International Journal of Modern Physics D

In this paper, we review some highlights from the String theory, the black hole physics and the doubly special relativity and some thought experiments which were suggested to probe the shortest distances and/or maximum momentum at the Planck scale. Furthermore, all models developed in order to implement the minimal length scale and/or the maximum momentum in different physical systems are analyzed and compared. They entered the literature as the generalized uncertainty principle (GUP) assuming modified dispersion relation, and therefore are allowed for a wide range of applications in estimating, for example, the inflationary parameters, Lorentz invariance violation, black hole thermodynamics, Saleker–Wigner inequalities, entropic nature of gravitational laws, Friedmann equations, minimal time measurement and thermodynamics of the high-energy collisions. One of the higher-order GUP approaches gives predictions for the minimal length uncertainty. A second one predicts a maximum momentum and a minimal length uncertainty, simultaneously. An extensive comparison between the different GUP approaches is summarized. We also discuss the GUP impacts on the equivalence principles including the universality of the gravitational redshift and the free fall and law of reciprocal action and on the kinetic energy of composite system. The existence of a minimal length and a maximum momentum accuracy is preferred by various physical observations. The concern about the compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action should be addressed. We conclude that the value of the GUP parameters remain a puzzle to be verified.

It is commonly anticipated that gravity is subjected to the standard principles of quantum mechanics. Yet some — including Einstein — have questioned that presumption, whose empirical basis is weak. Indeed, recently Dyson has emphasized that no conventional experiment is capable of detecting individual gravitons. However, as we describe, if inflation occurred, the universe, by acting as an ideal graviton amplifier, affords such access. It produces a classical signal, in the form of macroscopic gravitational waves, in response to spontaneous (not induced) emission of gravitons. Thus recent BICEP2 observations of polarization in the cosmic microwave background (CMB) will, if confirmed, provide firm empirical evidence for the quantization of gravity. Their details also support quantitative ideas concerning the unification of strong, electromagnetic and weak forces, and of all these with gravity.

Recently, it was argued [A. Almheiri et al., arXiv: 1207.3123, A. Almheiri et al., arXiv: 1304.6483], via a delicate thought experiment, that it is not consistent to simultaneously require that (a) Hawking radiation is pure, (b) effective field theory is valid outside a stretched horizon and (c) infalling observers encounter nothing unusual as they cross the horizon. These are the three fundamental assumptions underlying Black Hole Complementarity and the authors proposed that the most conservative resolution of the paradox is that (c) is false and the infalling observer burns up at the horizon (the horizon acts as a "firewall"). However, the firewall violates the equivalence principle and breaks the CPT invariance of quantum gravity. This led Hawking to propose recently that gravitational collapse may not end up producing event horizons, although he did not give a mechanism for how this may happen. Here we will support Hawking's conclusion in a quantum gravitational model of dust collapse. We will show that continued collapse to a singularity can only be achieved by combining two independent and entire solutions of the Wheeler–DeWitt equation. We interpret the paradox as simply forbidding such a combination. This leads naturally to a picture in which matter condenses on the apparent horizon during quantum collapse.

I show that in a general, dynamic spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. All static spacetimes maintain holographic equipartition; i.e. in these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk. It is the departure from holographic equipartition that drives the time evolution of the spacetime. This result, which is equivalent to Einstein's equations, provides an elegant, holographic, description of spacetime dynamics.

It has been argued that when black holes are treated as quantum systems there are implications at the horizon and not just the singularity. Infalling observers will meet a firewall of high energy quanta. We argue that the question of whether an observer falling into a black hole experiences a smooth horizon or a firewall is identical to the question of whether Schrödinger's cat is either in a definite state, alive or dead, or in a superposition of the two. Since experience with real macro-systems indicate the former, the black hole state vector is seen to describe a set of decoherent alternatives each with a smooth horizon and the entanglement puzzle is thereby side stepped.

At first glance, the (indirect) measurement of primordial tensor modes by the BICEP2 Collaboration supports an inflationary paradigm for early universe cosmology together with quantum vacuum fluctuations (aka gravitons) as the origin of the spectrum. In this paper, we argue the observed signal may instead be a signature of semiclassical sources of perturbations during inflation. In this scenario, despite a large tensor-to-scalar ratio r ≃ 0.2, it may be possible to write an effective field theory (EFT) of a rolling scalar field without super-Planckian excursions. If the results from BICEP2 withstand further scrutiny, measurements of primordial non-Gaussianity with large scale structure surveys, and direct detection of gravitational waves (GWs) with the new generation of observatories, will be of paramount importance to elucidate the (quantum) origin of structure in the universe.

It is shown by means of the optical medium analogy that the static Casimir force between two conducting plates is modulated by gravitational waves. The magnitude of the resulting force changes within the range of already existing small force metrology. It is suggested to enhance the effects on a Casimir force oscillator by mechanical parametric amplification driven by periodic illumination of interacting semiconducting boundaries. This represents a novel opportunity for the ground-based laboratory detection of gravitational waves on the nanoscale.

Modified theories of gravity have received a renewed interest due to their ability to account for the cosmic acceleration. In order to satisfy the solar system tests of gravity, these theories need to include a screening mechanism that hides the modifications on small scales. One popular and well-studied theory is chameleon gravity. Our own galaxy is necessarily screened, but less dense dwarf galaxies may be unscreened and their constituent stars can exhibit novel features. In particular, unscreened stars are brighter, hotter and more ephemeral than screened stars in our own galaxy. They also pulsate with a shorter period. In this paper, we exploit these new features to constrain chameleon gravity to level three orders of magnitude lower the previous measurements. These constraints are currently the strongest in the literature.

In this paper, we consider highly entangled states in theories with a gravity dual, where the entangled degrees of freedom are causally disconnected from each other. Using the basic rules of holography, we argue that there is a nontraversable wormhole in the gravity dual whose geometry encodes the pattern of the entanglement.

How to detect spacetime torsion? In this paper, we provide the theoretical basis for an answer to this question. Multipolar equations of motion for a very general class of gravitational theories with nonminimal coupling in spacetimes admitting torsion are given. Our findings provide a framework for the systematic testing of whole classes of theories with the help of extended test bodies. One surprising feature of nonminimal theories turns out to be their potential sensitivity to torsion of spacetime even in experiments with ordinary (not microstructured) test matter.

We analyzed the Rotation Curves (RCs) of two crucial objects, the dwarf galaxy Orion and the low luminosity Spiral NGC 3198, in the framework of Rⁿ gravity. We surprisingly found that the no dark matter (DM) power-law F(R) case fits them well, performing much better than LCDM halo models. The level of this unexpected success can be a boost for Rⁿ gravity.

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).

The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should be used in a given situation and the choice is dictated by experiments. It is expected that the Dirac equation holds for microscopic masses and the Kerr solution for macroscopic masses. This suggests that Einstein gravity and the Dirac theory are limiting cases of a common underlying theoretical framework. Here we propose that such a framework is provided by a geometric theory of gravity on a Riemann–Cartan spacetime, which includes torsion. The Dirac equation emerges as the torsion-dominated, gravity-free limit of this framework.

The assumed universality of the equivalence principle suggests that a particle in a gravitational field has identical physics to one in an accelerated frame. Yet, energy considerations prohibit radiation from a static particle in a gravitational field while the accelerating counterpart emits. Solutions to the fundamental problems of radiation from charges in a gravitational field and consequences to the equivalence principle usually contrast the far-field and global nature of radiation with the local validity of the equivalence principle. Here, we suggest reliable physical solutions that recognizes the essential need for motional currents and the magnetic component for radiation to occur. Our discussion reiterates the need for a fresh careful look at universality of free fall (UFF) for charged particles in a gravitational field.

The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger–Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

A new approach to gravitational radiation reaction is developed which is generalized from a successful solution to the electrodynamic problem in Minkowski spacetime.

The recent CMB data from Planck and BICEP2 observations have opened a new window for inflationary cosmology. In this paper, we compare three Starobinsky-like inflationary scenarios: (i) The original Starobinsky proposal, (ii) a family of dynamically broken SUGRA models, and (iii) a class of "decaying" vacuum Λ(H) cosmologies. We then focus on the Λ(H) variant, which spans the complete cosmic history of the universe from an early inflationary stage, followed by the "graceful exit" into the standard radiation regime, the matter epoch and, finally, the late-time accelerated expansion. Computing the effective potential we find that the "running" Λ(H) models also provide a prediction for the tensor-to-scalar ratio of the CMB spectrum, r ≃ 0.16, which is compatible to within 1σ with the value recently measured by the BICEP2 collaboration.

Traditional derivations of general relativity (GR) from the graviton degrees of freedom assume spacetime Lorentz covariance as an axiom. In this paper, we survey recent evidence that GR is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of GR, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not a property of spacetime. This result has revolutionary implications for fundamental physics.

The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.

We show that scalar hair can be added to rotating, vacuum black holes (BHs) of general relativity. These hairy black holes (HBHs) clarify a lingering question concerning gravitational solitons: Whether a BH can be added at the centre of a boson star (BS), as it typically can for other solitons. We argue that it can, but only if it is spinning. The existence of such HBHs is related to the Kerr superradiant instability triggered by a massive scalar field. This connection leads to the following conjecture: a (hairless) BH, which is afflicted by the superradiant instability of a given field, must allow hairy generalizations with that field.

Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional route. Our approach is simple and natural: we form a very general model and then apply two physical assumptions supported by experimental evidence. This easily reduces our construction to a model equivalent to general relativity. Finally, we suggest a simple way of modifying our theory to investigate nonstandard spacetime symmetries.

We propose a gravitational theory in which the effective Lagrangian of the gravitational field is given by an arbitrary function of the Ricci scalar, the trace of the matter energy–momentum tensor, and the contraction of the Ricci tensor with the matter energy–momentum tensor. The matter energy–momentum tensor is generally not conserved, thus leading to the appearance of an extra-force, acting on massive particles in a gravitational field. The stability conditions of the theory with respect to local perturbations are also obtained. The cosmological implications of the theory are investigated, representing an exponential solution. Hence, a Ricci tensor–energy–momentum tensor coupling may explain the recent acceleration of the universe, without resorting to the mysterious dark energy.

Using the quantum corrected Friedmann equation, obtained from the quantum Raychaudhuri equation, and assuming a small mass of the graviton (but consistent with observations and theory), we propose a resolution of the smallness problem (why is observed vacuum energy so small?) and the coincidence problem (why does it constitute most of the universe, about 70%, in the current epoch?).

Solar models suggest that four billion years ago the young Sun was ~25% fainter than it is today, rendering Earth's oceans frozen and lifeless. However, there is ample geophysical evidence that Earth had a liquid ocean teeming with life 4 Gyr ago. Since , the Sun's luminosity is exceedingly sensitive to small changes in the gravitational constant G. We show that a percent-level increase in G in the past would have prevented Earth's oceans from freezing, resolving the faint young Sun paradox. Such small changes in G are consistent with observational bounds on ΔG/G. Since , an increase in G leads to fainter supernovae, creating tension between standard candle and standard ruler probes of dark energy. Precisely such a tension has recently been reported by the Planck team.

The vacuum state in quantum field theory is known to exhibit an important number of fundamental physical features. In this work we explore the possibility that this state could also present a nontrivial spacetime structure on large scales. In particular, we will show that by imposing the renormalized vacuum energy–momentum tensor to be conserved and compatible with cosmological observations, the vacuum energy of sufficiently heavy fields behaves at late times as nonrelativistic matter rather than as a cosmological constant. In this limit, the vacuum state supports perturbations whose speed of sound is negligible and accordingly allows the growth of structures in the vacuum energy itself. This large-scale structure of vacuum could seed the formation of galaxies and clusters very much in the same way as cold dark matter does.

We study an isothermal system of semi-degenerate self-gravitating fermions in general relativity (GR). The most general solutions present is mass density profiles with a central degenerate compact core governed by quantum statistics followed by an extended plateau, and ending in a power law behavior r^-2. By fixing the fermion mass m in the keV regime, the different solutions depending on the free parameters of the model: the degeneracy and temperature parameters at the center, are systematically constructed along the one-parameter sequences of equilibrium configurations up to the critical point, which is represented by the maximum in a central density (ρ₀) versus core mass (M_c) diagram. We show that for fully degenerate cores, the Oppenheimer–Volkoff (OV) mass limit is obtained, while instead for low degenerate cores, the critical core mass increases showing the temperature effects in a nonlinear way. The main result of this work is that when applying this theory to model the distribution of dark matter (DM) in big elliptical galaxies from miliparsec distance-scales up to 10² Kpc, we do not find any critical core-halo configuration of self-gravitating fermions, able to explain both the most super-massive dark object at their center together with the DM halo simultaneously.

It has been taken as a truth that collapsing matter can eventually cross the horizon and enter into the interior of a black hole in a finite proper time. However, the Rindler/tachyon dual description we suggested recently implies that this should not be the case. A test particle falling towards the event horizon of a nonextreme black hole can actually be viewed as an unstable particle, whose dynamics is described by the tachyon field theory. This means that the collapsing process of a free particle in Rindler space is essentially a tachyon condensation process. In terms of the results in tachyon condensation, we learn that the infalling particle should strongly couple to bulk gravitational modes and should decay completely into something like gravitons before reaching the horizon. Hence, there should be no matter that can cross a horizon as still matter. The matter will get "dissolved" into spacetime when approaching the horizon.

The white-hole sector of Kruskal's solution is almost never used in physical applications. However, it might contain the solution to many of the problems associated with gravitational collapse and evaporation. This paper tries to draw attention to some bouncing geometries that make a democratic use of the black- and white-hole sectors. We will argue that these types of behavior could be perfectly natural in some approaches to the next physical level beyond classical general relativity.

We consider a quantum field theory on a spherically symmetric quantum spacetime described by loop quantum gravity. The spin network description of spacetime in such a theory leads to equations for the quantum field that are discrete. We show that to avoid significant violations of Lorentz invariance, one needs to consider specific nonlocal interactions in the quantum field theory similar to those that appear in string theory. This is the first sign that loop quantum gravity places restrictions on the type of matter considered, and points to a connection with string theory physics.

The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subadditivity has sorted out the possible resolutions into three sharp categories: (i) No new physics at r ≫ l_p; this necessarily implies remnants/information loss. A realization of remnants is given by a baby universe attached near r ~ 0. (ii) Violation of the "no-hair" theorem by nontrivial effects at the horizon r ~ M. This possibility is realized by fuzzballs in string theory, and gives unitary evaporation. (iii) Having the vacuum at the horizon, but requiring that Hawking quanta at r ~ M³ be somehow identified with degrees of freedom inside the black hole. A model for this "extreme nonlocality" is realized by conjecturing that wormholes connect the radiation quanta to the hole.

We propose a new probe to test the nature of gravity at various redshifts through large-scale cosmological observations. We use our void catalog, extracted from the Sloan Digital Sky Survey (SDSS, DR10), to trace the distribution of matter along the lines of sight to SNe Ia that are selected from the Union II catalog. We study the relation between SNe Ia luminosities and convergence and also the peculiar velocities of the sources. We show that the effects, on SNe Ia luminosities, of convergence and of peculiar velocities predicted by the theory of general relativity and theories of modified gravities are different and hence provide a new probe of gravity at various redshifts. We show that the present sparse large-scale data does not allow us to determine any statistically-significant deviation from the theory of general relativity but future more comprehensive surveys should provide us with means for such an exploration.

Quantum-gravitational pressure can stop gravitational collapse and cause a bounce. We observe that: (i) due to the huge time dilation, the process can last micro-seconds in local proper time and billions of years observed from the outside; (ii) the bounce volume can be much larger than planckian, because the onset of quantum-gravity effects is governed by density, not size; (iii) the emerging object can then be bigger than planckian by a factor (m/m_P)ⁿ, where m is the initial mass, m_P is the Planck mass, and n positive; (iv) the interior of an evaporating hole can keep memory of the initial mass, providing an independent scale for the physics of the final explosion. If so, primordial black holes could produce a detectable signal of quantum gravitational origin, which we estimate, under some hypotheses, around the wavelength 10^-14 cm.