Narrow Results

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states ρ_s(m, H) of mass m in Anti-de Sitter space–time. For high m, (high Hm → c/α′), no phase transition occurs at the Anti-de Sitter string temperature T_s = (1/2πk_B)L_clc²/α′, which is higher than the flat space (Hagedorn) temperature t_s. (L_cl = c/H, the Hubble constant H acts as producing a smaller string constant α′ and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti-de Sitter temperature scale T_sem = ℏc/(2πk_BL_cl). We compute the quantum string emission σ_string by a black hole in Anti-de Sitter (or asymptotically Anti-de Sitter) space–time (bhAdS). For T_{sem bhAdS} ≪ T_s (early evaporation stage), it shows the QFT Hawking emission with temperature T_{sem bhAdS} (semiclassical regime). For T_{sem bhAdS} → T_s, it exhibits a phase transition into a Anti-de Sitter string state of size , and Anti-de Sitter string temperature T_s. New string bounds on the black hole emerge in the bhAdS string regime. The bhAdS string regime determines a maximal value for H : H_max = 0.841c/l_s. The minimal black hole radius in Anti-de Sitter space–time turns out to be r_{g min} = 0.841l_s, and is larger than the minimal black hole radius in de Sitter space–time by a numerical factor equal to 2.304. We find a new formula for the full AdS entropy S_sem(H), as a function of the usual Bekenstein–Hawking entropy . For L_cl ≫ ℓ_Planck, i.e. for low H ≪ c/ℓ_Planck, or classical regime, is the leading term with its logarithmic correction, but for high H ≥ c/ℓ_Planck or quantum regime, no phase transition operates, in contrast to de Sitter space, and the entropy S_sem(H) is very different from the Bekenstein–Hawking term .

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T_sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature T_s at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M > m_Pl, angular momentum J and charge Q is a string state of temperature T_s, string mass M_s, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy S_s(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at T_s) we find for high j (extremal string states j → m²α′c), a new phase transition at a temperature , higher than T_s. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S_sem(M, J), as a function of the usual Bekenstein–Hawking entropy . For M ≫ m_Pl and J < GM²/c, is the leading term, but for high angular momentum, (nearly extremal case J = GM²/c), a gravitational phase transition operates and the whole entropy S_sem is drastically different from the Bekenstein–Hawking entropy . This new extremal black hole transition occurs at a temperature T_{sem J} = (J/ℏ)T_sem, higher than the Hawking temperature T_sem.

An effective string theory in physically relevant cosmological and black hole space–times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and anti-de Sitter AdS space–times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square-root branch point singularity in any space–time dimensions. This is of the type of the de Vega–Sánchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For dS background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition. (iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in nonthermal pure quantum radiation (no information loss). (vi) New lower string bounds are given for the Kerr–Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical–quantum (wave–particle) duality, which is universal irrespective of any symmetry or isommetry of the space–time and of the number or the kind of space–time dimensions.

We have previously shown that the singularity in a Schwarzschild black hole of stellar or larger mass may be avoided in a semiclassical manner by using as a source of gravity the stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, with a minimum spherical radius a few orders of magnitude larger than the Planck length. In this note we estimate the nonlocal contribution to the total SET due to particle creation from vacuum. We show that this contribution is negligibly small as compared to vacuum polarization and does not affect the previously suggested scenario.

We study particle production of coherently oscillating inflaton in semiclassical theory of gravity by representing inflaton in coherent and squeezed state formalisms. A comparative study of the inflaton in classical gravity with coherent state inflaton in semiclassical gravity is also presented.

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states ρ_s(m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature T_s = (1/2πk_B)L_cl c²/α', higher than the flat space (Hagedorn) temperature t_s (L_cl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature T_sem = ħ c/(2πk_BL_cl). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy S_sem(H), as a function of the usual Bekenstein–Hawking entropy . For L_cl ≫ ℓ_Planck, i.e. for low is the leading term, but for high H near c/ℓ_Planck, a new phase transition operates and the whole entropy S_sem (H) is drastically different from the Bekenstein–Hawking entropy . We compute the string quantum emission cross-section σ_string by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For T_{sem bhdS} ℓ T_s (early evaporation stage), it shows the QFT Hawking emission with temperature T_{sem bhdS} (semiclassical regime). For T_{sem bhdS} → T_s, σ_string exhibits a phase transition into a string de Sitter state of size , , and string de Sitter temperature T_s. Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius r_g emerge in the bhdS string regime: it can become r_g = L_s/2, or it can reach a more quantum value, r_g = 0.365 ℓ_s.

Nonclassical representation of a minimally coupled scalar field in the open and closed FRW universe, is studied in the semiclassical theory of gravity. Particle production of a nonclassical scalar field in the coherent and squeezed state formalisms in the open FRW universe is examined. Numerical solutions to the semiclassical Friedmann equations are obtained for both the closed and open models in the coherent and squeezed state formalisms. Mandel's Q parameter of the quantum optics is studied in the cosmological context with associated cosmological parameters, in the semiclassical theory of gravity.

We investigate the influence of vacuum polarization of quantum massive fields on the scalar sector of quasinormal modes in spherically symmetric black holes. We consider the evolution of a massless scalar field on the space–time corresponding to a charged semiclassical black hole, consisting of the quantum-corrected geometry of a Reissner–Nordström black hole dressed by a quantum massive scalar field in the large mass limit. Using a sixth order WKB approach we find a shift in the quasinormal mode frequencies due to vacuum polarization.

A minimally coupled nonclassical homogeneous scalar field is examined in the flat FRW universe in the semiclassical theory of gravity. Particle production in thermal coherent and squeezed states is studied for the flat FRW universe, in the oscillatory phase of the inflaton. Solutions for the semiclassical Friedmann equations are obtained in the thermal nonclassical states. Validity of the semiclassical theory is examined in the thermal coherent and squeezed states in the oscillatory phase of inflaton. Particle creation can be enhanced due to thermal and quantum effects. Quantum fluctuations of the inflaton in thermal coherent and squeezed state formalisms are also studied. Classical gravity differ from semiclassical gravity in the thermal coherent state only by an amplitude factor.

For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

The experimental results that test Bell’s inequality have found strong evidence suggesting that there are nonlocal aspects in nature. Evidently, these nonlocal effects, which concern spacelike separated regions, create an enormous tension between general relativity and quantum mechanics. In addition, by avoiding the coincidence limit, semiclassical gravity can also accommodate nonlocal aspects. Motivated by these results, we study if it is possible to construct geometrical theories of gravitation that are nonlocal in the sense of Bell. We propose three constructions of such theories, which could constitute an important step towards our understanding of the interplay between quantum mechanics and gravitation.

We show that the repulsive effects associated to the zero-point energies of quantum fields are capable of supporting ultracompact stars that overcome the compactness limits present in general relativity for any object in hydrostatic equilibrium. These objects are exact self-consistent solutions in semiclassical gravity that incorporate the backreaction of the renormalized stress-energy tensor (RSET) of quantum fields in vacuum. We arrive at stars of striking qualitative agreement through two independent modelings of the RSET, evidencing the generality and robustness of this result. The main physical properties of these novel black hole mimickers are reviewed.

Black holes play a pivotal role in the foundations of physics, but there is an alarming discrepancy between what is considered to be a black hole in observational astronomy and theoretical studies. Despite claims to the contrary, we argue that identifying the observed astrophysical black hole candidates as genuine black holes is not justified based on the currently available observational data, and elaborate on the necessary evidence required to support such a remarkable claim. In addition, we investigate whether the predictions of semiclassical gravity are equally compatible with competing theoretical models, and find that semiclassical arguments favor horizonless configurations.

In this paper, we discuss the corrections to the photon orbits of a nonrotating black hole due to semiclassical fluctuations of the metric. It is found that the photon orbit impact parameter differences with the critical impact parameter become of the order of the semiclassical fluctuations. We calculate the effect of the semiclassical fluctuations on the photon orbits and show that instead of circulating the black hole infinite number of times at the critical orbit, the photons bounce off the semiclassical geometry.

If entanglement builds spacetime, then conversely, disentanglement ought to destroy spacetime. From the quantum null energy condition and quantum focusing conjecture, we obtain disentanglement criteria which necessitate infinite energies and strong spacetime singularities. We apply our results to the strong cosmic censorship proposal, where singularities at the Cauchy horizons in black holes are desirable. Using our disentanglement criteria and without resorting to any detailed calculations, we provide an exceedingly general and physically transparent discussion of strong cosmic censorship in semiclassical black holes. We argue that strong cosmic censorship is enforced in asymptotically flat and de Sitter black holes by disentanglement and describe how similar disentanglement might be avoided in some anti-de Sitter cases.

Relativistic particles with momentum space described by a group manifold provide a very interesting link between gravity, quantum group symmetries and non-commutative field theories. We discuss how group valued momenta emerge in the context of three-dimensional Einstein gravity and describe the related non-commutative field theory. As an application we introduce a non-commutative heat-kernel, calculate the associated spectral dimension and comment on its non-trivial behavior. In four spacetime dimensions the only known example of momenta living on a group manifold is encountered in the context of the κ-Poincaré algebra introduced by Lukierski et al. 20 years ago. I will discuss the construction of a one-particle Hilbert space from the classical κ-deformed phase space and show how the group manifold structure of momentum space leads to an ambiguity in the quantization procedure. The tools introduced in the discussion of field quantization lead to a natural definition of deformed two-point function.

We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between a quantized Dirac field and a homogeneous time-dependent scalar field. We present the renormalized semiclassical equations that are needed in order to take into account the backreaction of the produced Dirac fermions in both gravitational and scalar background fields.

We derive and critically examine the consequences that follow from the formation of a regular black or white hole horizon in finite time of a distant observer. In spherical symmetry, only two distinct classes of solutions to the semiclassical Einstein equations are self-consistent. Both are required to describe the formation of physical black holes and violate the null energy condition in the vicinity of the outer apparent horizon. The near-horizon geometry differs considerably from that of classical solutions. If semiclassical physics is valid, accretion into a black hole is no longer possible after the horizon has formed. In addition, the two principal generalizations of surface gravity to dynamical spacetimes are irreconcilable, and neither can describe the emission of nearly-thermal radiation. Comparison of the required energy and timescales with established semiclassical results suggests that if the observed astrophysical black holes indeed have horizons, their formation is associated with new physics.

The evaporation of four-dimensional spherically symmetric black holes is presented in the framework of quantum field theory in curved spacetimes and semiclassical gravity. It is discussed how the evaporation process can be sourced by the presence of the trace anomaly of a massless, conformally coupled scalar field outside the apparent horizon of the black hole.

The semiclassical approximation takes into account the gravitational contribution of zero-point energies. We model this contribution via the renormalized stress-energy tensor (RSET) of a massless scalar field, which we compute in a cutoff-regularized version of the Polyakov approximation. When the field is in the Boulware vacuum state (the natural vacuum for stellar geometries), the RSET works in favor of violating the Buchdahl compactness limit. We review the family of classical constant-density stellar solutions, paying particular attention to the notion of criticality—the presence of offsets in the mass function—and use it as a warm up for the analysis of the semiclassical set of solutions. For stars that surpass Buchdahl limit by far, the critical solution has an irregular pressure. This divergence in pressure moves inward by introducing a negative offset in the mass. In the semiclassical theory we find something rather different, namely that the critical configuration already displays a pressure that diverges exactly at the center of the structure. This drastic difference between the classical and semiclassical space of solutions suggests that semiclassical gravity could potentially allow for the existence of ultracompact stellar objects.