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It is often argued that the Planck length (or mass) is the scale of quantum gravity, as shown by comparing the Compton length with the gravitational radius of a particle. However, the Compton length is relevant in scattering processes but does not play a significant role in bound states. We will derive a possible ground state for a dust ball composed of a large number of quantum particles entailing a core with the size of a fraction of the horizon radius. This suggests that quantum gravity becomes physically relevant for systems with compactness of order one for which the nonlinearity of General Relativity cannot be discarded. A quantum corrected geometry can then be obtained from the effective energy-momentum tensor of the core or from quantum coherent states for the effective gravitational degrees of freedom. These descriptions replace the classical singularity of black holes with integrable structures in which tidal forces remain finite and there is no inner Cauchy horizon. The extension to rotating systems is briefly mentioned. [ABSTRACT FROM AUTHOR]

We consider black holes generically sourced by quantum matter described by regular wavefunctions. This allows for integrable effective energy densities and the removal of Cauchy horizons in spherically symmetric configurations. Moreover, we identify the ultrarigid rotation of the Kerr spacetime as causing the existence of an inner horizon in rotating systems, and describe general properties for quantum matter cores at the centre of rotating black holes with integrable singularities and no Cauchy horizon. [ABSTRACT FROM AUTHOR]

We make a conceptual overview of a particular approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom. This idea goes back to Fock and Stueckelberg, leading to restrictions of the gauge symmetry of a theory, and it corresponds, in certain cases, to promoting constants of Nature to physical fields. Recently, different versions of this formulation have gained considerable attention in the literature, with several independent iterations, particularly in classical and quantum descriptions of gravity, cosmology, and electromagnetism. In particular, in the case of canonical quantum gravity, the Fock–Stueckelberg approach is relevant to the so-called problem of time. Our overview recalls and generalizes the work of Fock and Stueckelberg and its physical interpretation with the aim of conceptually unifying the different iterations of the idea that appear in the literature and of motivating further research. [ABSTRACT FROM AUTHOR]

In this paper, we present a quantum description of black holes given by coherent states of gravitons sourced by a matter core. The expected behavior in the weak-field region outside the horizon is recovered, with arbitrarily good approximation, but the classical central singularity is not resolved because the coherent states may not contain modes of arbitrarily short wavelength and the matter core must therefore have finite size. Ensuing quantum corrections both in the interior and exterior is also estimated by assuming that the mean-field approximation holds everywhere. These deviations from the classical black hole geometry can be viewed as quantum hair and will lead to a quantum corrected horizon radius and thermodynamics. [ABSTRACT FROM AUTHOR]

We consider compact objects in a classical and non-relativistic generalisation of Newtonian gravity, dubbed bootstrapped Newtonian theory, which includes higher-order derivative interaction terms of the kind generically present in the strong-field regime of gravity. By means of a field redefinition, the original bootstrapped Newtonian action is written in a canonical Newtonian form with non-linear source terms. Exact analytic solutions remain unattainable, but we show that perturbative solutions of the canonical theory can be efficiently used to derive approximate descriptions of compact objects. In particular, using the canonical potential, we can more directly and generally show that the Arnowitt–Deser–Misner mass differs from the (Newtonian) proper mass due to the non-linear couplings in the theory. A few examples of sources with different density profiles are explicitly reanalysed in this framework. [ABSTRACT FROM AUTHOR]

The Hawking–Penrose theorem is not covariant under field redefinitions. Should the invariance under such transformations be a true principle in nature, spacetime singularities become dubious objects. We here review the concept of covariant singularities, that is, singularities that are invariant under both spacetime diffeomorphisms and field redefinitions. [ABSTRACT FROM AUTHOR]

We consider the quantization of matter fields in a background described by the teleparallel equivalent to general relativity. The presence of local Lorentz and gauge symmetries gives rise to different coupling prescriptions, which we analyse separately. As expected, quantum matter fields produce divergences that cannot be absorbed by terms in the background action of teleparallel equivalent to general relativity. Nonetheless, the formulation of teleparallel gravity allows one to find out the source of the problem. By imposing local Lorentz invariance after quantization, we show that a modified teleparallel gravity, in which the coefficients in the action are replaced by free parameters, can be renormalized at one-loop order without introducing higher-order terms. This precludes the appearance of ghosts in the theory. [ABSTRACT FROM AUTHOR]

The assumptions of the Hawking–Penrose singularity theorem are not covariant under field redefinitions. Following the works on the covariant formulation of quantum field theory initiated by Vilkovisky and DeWitt in the 80s, we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with the other fields in the theory. From this viewpoint, a spacetime singularity might be just a singularity in the field-space coordinates, analogously to the standard coordinate singularities in General Relativity. Objects invariant under field-space coordinate transformations can then reveal whether certain spacetime singularity is indeed singular. We recall that observables in quantum field theory are scalar functionals in field space. Therefore, in principle, spacetime singularities corresponding to regular field-space curvature invariants would not affect physical observables. In this paper, we show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development. [ABSTRACT FROM AUTHOR]

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes. [ABSTRACT FROM AUTHOR]

Classical general relativity predicts the occurrence of spacetime singularities under very general conditions. Starting from the idea that the spacetime geometry must be described by suitable states in the complete quantum theory of matter and gravity, we shall argue that this scenario cannot be realised physically since no proper quantum state may contain the infinite momentum modes required to resolve the singularity. [ABSTRACT FROM AUTHOR]

We study the bootstrapped Newtonian potential generated by a localised source in one and two spatial dimensions, and show that both cases naturally lead to finite spatial extensions of the outer vacuum. We speculate that this implies the necessary existence of a cosmological (particle) horizon associated with compact sources. In view of the possible dimensional reduction occurring in ultra-high energy processes—like scatterings at Planckian energies, the gravitational collapse of compact objects or the end-point of black hole evaporation—one can consider such lower-dimensional 'bubbles' immersed in our Universe as describing (typically Planckian size) baby Universes relevant to those dynamics. [ABSTRACT FROM AUTHOR]

The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger–Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational theories to all orders in perturbation theory. Using non-perturbative techniques, we also show that neither the conformal sector of general relativity nor higher-derivative gravity features a minimum length. A minimum length scale, on the other hand, seems to always be present when one considers in-out amplitudes, from which one could extract the energy scale of scattering processes. [ABSTRACT FROM AUTHOR]

We show that the bootstrapped Newtonian potential generated by a uniform and isotropic source does not depend on the one-loop correction for the matter coupling to gravity. The latter, however, affects the relation between the proper mass and the Arnowitt–Deser–Misner (ADM) mass and, consequently, the pressure needed to keep the configuration stable. [ABSTRACT FROM AUTHOR]

We compute quantum corrections for the gravitational potential obtained by including a derivative self-coupling in its classical dynamics as a toy model for analysing quantum gravity in the strong field regime. In particular, we focus on quantum corrections to the classical solutions in the vacuum outside localised matter sources. [ABSTRACT FROM AUTHOR]

We study equilibrium configurations of a homogenous ball of matter in a bootstrapped description of gravity which includes a gravitational self-interaction term beyond the Newtonian coupling. Both matter density and pressure are accounted for as sources of the gravitational potential for test particles. Unlike the general relativistic case, no Buchdahl limit is found and the pressure can in principle support a star of arbitrarily large compactness. By defining the horizon as the location where the escape velocity of test particles equals the speed of light, like in Newtonian gravity, we find a minimum value of the compactness for which this occurs. The solutions for the gravitational potential here found could effectively describe the interior of macroscopic black holes in the quantum theory, as well as predict consequent deviations from general relativity in the strong field regime of very compact objects. [ABSTRACT FROM AUTHOR]

Black holes in d < 3 spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose–Einstein condensates (BEC) of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower-dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as N d ∼ (L d / ℓ p) d − 1 , where L d is the relevant length for the system in the (1 + d) -dimensional spacetime. In particular, this analysis shows that black holes cannot contain more than a few gravitons in d = 1. Since dimensional reduction is a common feature of many models of quantum gravity, this result can shed light on the end of the Hawking evaporation. We also consider (1 + 1) -dimensional cosmology in the context of corpuscular gravity and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions. [ABSTRACT FROM AUTHOR]

We study the quantum hair associated with coherent states describing slowly rotating black holes and show how it can be naturally related with the Bekenstein–Hawking entropy and with 1-loop quantum corrections of the metric for the (effectively) non-rotating case. We also estimate corrections induced by such quantum hair to the temperature of the Hawking radiation through the tunnelling method. [ABSTRACT FROM AUTHOR]

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured. [ABSTRACT FROM AUTHOR]

In this short paper, we discuss the possibility of testing the nature of astrophysical black holes using the recently observed black hole mergers. We investigate the possibility that a secondary black hole is created in the merger of two astrophysical black holes and discuss potential astrophysical signatures. We point out that black hole mergers are a possible astrophysical mechanism for the creation of quantum black holes with masses close to the Planck mass. [ABSTRACT FROM AUTHOR]

Static and stationary regular black holes are examined under a minimal set of requirements consisting of (i) the existence of a well defined event horizon and (ii) the weak energy condition for matter sourcing the geometry. We perform our analysis by means of the gravitational decoupling approach and find hairy solutions free of curvature singularities. We identify the matter source producing a deformation of the Minkowski vacuum such that the maximum deformation is the Schwarzschild solution for the static case, and the Kerr metric for the stationary case. [ABSTRACT FROM AUTHOR]

We describe the ground state for a gravitationally collapsed ball of dust as the direct product of wavefunctions for dust particles distributed over an arbitrary number of nested layers. This allows us to estimate the expectation value of the global radius as well as the effective energy density and pressures for the dust core of quantum black holes. In particular, the size of the quantum core does not depend on the number of layers and the mass function is shown to grow linearly with the areal radius up to the outermost layer. [ABSTRACT FROM AUTHOR]

The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. [ABSTRACT FROM AUTHOR]

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical 'Hamiltonian' constraint that relates the gravitational radius to the ADM mass, thus giving rise to a 'horizon wave-function'. This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes. [ABSTRACT FROM AUTHOR]

The notions of minimum geometrical length and minimum length scale are discussed with reference to correlation functions obtained from in-in and in-out amplitudes in quantum field theory. Whereas the in-in propagator for metric perturbations does not admit the former, the in-out Feynman propagator shows the emergence of the latter. A connection between the Feynman propagator of quantum field theories of gravity and the deformation parameter δ 0 of the generalised uncertainty principle (GUP) is then exhibited, which allows to determine an exact expression for δ 0 in terms of the residues of the causal propagator. A correspondence between the non-renormalisability of (some) theories (of gravity) and the existence of a minimum length scale is then conjectured to support the idea that non-renormalisable theories are self-complete and finite. The role played by the sign of the deformation parameter is further discussed by considering an implementation of the GUP on the lattice. [ABSTRACT FROM AUTHOR]

It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in configuration space. We show that any path-integral approach to quantum gravity leads to a tension between these properties, such that they cannot hold simultaneously. • Invariance under field redefinitions requires a metric in configuration space. • The configuration-space metric is an absolute structure. • Field redefinition invariance and background independence cannot hold simultaneously. [ABSTRACT FROM AUTHOR]

We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic Eötvös brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose–Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy. [ABSTRACT FROM AUTHOR]

We consider the effects of gravitons in the collapse of baryonic matter that forms a black hole. We first note that the effective number of (soft off-shell) gravitons that account for the (negative) Newtonian potential energy generated by the baryons is conserved and always in agreement with Bekenstein's area law of black holes. Moreover, their (positive) interaction energy reproduces the expected post-Newtonian correction and becomes of the order of the total ADM mass of the system when the size of the collapsing object approaches its gravitational radius. This result supports a scenario in which the gravitational collapse of regular baryonic matter produces a corpuscular black hole without central singularity, in which both gravitons and baryons are marginally bound and form a Bose–Einstein condensate at the critical point. The Hawking emission of baryons and gravitons is then described by the quantum depletion of the condensate and we show the two energy fluxes are comparable, albeit negligibly small on astrophysical scales. [ABSTRACT FROM AUTHOR]

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general ( 1 + D ) -dimensional space-time, for D > 3 and including the D = 1 case. We find that the probability P BH that such objects are (quantum) black holes behaves similarly to the probability in the ( 3 + 1 ) framework for D > 3 . In fact, for D ≥ 3 , the probability increases towards unity as the mass grows above the relevant D -dimensional Planck scale m D . At fixed mass, however, P BH decreases with increasing D , so that a particle with mass m ≃ m D has just about 10 % probability to be a black hole in D = 5 , and smaller for larger D . This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for D = 1 , we find the probability is comparably larger for smaller masses, but P BH < 0.5 , suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass m D in D > 3 . For D = 1 we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists. [ABSTRACT FROM AUTHOR]

It is congruous with the quantum nature of the world to view the spacetime geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the spacetime manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantization of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the 'superspace' of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble 'minisuperspace' approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability that they are black holes (BHs) rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the 'horizon wave function (HWF),' the latter being determined by the quantum state of the source. This formalism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum BHs. [ABSTRACT FROM AUTHOR]

We study binary mergers in bootstrapped Newtonian gravity, where higher-order couplings are added to the non-relativistic Lagrangian for the Newtonian potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from both the proper mass of Newtonian gravity and the proper mass of general relativity, which affects the interpretation of astrophysical and cosmological events. The aforementioned difference particularly provides important phenomenological constraints for the mass of the emitted matter and the compactness of the final object after the merger. The interpretation of the GW150914 signal in this theory also shows that LIGO's findings do not violate the mass gap, contrary to usual claims. We indeed find that typical stellar black hole masses can fit LIGO's data for a considerable range of compactness values. We calculate the black hole entropy in this context, which leads to a generalised black hole area law. Non-linear effects are found to effectively change only the gravitational strength via the renormalisation of Newton's constant in this case. [ABSTRACT FROM AUTHOR]

We review some features of Bose-Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein-Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately) one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons), resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole) and a continuous spectrum with energy ! > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature). Assuming the main effect of the internal scatterings is the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = Nm and a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ! > m is also shown to reduce the Hawking flux. The above corrections suggest that for black holes in this quantum state, the evaporation properly stops for a vanishing mass. [ABSTRACT FROM AUTHOR]

We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α > 1 ), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α 2 < 2 , and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for α 2 > 2 , and the uncertainty in the location of the horizon blows up at α 2 = 2 , signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2 ) can exist. [ABSTRACT FROM AUTHOR]

Abstract: We reconsider perturbative unitarity violation in the standard model Higgs inflation model. We show that the Cutkosky cutting rule implied by perturbative unitarity is fulfilled at one-loop. This is a strong indication that unitarity is restored order by order in perturbation theory. We then resum certain one-loop diagrams and show that the relevant dressed amplitude fulfills the Cutkosky rule exactly. This is an example of the self-healing mechanism. The original Higgs inflation model is thus consistent and does not require any new physics beyond the standard model at least up to the Planck scale. [Copyright &y& Elsevier]

Abstract: We address the issue of (quantum) black hole formation by particle collision in quantum physics. We start by constructing the horizon wave-function for quantum mechanical states representing two highly boosted non-interacting particles that collide in flat one-dimensional space. From this wave-function, we then derive a probability that the system becomes a black hole as a function of the initial momenta and spatial separation between the particles. This probability allows us to extend the hoop conjecture to quantum mechanics and estimate corrections to its classical counterpart. [Copyright &y& Elsevier]

Using the effective four-dimensional Einstein field equations, we build analytical models of spherically symmetric stars in the brane-world, in which the external space-time contains both an ADM mass and a tidal charge. In order to determine the interior geometry, we apply the principle of minimal geometric deformation, which allows one to map general relativistic solutions to solutions of the effective four-dimensional brane-world equations. We further restrict our analysis to stars with a radius linearly related to the total general relativistic mass, and obtain a general relation between the latter, the brane-world ADM mass and the tidal charge. In these models, the value of the star's radius can then be taken to zero smoothly, thus obtaining brane-world black hole metrics with a tidal charge solely determined by the mass of the source and the brane tension. We find configurations which entail a partial screening of the gravitational mass, and general conclusions regarding the minimum mass for semiclassical black holes are also drawn. [ABSTRACT FROM AUTHOR]

A localized particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. To combine these two pictures, we introduce a horizon wave function determined by the particle wave function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass may be a black hole. We also show that our construction entails an effective generalized uncertainty principle (GUP), simply obtained by adding the uncertainties coming from the two wave functions associated with a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts. [ABSTRACT FROM AUTHOR]

Abstract: We explore the possibility that, in a quantum field theory with Planck scale cutoff , observable quantities for low-energy processes respect the Lorentz symmetry. In particular, we compute the one-loop radiative correction Π to the self-energy of a scalar field with interaction, using a modified (non-invariant) propagator which vanishes in the trans-Planckian regime, as expected in the “classicalisation” scenario. We then show that, by imposing the result does not depend on Λ (in the limit ), an explicit (albeit not unique) expression for Π can be derived, which is similar to the one simply obtained with the standard Feynman propagator and a cutoff . [Copyright &y& Elsevier]

We review the General Relativistic model of a (quasi-)pointlike particle represented by a massive shell of electrically charged matter, which displays an ADM mass M equal to the electric charge |Q| in the small-volume limit. We employ the Israel-Darboux's junction equations to explicitly derive this result, and then study the modifications introduced by the existence of a minimum length scale λ. For λ of the order of the Planck length (or larger), we find that the ADM mass becomes equal to the bare mass m0 of the shell, like it occurs for the neutral case. [ABSTRACT FROM AUTHOR]

We propose to include gravity in quantum field theory nonperturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space--time determined by the four-momenta of the other particles in the same graph. By making additional working assumptions, we are able to put this idea at work in a simplified context, and obtain a modified Feynman propagator for the massless neutral scalar field. Our expression shows a suppression at high momentum, strong enough to entail finite results, to all loop orders, for processes involving at least two virtual particles. [ABSTRACT FROM AUTHOR]

The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existence is predicted in models with extra-spatial dimensions. [ABSTRACT FROM AUTHOR]

Abstract: We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of neutral matter which has vanishing total energy in the small-volume limit. We then show that, by assuming a Generalised Uncertainty Principle, which implies the existence of a minimum length of the order of the Planck scale, the total energy instead remains finite and equal to the shell''s proper mass both for very heavy and very light particles. This suggests that the quantum structure of space–time might be related to the classical Equivalence Principle and possible implications for the late stage of evaporating black holes are briefly mentioned. [Copyright &y& Elsevier]

It has recently been debated whether a class of generalized uncertainty principles that include gravitational sources of error is compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space–time dimensions are present. However, we shall show here that the validity of the holographic counting can be maintained also in models with extra spatial dimensions, but at than intriguing price — the equivalence principle for a pointlike source is violated and the inertial mass differs from the gravitational mass in a specific, nontrivial way. [ABSTRACT FROM AUTHOR]

Abstract: We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1% with the standard slow-roll results. Moreover, the leading WKB approximation to second order in the slow-roll parameters leads to analytical predictions in qualitative agreement with those obtained by the Green''s function method. [Copyright &y& Elsevier]

We study the propagation of classical electromagnetic waves on the simplest four-dimensional spherically symmetric metric with a dilaton background field. Solutions to the relevant equations are obtained perturbatively in a parameter which measures the strength of the dilaton field (hence parameterizes the departure from Schwarzschild geometry). The loss of energy from outgoing modes is estimated as a back-scattering process against the dilaton background, which would affect the luminosity of stars with a dilaton field. The radiation emitted by a freely falling point-like source on such a background is also studied by numerical methods. [ABSTRACT FROM AUTHOR]

Current theoretical investigations seem to indicate the possibility of observing signatures of short distance physics in the cosmic microwave background spectrum. We try to gain a deeper understanding on why all information about this regime is lost in the case of black hole radiation but not necessarily so in a cosmological setting by using the moving mirror as a toy model for both backgrounds. The different responses of the Hawking and cosmic microwave background spectra to short distance physics are derived in the appropriate limit when the moving mirror mimics a black hole background or an expanding universe. The different sensitivities to new physics, displayed by both backgrounds, are clarified through an averaging prescription that accounts for the intrinsic uncertainty in their quantum fluctuations. We then proceed to interpret the physical significance of our findings for time-dependent backgrounds in the light of nonlocal string theory. [ABSTRACT FROM AUTHOR]

There is evidence that trans-Planckian physics does not affect the Hawking radiation in four dimensions and, consequently, deviations from the linear dispersion relation (for massless particles) at very high energies cannot be revealed using four-dimensional black holes. We study this issue in the context of models with extra-spatial dimensions and show that small black holes that could be produced in accelerators might also provide a chance of testing the high energy regime where non-linear dispersion relations are generally expected. [Copyright &y& Elsevier]

We propose a method to extend to the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow the exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parametrized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat “pancake” for astrophysical sources. [ABSTRACT FROM AUTHOR]