arXiv subjects
Publications and source records attributed to Jennie Traschen.
This is a personal account of the early work that led to what is now known as the ``preheating stage" of inflationary cosmology. The broader applicability of the underlying instability mechanisms in cosmology are indicated.
Light propagating from near a black hole horizon to the outside world is highly redshifted. In the limit that the emitter passes through the horizon, the redshift becomes infinite. In this sense the near horizon region is unobservable, as emission energies fall below some detectability bound. However, in Schwarzschild de Sitter (SdS) spacetime there is a second, cosmological, horizon due to the positive cosmological constant. Judiciously placed observers can take advantage of the blueshift due to this horizon. The frequency of signals emitted from near the black hole can be shifted back upward to an observable value. This effect is computed for a variety of accelerated and geodesic observers. An analysis of radial and circular geodesics in SdS is a key component of the paper. We find a ``cresting-wave" shaped critical curve in the SdS-geodesic parameter space such that under the curve there are three circular orbits, on the curve there are two orbits, and elsewhere there is one. It is found that the best strategy for observing photons from an emitter falling into the black hole is for the receiver to be near the cosmological horizon and also moving towards the black hole. For photons emitted from the smallest circular orbit and received at the largest circular orbit, the nonzero cosmological constant enhances observations by a factor that varies from zero to three.
Kerr-Newman de Sitter (KNdS) spacetimes have a rich thermodynamic structure that involves multiple horizons, and so differs in key respects from asymptotically flat or AdS black holes. In this paper, we show that certain features of KNdS spacetimes can be reproduced by a constrained system of $N$ non-interacting spins in a magnetic field. Both the KNdS and spin systems have bounded energy and entropy, a maximum of the entropy in the interior of the energy range, and a symmetry that maps lower energy states to higher energy states with the same entropy. Consequently, both systems have a temperature that can be positive or negative, where the gravitational temperature is defined analogously to that of the spins. We find that the number of spins $N$ corresponds to $1/Λ$ for black holes with very small charge $q$ and rotation parameter $a$, and scales like $\sqrt{(a^2+q^2)/Λ}$ for larger values of $a$ and $q$. By studying constrained spin systems, we provide insight into the thermodynamics of KNdS spacetimes and its quantum mechanical description.
Two-dimensional Schwarzschild-de Sitter is a convenient spacetime in which to study the effects of horizons on quantum fields since the spacetime contains two horizons, and the wave equation for a massless minimally coupled scalar field can be solved exactly. The two-point correlation function of a massless scalar is computed in the Unruh state. It is found that the field correlations grow linearly in terms of a particular time coordinate that is good in the future development of the past horizons, and that the rate of growth is equal to the sum of the black hole plus cosmological surface gravities. This time dependence results from additive contributions of each horizon component of the past Cauchy surface that is used to define the state. The state becomes the Bunch-Davies vacuum in the cosmological far field limit. The two point function for the field velocities is also analyzed and a peak is found when one point is between the black hole and cosmological horizons and one point is outside the future cosmological horizon.
The symmetric two-point function for a massless, minimally coupled scalar field in the Unruh state is examined for Schwarzschild-de Sitter spacetime in two dimensions. This function grows linearly in terms of a time coordinate that is well-defined on the future black hole and cosmological horizons, when the points are split in the space direction. This type of behavior also occurs in two dimensions for other static black hole spacetimes when the field is in the Unruh state, and at late times it occurs in spacetimes where a black hole forms from the collapse of a null shell. The generalization to the case of the symmetric two-point function in two dimensions for a massive scalar field in Schwarzschild-de Sitter spacetime is discussed.
We study asymptotically AdS generalizations of Melvin spacetimes, describing gravitationally bound tubes of magnetic flux. We find that narrow fluxtubes, carrying strong magnetic fields but little total flux, are approximately unchanged from the $Λ=0$ case at scales smaller than the AdS scale. However, fluxtubes with weak fields, which for $Λ=0$ can grow arbitrarily large in radius and carry unbounded magnetic flux, are limited in radius by the AdS scale and like the narrow fluxtubes carry only small total flux. As a consequence, there is a maximum magnetic flux $Φ_{max} = 2π/\sqrt{-Λ}$ that can be carried by static fluxtubes in AdS. For flux $Φ_{tot}<Φ_{max}$ there are two branches of solutions, with one branch always narrower in radius than the other. We compute the ADM mass and tensions for AdS-Melvin fluxtube, finding that the wider radius branch of solutions always has lower mass. In the limit of vanishing flux, this branch reduces to the AdS soliton.
We compute the spectra and total fluxes of quantum mechanically produced particles crossing the black hole and cosmological horizons in Schwarzschild de Sitter (SdS). Particle states are defined with respect to well-behaved, Kruskal coordinates near the horizons, and as a consequence we find that these spectra are generally non-thermal. The non-thermal Bogoliubov coefficient for a vacuum fluctuation near the black hole horizon to produce a particle that crosses the cosmological horizon is shown to equal to the convolution of two thermal coefficients, one at the cosmological temperature and one at the black hole temperature, weighted by the transmission coefficient for wave propagation in static SdS coordinates. In this sense virtual thermal propagation underlies the production process. This representation leads to the useful result that the geometric optics approximation is reliable when used together with a low frequency cut-off determined by the transmission coefficient. The large black hole limit is a quasi-equilibrium situation as both temperatures approach the common value of zero, the particle spectra become equal, and both emissions are exponentially suppressed. Small black holes radiate as thermal bodies and absorb a tiny flux of cosmological particles. The behavior of the quantum fluctuations on the horizons is seen to be consistent with the Schottky anomaly behavior of classical gravitational fluctuations.
The interplay of black hole and cosmological horizons introduces distinctive thermodynamic behavior for deSitter black holes, including well-known upper bounds for the mass and entropy. We point to a new such feature, a Schottky peak in the heat capacity of Schwarzschild-deSitter (SdS) black holes. With this behavior in mind, we explore statistical models for the underlying quantum degrees of freedom of SdS holes. While a simple two-state spin model gives Schottky behavior, in order to capture the non-equilibrium nature of the SdS system we consider a system with a large number of non-interacting spins. We examine to what extent constrained states of this system reproduce the thermodynamic properties of the black hole. We also review results of a recent study of particle production in SdS spacetimes in light of the Schottky anomaly and our spin models.
The mass of an AdS black hole represents its enthalpy, which in addition to internal energy, generally includes the energy required to assemble the system in its environment. In this paper, we consider black holes immersed in a more complex environment, generated by a scalar field with an exponential potential. In the analogue of the AdS vacuum, which we call dilaton-AdS, the scalar field has non-trivial behavior, breaking the hyperscaling symmetry of AdS and modifying the asymptotic form of the spacetime. We find that the scalar field falloff at infinity makes novel contributions to the ADM mass and spatial tensions of dilaton-AdS black holes. We derive a first law and Smarr formula for planar dilaton-AdS black holes. We study the analogue of thermodynamic volume in this system and show that the mass of a black hole again represents its enthalpy.
We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of Schwarzschild-de Sitter like metrics with time dependent cosmological constant and mass parameters, such that the cosmological constant is instantaneously equal to the value of the scalar potential. The areas of the black hole and cosmological horizons each increase in time as the effective cosmological constant decreases, and the fractional area increase is proportional to the fractional change of the cosmological constant, times a geometrical factor. For black holes ranging in size from much smaller than to comparable to the cosmological horizon, the pre-factor varies from very small to order one. The "mass first law" and the "Schwarzschild-de Sitter patch first law" of thermodynamics are satisfied throughout the evolution.
We study evolution and thermodynamics of a slow-roll transition between early and late time de Sitter phases, both in the homogeneous case and in the presence of a black hole, in a scalar field model with a generic potential having both a maximum and a positive minimum. Asymptotically future de Sitter spacetimes are characterized by ADM charges known as cosmological tensions. We show that the late time de Sitter phase has finite cosmological tension when the scalar field oscillation around its minimum is underdamped, while the cosmological tension in the overdamped case diverges. We compute the variation in the cosmological and black hole horizon areas between the early and late time phases, finding that the fractional change in horizon area is proportional to the corresponding fractional change in the effective cosmological constant. We show that the extended first law of thermodynamics, including variation in the effective cosmological constant, is satisfied between the initial and final states, and discuss the dynamical evolution of the black hole temperature.
We study the problem of finding brane-like solutions to Lovelock gravity, adopting a general approach to establish conditions that a lower dimensional base metric must satisfy in order that a solution to a given Lovelock theory can be constructed in one higher dimension. We find that for Lovelock theories with generic values of the coupling constants, the Lovelock tensors (higher curvature generalizations of the Einstein tensor) of the base metric must all be proportional to the metric. Hence, allowed base metrics form a subclass of Einstein metrics. This subclass includes so-called `universal metrics', which have been previously investigated as solutions to quantum-corrected field equations. For specially tuned values of the Lovelock couplings, we find that the Lovelock tensors of the base metric need to satisfy fewer constraints. For example, for Lovelock theories with a unique vacuum there is only a single such constraint, a case previously identified in the literature, and brane solutions can be straightforwardly constructed.
We show that asymptotically future deSitter (AFdS) spacetimes carry 'genuine' cosmic hair; information that is analogous to the mass and angular momentum of asymptotically flat spacetimes and that characterizes how an AFdS spacetime approaches its asymptotic form. We define new 'cosmological tension' charges associated with future asymptotic spatial translation symmetries, which are analytic continuations of the ADM mass and tensions of asymptotically planar AdS spacetimes, and which measure the leading anisotropic corrections to the isotropic, exponential deSitter expansion rate. A cosmological Smarr relation, holding for AFdS spacetimes having exact spatial translation symmetry, is derived. This formula relates cosmological tension, which is evaluated at future infinity, to properties of the cosmology at early times, together with a 'cosmological volume' contribution that is analogous to the thermodynamic volume of AdS black holes. Smarr relations for different spatial directions imply that the difference in expansion rates between two directions at late times is related in a simple way to their difference at early times. Hence information about the very early universe can be inferred from cosmic hair, which is potentially observable in a late time deSitter phase. Cosmological tension charges and related quantities are evaluated for Kasner-deSitter spacetimes, which serve as our primary examples.
Janis-Newman-Winicour (JNW) spacetimes generalize the Schwarzschild solution to include a massless scalar field. Although suffering from naked singularities, they share the `frozen star' features of Schwarzschild black holes. Cosmological versions of the JNW spacetimes were discovered some time ago by Husain, Martinez and Nunez and by Fonarev. Unlike Schwarzschild-deSitter black holes, these solutions are dynamical, and the scarcity of exact solutions for dynamical black holes in cosmological backgrounds motivates their further study. Here we show how the cosmological JNW spacetimes can be built, starting from simpler, static, higher dimensional, vacuum `JNW brane' solutions via two different generalized dimensional reduction schemes that together cover the full range of JNW parameter space. Cosmological versions of a BPS limit of charged dilaton black holes are also known. JNW spacetimes represent a different limiting case of the charged, dilaton black hole family. We expect that understanding this second data point may be key to finding cosmological versions of general, non-BPS black holes.
The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation $δa$ of the A-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension $δa^*$ to include odd dimensional boundaries, times the ratio $S/a^*$. Since $a^*$ is a measure of the number of degrees of freedom $N$ per unit volume of the boundary CFT, this new term has the form $μδN$, where the chemical potential $μ$ is given by the entanglement entropy per degree of freedom.
We present a new analysis of Kerr-Newman-deSitter black holes in terms of thermodynamic quantities that are defined in the observable portion of the universe; between the black hole and cosmological horizons. In particular, we replace the mass $m$ with a new 'area product' parameter $X$. The physical region of parameter space is found analytically and thermodynamic quantities are given by simple algebraic functions of these parameters. We find that different geometrical properties of the black holes are usefully distinguished by the sum of the black hole and cosmological entropies. The physical parameter space breaks into a region in which the total entropy, together with $Λ$, $a$ and $q$ uniquely specifies the black hole, and a region in which there is a two-fold degeneracy. In this latter region, there are isentropic pairs of black holes, having the same $Λ$, $a$, and $q$, but different $X$. The thermodynamic volumes and masses differ in such that there are high and low density branches. The partner spacetimes are related by a simple inversion of $X$, which has a fixed point at the state of maximal total entropy. We compute the compressibility at fixed total entropy and find that it diverges at the maximal entropy point. Hence a picture emerges of high and low density phases merging at this critical point.
We explore a correspondence between Melvin magnetic fluxtubes and anisotropic cosmological solutions, which we call `Melvin cosmologies'. The correspondence via analytic continuation provides useful information in both directions. Solution generating techniques known on the fluxtube side can also be used for generating cosmological backgrounds. Melvin cosmologies interpolate between different limiting Kasner behaviors at early and late times. This has an analogue on the fluxtube side between limiting Levi-Civita behavior at small and large radii. We construct generalized Melvin fluxtubes and cosmologies in both Einstein-Maxwell theory and dilaton gravity and show that similar properties hold.
Entanglement entropy in conformal field theories is known to satisfy a first law. For spherical entangling surfaces, this has been shown to follow via the AdS/CFT correspondence and the holographic prescription for entanglement entropy from the bulk first law for Killing horizons. The bulk first law can be extended to include variations in the cosmological constant $Λ$, which we established in earlier work. Here we show that this implies an extension of the boundary first law to include varying the number of degrees of freedom of the boundary CFT. The thermodynamic potential conjugate to $Λ$ in the bulk is called the thermodynamic volume and has a simple geometric formula. In the boundary first law it plays the role of a chemical potential. For the bulk minimal surface $Σ$ corresponding to a boundary sphere, the thermodynamic volume is found to be proportional to the area of $Σ$, in agreement with the variation of the known result for entanglement entropy of spheres. The dependence of the CFT chemical potential on the entanglement entropy and number of degrees of freedom is similar to how the thermodynamic chemical potential of an ideal gas depends on entropy and particle number.