Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

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The Cosmological Constant and Dark Energy

In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.

https://iopscience.iop.org/article/10.1088/0034-4885/68/8/R01/pdf

Smoothed particle hydrodynamics

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

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The Confrontation Between General Relativity and Experiment

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

http://cds.cern.ch/record/385991/files/9904398.pdf

The Case for a Positive Cosmological Λ-Term

The exact spacetime metric representing the exterior of a static cylindrically symmetric string is found. The geometry is conical, with a deficit angle of 8\ensuremath{\pi}G\ensuremath{\mu}, where \ensuremath{\mu} is the linear energy density of the string. The results of Vilenkin, obtained using linearized gravity, are thus shown to be correct to all orders in G\ensuremath{\mu}. Strings with G\ensuremath{\mu}\ensuremath{\ge}(1/4) are found to collapse the exterior spacetime, resulting in dimensional reduction.

Exact Gravitational Field of a String

To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted ~after averaging over source position and polarization! by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first ~mostly! analytic calculation of the gravitational wave transfer function is presented. Example sensitivity curve calculations are presented for the proposed LISA interferometer. PACS number~s!: 04.80.Nn, 95.55.Ym Advances in modern technology have ushered in an era of large laser interferometers designed to be used in the detection of gravitational radiation, both on the ground and in space. Such projects include the Laser Interferometric Gravitational Wave Observatory ~LIGO! and VIRGO @1,2# ground-based interferometers, and the proposed Laser Interferometer Space Antenna ~LISA! and OMEGA @3,4# spacebased interferometers. As these detectors come on-line, a new branch of astronomy will be created and a radically new view of the Universe is expected to be revealed. With the era of gravitational wave astronomy on the horizon, much effort has been devoted to the problem of categorizing sources of gravitational radiation, and extensive studies are underway to determine what sources will be visible to the various detectors. Typically, the sensitivity of detectors to sources of gravitational radiation has been illustrated using graphs which compare source strengths ~dimensionless strain! to instrument noise as functions of the gravitational wave frequency. Many different types of plots have appeared in the literature, ranging from single plots of spectral density to separate am

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Sensitivity curves for spaceborne gravitational wave interferometers

This paper analyzes the dispersion relations for linear plane waves in the Eckart and the Israel-Stewart theories of dissipative relativistic hydrodynamics. We show that in the long-wavelength (compared to a typical mean-free-path-length) limit the complicated dynamical structure of the Israel-Stewart theory reduces to the familiar dynamics of classical fluids: 9 of the 14 modes of an Israel-Stewart fluid are strongly damped in this limit, two propagate at the adiabatic sound speed (with appropriate viscous and thermal damping), two transverse shear modes decay at the classical viscous damping rate, and the final longitudinal mode is damped at the classical thermal diffusion rate. The short-wavelength limit of these dispersion relations is also examined. We demonstrate that the phase and group velocities of these waves must approach the characteristic velocities in the short-wavelength limit. Finally, we show how some of the perturbations of an Eckart fluid violate causality.

Linear plane waves in dissipative relativistic fluids.

The equations governing a flat Robertson-Walker cosmological model containing a dissipative Boltzmann gas are integrated numerically The bulk viscous stress is modeled using the Eckart and Israel-Stewart theories of dissipative relativistic fluids; the resulting cosmologies are compared and contrasted The Eckart models are shown to always differ in a significant quantitative way from the Israel-Stewart models It thus appears inappropriate to use the pathological (nonhyperbolic) Eckart theory for cosmological applications For large bulk viscosities, both cosmological models approach asymptotic nonequilibrium states; in the Eckart model the total pressure is negative, while in the Israel-Stewart model the total pressure is asymptotically zero The Eckart model also expands more rapidly than the Israel-Stewart models These results suggest that bulk-viscous'' inflation may be an artifact of using a pathological fluid theory such as the Eckart theory

Dissipative Boltzmann-Robertson-Walker cosmologies.

The evaporative evolution of charged nonrotating black holes is studied by numerically integrating a set of coupled differential equations describing the charge and mass as functions of time. We find that large charged black holes will evolve through a region (in the black-hole configuration space) of positive specific heat, undergoing two phase transitions as they evaporate. The region is approximately bounded by $\frac{3}{4}l{(\frac{Q}{M})}^{2}l1$ and $Mg2.03\ifmmode\times\else\texttimes\fi{}{10}^{7}{M}_{\ensuremath{\bigodot}}$. Unlike rotating black holes (which always evolve toward the Schwarzschild limit), sufficiently large charged black holes will initially evolve toward the extreme Reissner-Nordstr\"om limit; their lifetime may be many orders of magnitude larger than the lifetime of a Schwarzschild black hole with the same initial mass.

William A. Hiscock

Papers

Exact Gravitational Field of a String

Sensitivity curves for spaceborne gravitational wave interferometers

Linear plane waves in dissipative relativistic fluids.

Dissipative Boltzmann-Robertson-Walker cosmologies.

Evolution of Charged Evaporating Black Holes