Brout–Englert–Higgs mechanism of mass creation in the standard model via spontaneous symmetry breaking. The new results obtained by the ATLAS and CMS [...] Read more.
The discovery and study of the Higgs boson at the Large Hadron Collider of CERN has proven the validity of the Brout–Englert–Higgs mechanism of mass creation in the standard model via spontaneous symmetry breaking. The new results obtained by the ATLAS and CMS Collaborations at the LHC show that all measured cross-sections agree within uncertainties with the predictions of the theory. However, the standard model has obvious difficulties (nonzero neutrino masses, hierarchy problem, existence of dark matter, non-existence of antimatter galaxies, etc.), which point towards more possible violated symmetries. We first summarize the present status of the studies of the Higgs boson, including the latest results at 13 TeV p-p collision energy, then enlist some of the problems with possible solutions and the experimental situation regarding them. Full article
(This article belongs to the Special Issue The Zimányi School and Analytic Hydrodynamics in High Energy Physics)
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Open AccessCommunication
Neutron Star Mass and Radius Measurements
Universe 2019, 5(7), 159; https://doi.org/10.3390/universe5070159 - 28 Jun 2019
Cited by 13 | Viewed by 1192
Abstract
Constraints on neutron star masses and radii now come from a variety of sources: theoretical and experimental nuclear physics, astrophysical observations including pulsar timing, thermal and bursting X-ray sources, and gravitational waves, and the assumptions inherent to general relativity and causality of the [...] Read more.
Constraints on neutron star masses and radii now come from a variety of sources: theoretical and experimental nuclear physics, astrophysical observations including pulsar timing, thermal and bursting X-ray sources, and gravitational waves, and the assumptions inherent to general relativity and causality of the equation of state. These measurements and assumptions also result in restrictions on the dense matter equation of state. The two most important structural parameters of neutron stars are their typical radii, which impacts intermediate densities in the range of one to two times the nuclear saturation density, and the maximum mass, which impacts the densities beyond about three times the saturation density. Especially intriguing has been the multi-messenger event GW170817, the first observed binary neutron star merger, which provided direct estimates of both stellar masses and radii as well as an upper bound to the maximum mass. Full article
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