Future Infinity Research Articles

State Independence for Tunnelling Processes Through Black Hole Horizons and Hawking Radiation

Tunneling processes through black hole horizons have recently been investigated in the framework of WKB theory discovering interesting interplay with the Hawking radiation. In this paper we instead adopt the point of view proper of QFT in curved spacetime, namely, we use a suitable scaling limit technique to obtain the leading order of the correlation function related with some tunneling process through a Killing horizon. The computation is done for certain large class of reference quantum states for scalar fields. In the limit of sharp localization either on the external side or on opposite sides of the horizon, the quantum correlation functions appear to have thermal nature, where in both cases the characteristic temperature is the Hawking one. Our approach is valid for every stationary charged rotating non extremal black hole, however, since the computation is completely local, it covers the case of a Killing horizon which just temporarily exists in some finite region too. These results give a strong support to the idea that the Hawking radiation, which is detected at future infinity and needs some global structures to be defined, is actually related to a local phenomenon taking place even for local geometric structures (local Killing horizons) existing just for a while.

Puncture black hole initial data in the conformal thin-sandwich formalism

We revisit the construction of puncture black hole initial data in the conformal thin-sandwich (CTS) decomposition of Einstein's constraint equations. It has been shown previously that this approach cannot yield quasiequilibrium wormhole data, which connect two asymptotically flat spatial infinities. This argument does not apply to trumpet data, which connect the spatial infinity in one universe with the future timelike infinity of another. As a numerical demonstration, we present results for a single boosted trumpet-puncture black hole, constructed in the original version of the CTS formalism.

Holography for a De Sitter-Esque geometry

Warped dS3 arises as a solution to topologically massive gravity (TMG) with positive cosmological constant +1/ℓ 2 and Chern-Simons coefficient 1/μ in the region μ 2 ℓ 2 < 27. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS3 asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regular de Sitter space. The asymptotic symmetry group resides at future infinity and is given by a semi-direct product of a Virasoro algebra and a current algebra. The right moving central charge vanishes when μ 2 ℓ 2 = 27/5. We discuss the possible holographic interpretation of these de Sitter-esque spacetimes.

Late-time tails of self-gravitating skyrmions

We consider the long-time behaviour of spherically symmetric solutions in the Einstein-Skyrme model. Using nonlinear perturbation analysis we obtain the leading order estimation of the tail in the topologically trivial sector (B = 0) of the model. We show that solutions starting from small compactly supported initial data decay as 1/t^4 at future timelike infinity and as 1/u^2 at future null infinity. We also verified that long-time behaviour for the tail in Einstein-Skyrme model is exactly the same as it was obtained for wave maps.

A De Sitter hoedown

Rotating black holes in de Sitter space are known to have interesting limits where the temperatures of the black hole and cosmological horizon are equal. We give a complete description of the thermal phase structure of all allowed rotating black hole configurations. Only one configuration, the rotating Nariai limit, has the black hole and cosmological horizons both in thermal and rotational equilibrium, in that both the temperatures and angular velocities of the two horizons coincide. The thermal evolution of the spacetime is shown to lead to the pure de Sitter spacetime, which is the most entropic configuration. We then provide a comprehensive study of the wave equation for a massless scalar in the rotating Nariai geometry. The absorption cross section at the black hole horizon is computed and a condition is found for when the scattering becomes superradiant. The boundary-to-boundary correlators at finite temperature are computed at future infinity. The quasinormal modes are obtained in explicit form. Finally, we obtain an expression for the expectation value of the number of particles produced at future infinity starting from a vacuum state with no incoming particles at past infinity. Some of our results are used to provide further evidence for a recent holographic proposal between the rotating Nariai geometry and a two-dimensional conformal field theory.

Late-time tails of wave maps coupled to gravity

We consider the late-time asymptotic behavior for solutions of Einstein's equations with the wave map matter. Using the third-order perturbation expansion about the flat spacetime we show that solutions starting from small compactly supported ℓ-equivariant initial data with ℓ ⩾ 1 decay as t−(2ℓ+2) at future timelike infinity and as u−(ℓ+1) at future null infinity.

HYBRID CHAPLYGIN GAS

Hybrid Chaplygin gas model is put forward, in which the gases play the role of dark energy. For this model the coincidence problem is greatly alleviated. The effective equation of state of the dark energy may cross the phantom divide w = -1. Furthermore, the crossing behavior is decoupled from any gravity theories. In the present model, w &lt; -1 is only a transient behavior. There is a de Sitter attractor in the future infinity. Hence, the big rip singularity, which often afflicts the models with matter whose effective equation of state less than -1, naturally disappears. There exist stable scaling solutions, both at the early universe and the late universe. We discuss the perturbation growth of this model. We find that the index is consistent with observations.

Dissipation and nonlocality in a general expanding braneworld universe

We study the evolution of both scalar and tensor cosmological perturbations in a Randall-Sundrum braneworld having an arbitrary expansion history. We adopt a four dimensional point of view where the degrees of freedom on the brane constitute an open quantum system coupled to an environment composed of the bulk gravitons. Because of the expansion of the universe, the brane degrees of freedom and the bulk degrees of freedom interact as they propagate forward in time. Brane excitations may decay through the emission of bulk gravitons which may escape to future infinity, leading to a sort of dissipation from the four dimensional point of view of an observer on the brane. Bulk gravitons may also be reflected off of the curved bulk and reabsorbed by the brane, thereby transformed into quanta on the brane, leading to a sort of nonlocality from the four dimensional point of view. The dissipation and the nonlocality are encoded into the retarded bulk propagator. We estimate the dissipation rates of the bound state as well as of the matter degrees of freedom at different cosmological epochs and for different sources of matter on the brane. We use a near-brane limit of the bulk geometry for the study when purely nonlocal bulk effects are encountered.

The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property of the volume is checked in two cases: in vacuum and in the presence of a massless scalar field. In vacuum, the volume flow (with respect to cosmological time) asymptotically vanishes if and only if future space-like infinity is 3-manifold of constant curvature. The volume flow thus represents irreversibility of asymptotic evolution in spacetimes with positive cosmological constant.

Spacelike hypersurfaces with constant mean curvature in the steady state space

We consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that if the hypersurface is bounded away from the infinity of the ambient space, then the mean curvature must be H = 1. Moreover, in the 2-dimensional case we obtain that the only complete spacelike surfaces with constant mean curvature which are bounded away from the infinity are the totally umbilical flat surfaces. We also derive some other consequences for hypersurfaces which are bounded away from the future infinity. Finally, using an isometrically equivalent model for the steady state space, we extend our results to a wider family of spacetimes.

Information is Not Lost in the Evaporation of 2D Black Holes

We analyze Hawking evaporation of the Callan-Giddings-Harvey-Strominger black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that (i) the future null infinity of the quantum space-time is sufficiently long for the past vacuum to evolve to a pure state in the future, (ii) this state has a finite norm in the future Fock space, and (iii) all the information comes out at future infinity; there are no remnants.

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M. It is now focused on the quantum state λ M , of a massless conformally coupled scalar field \(\phi\) propagating in M. λ M is “holographically” induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity \(\Im^{+}\) of M. It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the spacetime M and the associated unphysical one, M͂, are globally hyperbolic and M admits future time infinity i +. λ M coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M, the state λ M enjoys the following further remarkable properties: (i) λ M is invariant under the (unit component of the Lie) group of isometries of the bulk spacetime M. (ii) λ M fulfills a natural energy-positivity condition with respect to every notion of Killing time (if any) in the bulk spacetime M: If M admits a time-like Killing vector, the associated one-parameter group of isometries is represented by a strongly-continuous unitary group in the GNS representation of λ M . The unitary group has positive self-adjoint generator without zero modes in the one-particle space. In this case λ M is a so-called regular ground state. (iii) λ M is (globally) Hadamard in M and thus it can be used as the starting point for the perturbative renormalisation procedure of QFT of \(\phi\) in M.

Boundaries on spacetimes: causality, topology, and group actions

The future causal boundary on a spacetime serves to explicate the causal behavior of the spacetime at future infinity. The purely causal nature of this boundary has a categorically universal nature, the category being that of chronological sets. There is an associated topology with any chronological set, replicating the appropriate topology for a spacetime. Adding the future causal boundary (and using this topology) provides a quasi-compactification. The boundary for a product spacetime \(M \times \mathbb L^1\) can be detailed in terms of the Riemannian factor M.

Colliding with a crunching bubble

In the context of eternal inflation we discuss the fate of Lambda = 0 bubbles when they collide with Lambda < 0 crunching bubbles. When the Lambda = 0 bubble is supersymmetric, it is not completely destroyed by collisions. If the domain wall separating the bubbles has higher tension than the BPS bound, it is expelled from the Lambda = 0 bubble and does not alter its long time behavior. If the domain wall saturates the BPS bound, then it stays inside the Lambda = 0 bubble and removes a finite fraction of future infinity. In this case, the crunch singularity is hidden behind the horizon of a stable hyperbolic black hole.

Uniqueness of de Sitter space

All inextendible null geodesics in four-dimensional de Sitter space dS4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS4 are eternal, i.e. extend from future infinity all the way back to past infinity . We show that the property of having a null line (inextendible achronal null geodesic) that extends from to characterizes dS4 among all globally hyperbolic and asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations with positive cosmological constant. This result is then further extended to allow for a class of matter models that includes perfect fluids.

Unitarity at infinity and topological holography

Recently it has been suggested that non-Gaussian inflationary perturbations can be usefully analysed in terms of a putative dual gauge theory defined on the future conformal infinity generated by an accelerating cosmology. The problem is that unitarity of this gauge theory implies a strong constraint (the “Strominger bound”) on the matter fields in the bulk. We argue that the bound is just a reflection of the equation of state of cosmological matter. The details motivate a discussion of the possible relevance of the “dS/CFT correspondence” to the resolution of the Big Bang singularity. It is argued that the correspondence may require the Universe to come into existence along a non-singular spacelike hypersurface, as in the theories of “creation from nothing” discussed by Firouzjahi, Sarangi, and Tye, and also by Ooguri et al. and others. The argument makes use of the unusual properties of gauge theories defined on topologically non-trivial spaces.

Supergravity solutions for harmonic, static and flux S-branes

We seek S-brane solutions in D=11 supergravity which can be characterized by a harmonic function H on the flat transverse space. It turns out that the Einstein's equations force H to be a linear function of the transverse coordinates. The codimension one H=0 hyperplane can be spacelike, timelike or null and the spacelike case reduces to the previously obtained SM2 or SM5 brane solutions. We then consider static S-brane configurations having smeared timelike directions where the transverse Lorentzian symmetry group is broken down to its maximal orthogonal subgroup. Assuming that the metric functions depend on a radial spatial coordinate, we construct explicit solutions in D=11 supergravity which are non-supersymmetric and asymptotically flat. Finally, we obtain spacelike fluxbrane backgrounds which have timelike electric or magnetic fluxlines extending from past to future infinity.

Eguchi–Hanson solitons in odd dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or a negative cosmological constant. These solutions resemble the even-dimensional Eguchi–Hanson–(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dSd+1/Zp. In the AdS case, their energy is negative relative to that of pure AdS. We present perturbative evidence in five dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case, these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.

Gravitational collapse disturbs the dS/CFT correspondence?

We study the gravitational collapse in five-dimensional de Sitter (dS) spacetime and discuss the existence of the conformal boundaries at future timelike infinity from the perspective of the dS/CFT correspondence. We investigate the motion of a spherical dust shell and the black hole area bounds. The latter includes the analysis of the trapping horizon and the initial data with spindle-shaped matter distribution. In all above analyses we find the evidences that guarantee the existence of the conformal boundaries at future timelike infinity which are essential to apply the dS/CFT correspondence.

Entropy and mass bounds of Kerr–de Sitter spacetimes

We consider Kerr-de Sitter spacetimes and evaluate their mass, angular momentum and entropy according to the boundary counterterm prescription. We provide a physicall interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr-de Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the entropic N-bound. Moreover, we show that maximal mass conjecture which states any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity is respected by asymptotically de Sitter spacetimes with rotation. We furthermore consider the possibility of strengthening the conjecture to state that any asymptotically dS spacetime will have mass greater than dS if and only if it has a cosmological singularity and find that Kerr-de Sitter spacetimes do not respect this stronger statement. We investigate the behavior of the c-function for the Kerr-de Sitter spacetimes and show that it is no longer isotropic. However an average of the c-function over the angular variables yields a renormalization group flow in agreement with the expansion of spacetime at future infinity.