International Journal of Modern Physics D

We discuss some of the drawbacks of using event horizons to define black holes and suggest ways in which black holes can be described without event horizons, using trapping horizons. We show that these trapping horizons give rise to thermodynamic behavior and possibly Hawking radiation too. This raises the issue of whether the event horizon or the trapping horizon should be seen as the true boundary of a black hole. This difference is important if we believe that quantum gravity will resolve the central singularity of the black hole and clarifies several of the issues associated with black hole thermodynamics and information loss.

We show that cosmological topologically massive gravity at the chiral point allows not only Brown–Henneaux boundary conditions as consistent boundary conditions, but also slightly more general ones which encompass the logarithmic primary found in J. High Energy Phys.07 (2008) 134 as well as all its descendants.

This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of string theory within the broader context of six decades of failed attempts at an autonomous S matrix approach to particle theory.

The central message, contained in Secs. 5 and 6, is that string theory is not what its name suggests, namely a theory of objects in space–time whose localization is string-instead of pointlike. Contrary to popular opinion, the oscillators corresponding to the Fourier models of a quantum-mechanical string do not become embedded in space–time and neither does the "range space" of a chiral conformal QFT acquire the interpretation of stringlike-localized quantum matter.

Rather, string theory represents a solution to a problem which enjoyed some popularity in the 1960s: find a principle which, similar to the SO(4,2) group in the case of the hydrogen spectrum, determines an infinite component wave function with a (realistic) mass/spin spectrum. Instead of the group theory used in the old failed attempts, it creates this mass/spin spectrum by combining an internal oscillator quantum mechanics with a pointlike-localized quantum-field-theoretic object, i.e. the mass/spin tower "sits" over one point and does not arise from a wiggling string in space–time.

The widespread acceptance of a theory whose interpretation has been based on metaphoric reasoning had a corroding influence on particle theory, a point which will be illustrated in the last section with some remarks of a more sociological nature. These remarks also lend additional support to observations on connections between the discourse in particle physics and the present Zeitgeist of the post–Cold War period that are made in the introduction.

Holography gives us a tool for viewing the Hawking effect from a new, classical perspective. In the context of Randall–Sundrum braneworld models, we show that the basic features of four-dimensional evaporating solutions are nicely translated into classical, five-dimensional language. This includes the possible dual bulk description of particles tunneling through the horizon.

We point out that in the context of quantum fields in time-dependent classical backgrounds, the number of created particles with a given momentum largely deviates about its mean value. Since the corresponding Fourier modes are nonlocal, this deviation shows that the expectation value of the number operator can make sense only in an ensemble of space–times. Using a complete orthonormal family of localized wave packets, we show how an ensemble interpretation can be given to cosmological particle creation in local terms. The reheating process following inflation is re-examined in the light of this construction.

Robinson and Wilczek have suggested that loop corrections in quantum gravity can alter the running gauge coupling constants from the behaviour found in the absence of gravity. Although their original calculation is not correct, the basic idea behind their paper has been re-examined recently for quantized Einstein–Maxwell theory with a cosmological constant. In this essay I discuss some of the issues surrounding the calculation and mention some of the implications. I argue that it is possible for a theory that is not conventionally asymptotically free to become so in the presence of gravity, and for gravity to lead to a new ultraviolet fixed point. This establishes a provocative link between the microscopic and macroscopic realms.

The quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus a contribution coming from the spatial part of the action gives the correct temperature.

Nonlinear resonance is ubiquitous in nature. Resonance is relevant to understanding phenomena in quite distinct areas such as music, cellular structure, and astrophysics, and in the very early universe. In order to see the crucial role played by resonance in cosmology, we assume that closed FRW universes with a massive inflaton field evolve according to the field equations that contain additional terms arising from high energy corrections to cosmological scenarios. As a consequence, nonsingular bounces in the early evolution of the universe are produced. We have shown that in narrow windows of the parameter space of the models, nonlinear resonance phenomena of KAM tori occur and lead to the destruction of those tori that trap the inflaton, resulting in the escape of the universe into inflation. These resonance windows are labeled by an integer n ≥ 2; n is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom.

We propose, as a compelling pattern for the holographic principle, a covariant entropy bound conjecture for more general dynamical horizons. Then we apply our conjecture to ΛCDM cosmological models, where we find that it imposes a novel upper bound, 10^-90, on the cosmological constant for our own universe by taking into account the dominant entropy contribution from supermassive black holes, which thus provides an alternative macroscopic perspective for understanding the long-standing cosmological constant problem. As an intriguing implication of this conjecture, we also discuss the possible profound relation between the present cosmological constant, the origin of mass, and the anthropic principle.

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects, including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents space–time in a fundamentally piecewise-linear fashion or, more generally, which has large curvature fluctuations at small scales. The appearance of unusual statistics may be a generic feature (such as the deformed position–momentum uncertainty relations and the appearance of a fundamental length scale) which is to be expected in any theory of quantum gravity, and which could be testable.

It is discussed whether some of the consistency problems of present day physics could be solved by replacing special relativity, whose underlying kinematics is ruled by the Poincaré group, with de Sitter relativity, whose underlying kinematics is ruled by the de Sitter group. In contrast to ordinary special relativity, which seems to fail at the Planck scale, this new relativity is "universal," in the sense that it holds at all energy scales.

Searches for transient astrophysical pulses could open an exciting new window into the fundamental physics of quantum gravity. In particular, an evaporating primordial black hole in the presence of an extra dimension can produce a detectable transient pulse. Observations of such a phenomenon can in principle explore the electroweak energy scale, indicating that astrophysical probes of quantum gravity can successfully complement the exciting new physics expected to be discovered in the near future at the Large Hadron Collider.

The recent suggestion that late time quantum dynamics may be important for resolving cosmological issues associated with our observed universe requires a consideration of several subtle issues associated with quantum cosmology, as we describe here. The resolution of these issues will be important if we are to be able to properly ascribe probability measures associated with eternal inflation, and a string landscape.

We show that small deviations from spherical symmetry, described by means of exact solutions to Einstein equations, provide a mechanism to "bleach" the information about the collapsing body as it falls through the apparent horizon, thereby resolving the information loss paradox. The resulting picture and its implication related to Landauer's principle in the presence of a gravitational field is discussed.

We propose a theory of quantum gravity which formulates the quantum theory as a nonperturbative path integral, where each space–time history appears with the weight exp(iS^EH), with S^EH the Einstein–Hilbert action of the corresponding causal geometry. The path integral is diffeomorphism-invariant (only geometries appear) and background-independent. The theory can be investigated by computer simulations, which show that a de Sitter universe emerges on large scales. This emergence is of an entropic, self-organizing nature, with the weight of the Einstein–Hilbert action playing a minor role. Also, the quantum fluctuations around this de Sitter universe can be studied quantitatively and remain small until one gets close to the Planck scale. The structures found to describe Planck-scale gravity are reminiscent of certain aspects of condensed-matter systems.

It is explained why the curvature associated with the vacuum energy density arising from SUSY breaking cannot be completely transferred to the extra spatial dimensions of a bulk space–time manifold, and it is shown — without using hierarchy arguments but only the results of current large-scale observations — why the TeV scale should correspond to the maximal allowed SUSY-breaking scale.

We outline an improved cosmology which uses a higher-dimensional space of the type implied by unification, where the cosmological "constant" decays from an unbounded value at the big bang to an acceptable value today. This model leads to a better understanding of inflation and is in good agreement with observations of galaxies.

When one takes into account gravitation, the measurement of space and time cannot be carried out with infinite accuracy. When quantum mechanics is reformulated taking into account this lack of accuracy, the resolution of the measurement problem can be performed via decoherence without the usual pitfalls. The resulting theory has the same physical predictions of quantum mechanics with a reduction postulate, but is radically different, with the quantum states evolving unitarily in terms of the underlying variables. Gravitation therefore makes this worrisome situation, potentially leading to two completely different views of reality, irrelevant from an empirical point of view. It may, however, be highly relevant from a philosophical point of view.

Hawking radiation is obtained from anomalies resulting from a breaking of diffeomorphism symmetry near the event horizon of a black hole. Such anomalies, manifested as a nonconservation of the energy–momentum tensor, occur in two different forms — covariant and consistent. The crucial role of covariant anomalies near the horizon is revealed, since this is the only input required to obtain the Hawking flux, thereby highlighting the universality of this effect. A brief description of the application of this method to obtain thermodynamic entities like entropy or temperature is provided.

Observations of the expansion rate of the universe at late times disagree by a factor of 1.5–2 with the prediction of homogeneous and isotropic models based on ordinary matter and gravity. We discuss how the departure from linearly perturbed homogeneity and isotropy due to structure formation could explain this discrepancy. We evaluate the expansion rate in a dust universe which contains nonlinear structures with a statistically homogeneous and isotropic distribution. The expansion rate is found to increase relative to the exactly homogeneous and isotropic case by a factor of 1.1–1.3 at some tens of billions of years. The time scale follows from the cold dark matter transfer function and the amplitude of primordial perturbations without additional free parameters.

Using simple conditions drawn from the stability of the cosmos in terms of vacuum energy density, the cutoff momentum of entanglement is related to the Planckian mass. In so doing the black hole entropy is shown to be independent of the number of field species that contribute to vacuum fluctuations. And this is in spite of the fact that the number of field species is a linear multiplicand of the entanglement entropy when the latter is expressed in terms of the fundamental momentum cutoff of all fields.

We describe how a certain simple modification of general relativity, in which the local cosmological constant is allowed to depend on the space–time curvature, predicts the existence of halos of modified gravity surrounding spherically symmetric objects. We show that the gravitational mass of an object weighed together with its halo can be much larger than its gravitational mass as seen from inside the halo. This effect could provide an alternative explanation of the dark-matter phenomenon in galaxies. In this case, the local cosmological constant in the solar system must be some six orders of magnitude larger than its cosmic value obtained in the supernova type Ia experiments. This is well within the current experimental bounds, but may be directly observable in future high-precision experiments.

Gravity in a higher-dimensional scenario is one of the most topical of research subjects due to the possibility of decisive results from experiments. The field exhibits duality of various kinds. On the one hand, the weakness of gravity and the hierarchy issues are handled with some success as one cascades from a larger number of small dimensions with strong gravity to a smaller number of dimensions of larger space with weaker effective gravity. On the experimental front, the highest energy accelerator and the weakest energy mechanical oscillators available to us today are simultaneously focussed at the TeV scale to address new features in gravity physics. This intriguing scenario and its conceptual and phenomenological aspects are examined here, with new results from considerations of hitherto-unexplored higher-dimensional gravitomagnetic effects at the atomic scale.

We establish an explicit connection between the evolution of generic inhomogeneous black brane solutions in asymptotically AdS space–times and the evolution of relativistic conformal fluids in one lower dimension. Specifically, given any solution to a particular set of fluid-dynamical equations, one can construct an inhomogeneous black brane solution with a regular event horizon. This connection is reminiscent of the membrane paradigm for black holes; in our case the dynamics of the entire space–time is encoded in a fluid living at the boundary. This fluid–gravity correspondence leads to interesting implications for both gravitational physics and fluid dynamics.

In this note we study the possibility of obtaining a dark energy solution in a D-brane scenario against a warped background that includes brane-position-dependent corrections for the nonperturbative superpotential. The volume modulus is stabilized at instantaneous minima of the potential. Though the model can account for the existence of dark energy within the present observational bound, fine-tuning of the model parameters becomes unavoidable. Moreover, the model does not possess a tracker solution.

It is well known that one could determine the kinematics of gravity by using the Principle of Equivalence and local inertial frames. I describe how the dynamics of gravity can be similarly understood by suitable thought experiments in a local Rindler frame. This approach puts in proper context several unexplained features of gravity and describes the dynamics of space–time in a broader setting than in Einstein's theory.

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical space–time manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the "weakly quantum, strongly gravitational" dynamics of a relativistic particle whose mass is much greater than the Planck mass is dual to the "strongly quantum, weakly gravitational" dynamics of another particle whose mass is much less than the Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of the Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found.

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved space–time, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved space–time does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a "vacuum state" and "particles". We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients — and, thus, the quantum field theory. By contrast, ground/vacuum states — in space–times, such as Minkowski space–time, where they may be defined — cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.

Identifying the fundamental degrees of freedom of a black hole poses a long-standing puzzle. Recently Goldberger and Rothstein forwarded a theory of the low frequency degrees of freedom within the effective field theory approach, where they are relevancy-ordered but of unclear physical origin. Here these degrees of freedom are identified with near-horizon but non-compact gravitational perturbations which are decomposed into delocalized multipoles. Their world-line (kinetic) action is determined within the classical effective field theory (CLEFT) approach and their interactions are discussed. The case of the long-wavelength scattering of a scalar wave off a Schwarzschild black hole is treated in some detail, interpreting within the CLEFT approach the equality of the leading absorption cross section with the horizon area.