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

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ''shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.

/pdf/observational-signatures-and-non-gaussianities-of-general-13ujqm75sl.pdf

Observational signatures and non-Gaussianities of general single-field inflation

This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle. What remains after subtraction is a smooth field that is fully responsible for the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors. It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line. It continues with a thorough discussion of Green's functions in curved spacetime. The review presents a detailed derivation of each of the three equations of motion. Because the notion of a point mass is problematic in general relativity, the review concludes with an alternative derivation of the equations of motion that applies to a small body of arbitrary internal structure.

/pdf/the-motion-of-point-particles-in-curved-spacetime-2hw7vyn00m.pdf

The Motion of Point Particles in Curved Spacetime

Vorlesungen uber theoretische Physik Von Prof. Arnold Sommerfeld. Band 1: Mechanik. Vierte, neubearbeitete Auflage. Pp. xii + 276. 18 D. marks. Band 2: Mechanik der deformierbaren Medien. Pp. xv + 376 + 4 plates. 18 D. marks. Band 3: Elektrodynamik. Pp. xvi + 368. 18 D. marks. Band 6: Partielle Differentialgleichungen der Physik. Pp. xiii + 332. 18 D. marks. (Wiesbaden: Dieterich'sche Verlagsbuchhandlung, 1947–1949.)

/pdf/lectures-on-theoretical-physics-4m0v0ffz5s.pdf

Lectures on Theoretical Physics

There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan?Brans?Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

https://iopscience.iop.org/article/10.1088/0264-9381/20/20/201/pdf

General relativistic boson stars

We show that global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The $O(4,1)$ de Sitter invariant state is a definite phase coherent superposition of particle and antiparticle solutions in both the asymptotic past and future and, therefore, is not a true vacuum state. In the closely related case of particle creation by a constant, uniform electric field, a time symmetric state analogous to the de Sitter invariant one is constructed, which is also not a stable vacuum state. We provide the general framework necessary to describe the particle creation process, the mean particle number, and dynamical quantities such as the energy-momentum tensor and current of the created particles in the de Sitter and electric field backgrounds respectively in real time, establishing the connection to kinetic theory. We compute the energy-momentum tensor for adiabatic vacuum states in de Sitter space initialized at early times in global ${\mathbb{S}}^{3}$ sections and show that particle creation in the contracting phase results in exponentially large energy densities at later times, necessitating an inclusion of their backreaction effects and leading to large deviation of the spacetime from global de Sitter space before the expanding phase can begin.

Instability of global de Sitter space to particle creation

Stress-energy tensor of quantized scalar fields in static spherically symmetric spacetimes.

An effective action technique for the time evolution of a closed system consisting of one or more mean fields interacting with their quantum fluctuations is presented. By marrying large-N expansion methods to the Schwinger-Keldysh closed time path formulation of the quantum effective action, causality of the resulting equations of motion is ensured and a systematic, energy-conserving and gauge-invariant expansion about the quasiclassical mean field(s) in powers of 1/N developed. The general method is exposed in two specific examples, O(N) symmetric scalar \ensuremath{\lambda}${\mathrm{\ensuremath{\Phi}}}^{4}$ theory and quantum electrodynamics (QED) with N fermion fields. The \ensuremath{\lambda}${\mathrm{\ensuremath{\Phi}}}^{4}$ case is well suited to the numerical study of the real time dynamics of phase transitions characterized by a scalar order parameter. In QED the technique may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes in a relativistic ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ plasma. A simple renormalization scheme that makes practical the numerical solution of the equations of motion of these and other field theories is described.

Nonequilibrium quantum fields in the large-N expansion.

The Euclidean or Bunch-Davies $O(4,1)$ invariant state for quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with energy density that is arbitrarily small at early times, is exponentially blueshifted in the contracting phase of ``eternal'' de Sitter space, and becomes large enough to disturb the classical geometry through the semi-classical Einstein equations at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. In de Sitter space, the same results are obtained either directly from the renormalized stress tensor of a massive scalar field, or for massless conformal fields of any spin, more directly from the effective action and stress tensor associated with the conformal trace anomaly. The anomaly stress tensor shows that states invariant under the $O(4)$ subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the $O(4,1)$ isometry group and its $O(4)$ subgroup are broken by quantum fluctuations. Potential consequences of this result for cosmology and the problem of vacuum energy are discussed.

/pdf/quantum-vacuum-instability-of-eternal-de-sitter-space-4xy4arrwzn.pdf

Quantum Vacuum Instability of 'Eternal' de Sitter Space

The stress-energy tensor of a free quantized scalar field is calculated in the extreme Reissner-Nordstr\"om black hole spacetime in the zero-temperature vacuum state. The stress-energy appears to be regular on the event horizon, contrary to the suggestion provided by two-dimensional calculations. An analytic calculation on the event horizon for a thermal state shows that if the temperature is nonzero then the stress-energy diverges strongly there.

Paul R. Anderson

Papers

Instability of global de Sitter space to particle creation

Stress-energy tensor of quantized scalar fields in static spherically symmetric spacetimes.

Nonequilibrium quantum fields in the large-N expansion.

Quantum Vacuum Instability of 'Eternal' de Sitter Space

Semiclassical stability of the extreme Reissner-Nordström black hole.