International Journal of Modern Physics D

There is a general belief, reinforced by statements in standard textbooks, that: (i) one can obtain the full nonlinear Einstein theory of gravity by coupling a massless, spin 2 field h_ab self-consistently to the total energy–momentum tensor, including its own; (ii) this procedure is unique and leads to Einstein–Hilbert (EH) action; and (iii) it uses only standard concepts in Lorentz-invariant field theory and does not involve any geometrical assumptions. After providing several reasons why such beliefs are suspect — and critically re-examining several previous attempts — we provide a detailed analysis aimed at clarifying the situation. First, we prove that it is impossible to obtain the EH action, starting from the standard action for gravitons in linear theory and iterating repeatedly. This result follows from the fact that EH action has a part (viz. the surface term arising from second derivatives of the metric tensor) which is nonanalytic in the coupling constant, when expanded in terms of the graviton field. Thus, at best, one can only hope to obtain the remaining, quadratic, part of the EH Lagrangian (viz. the Γ² Lagrangian) if no additional assumptions are made. Second, we use the Taylor series expansion of the action for Einstein's theory, to identify the tensor , to which the graviton field h_ab couples to the lowest order (through a term of the form in the Lagrangian). We show that the second rank tensor is not the conventional energy–momentum tensor T^ab of the graviton and provide an explanation for this feature. Third, we construct the full nonlinear Einstein theory with the source being a spin 0 field, a spin 1 field or relativistic particles by explicitly coupling the spin 2 field to this second rank tensor order by order and summing up the infinite series. Finally, we construct the theory obtained by self-consistently coupling h_ab to the conventional energy–momentum tensor T^ab order by order and show that this does not lead to Einstein's theory. The implications are discussed.

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of this paper could be "Why Are We Still Unable to Write a Guide on How to Propose Viable Alternatives to General Relativity?". Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein equivalence principle, into quantitative ones, such as the metric postulates, stand on rather shaky ground — probably contrary to popular belief — as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions (such as those of the stress–energy tensor or classical vacuum) on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the equivalence principle, the use of conformal frames and equivalence between theories are clarified.

We offer a critical assessment of some generic features of various current approaches to the construction of a theory of quantum gravity. We argue that there is a need for further conceptual clarifications before such an enterprise can be launched in a truly well-grounded setting, and that one of the guiding principles that can be viewed as part of the reasons for successes of the past theoretical developments is the identification of unspeakables — concepts that should not only play no role in the formulation of the theories, but ones that the formalism of the theory itself should prevent from ever being spoken about.

In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space–time at the smallest scale. Of particular relevance is the possible definition of physical coordinate functions within the theory and the study of their algebraic properties, such as noncommutativity. Here we approach this issue from the perspective of loop quantum gravity and the picture of quantum geometry that the formalism offers. In particular, as we argue here, this emerging picture has two main elements: (i) the nature of the quantum geometry at the Planck scale is one-dimensional, and polymeric with quantized geometrical quantities; and (ii) appropriately defined operators corresponding to coordinates by means of intrinsic, relational constructions become noncommuting. This particular feature of the operators, which operationally localize points on space, gives rise to an emerging geometry that is also, in a precise sense, fuzzy.

A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth–Sun L2 point. Such an artificial planetary system in space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the periapsis shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.

Recently, in a series of papers, Mukhopadhyay and his collaborators have argued for possible pure hydrodynamic turbulence in a Keplerian accretion disk. This is essentially important to solving the puzzle of the transport mechanism in cold accretion disk systems where the temperature could be lower than 5000 K, where magnetorotational instability seems not to be working to trigger turbulence. Here we quantify the corresponding instability and turbulence in terms of turbulent viscosity and obtain the famous Shakura–Shunyaev viscosity parameter, α. It is exciting that the range of α obtained from our analysis is 0.1 ≳ α ≳ 0.0001 for a realistic parameter region. This range also suggests that once the hydrodynamic instability described by Mukhopadhyay and his collaborators leads to turbulence — an effect which should exist in systems independent of being hot or cold — the effect may compete with the magnetohydrodynamic effect even in hot accretion disks and thus may be effective in transporting matter in hot gas systems as well.

Exact stationary axially symmetric solutions to the four-dimensional Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with an approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments overestimate the amount of matter needed to explain such curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down in an extended rotating region, even though it is valid locally everywhere. No conflict with solar system tests arises.

Lorentz invariance plays a pivotal role in the derivation of the Hawking effect, which crucially requires an integration in arbitrarily small distances or, equivalently, in unbounded energies. New physics at the Planck scale could, therefore, potentially modify the emission spectrum. We argue, however, that the kinematic invariance can be deformed in such a way that the thermal spectrum remains insensitive to trans-Planckian physics.

We argue that quantum gravity theories that carry a Lie-algebraic modification of the Poincaré and Heisenberg algebras inevitably provide inhomogeneities that may serve as seeds for cosmological structure formation. Furthermore, in this class of theories one must expect a strong polarization and spin dependence of various quantum gravity effects.

Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand the gravity and dynamics of black objects in higher dimensions. We provide evidence that:

(i) The gravitational Gregory–Laflamme instability has a classical counterpart in the Rayleigh–Plateau instability of fluids. Each known feature of the gravitational instability can be accounted for in the fluid model. These features include threshold mode, dispersion relation, time evolution and critical dimension of certain phase transitions. Thus, we argue that black strings break in much the same way as water from a faucet breaks up into small droplets.

(ii) General rotating black holes can also be understood with this analogy. In particular, instability and bifurcation diagrams for black objects can easily be inferred.

This correspondence can and should be used as a guiding tool for understanding and exploring the physics of gravity in higher dimensions.

We propose a mechanism for the origin of matter in the universe in the framework of Einstein–Gauss–Bonnet gravity in higher dimensions. The new static black hole solution recently discovered by the authors,¹ with the Kaluza–Klein split of space–time as a product of the usual with a space of negative constant curvature, is indeed a pure gravitational creation of a black hole which is also endowed with a Maxwell-like gravitational charge in four-dimensional vacuum space–time. This solution has been further generalized to include radially flowing radiation, which means that extra-dimensional curvature also produces matter distribution asymptotically, resembling charged null dust. The static black hole could thus be envisioned as being formed from anti–de Sitter space–time by the collapse of radially inflowing charged null dust. It thus establishes the remarkable reciprocity between matter and gravity — as matter produces gravity (curvature), gravity produces matter. After the Kaluza–Klein generation of the Maxwell field, this is the first instance of realization of matter without matter in the classical framework.

In this essay I first discuss the physical relevance of the inequality for axially symmetric (nonstationary) black holes, where m is the mass and J the angular momentum of the space–time. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture about the physical implications of this characterization for the nonlinear stability problem for black holes.

Recent work has revealed intriguing connections between a Belinsky–Khalatnikov–Lifshitz-type analysis of spacelike singularities in general relativity and certain infinite-dimensional Lie algebras, particularly the "maximally extended" hyperbolic Kac–Moody algebra E₁₀. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(–time) at the Planck scale, and hence — via an effective "de-emergence" of space near the singularity — to a novel mechanism for achieving background independence in quantum gravity.

We explore the method of Robinson and Wilczek for deriving the Hawking temperature of a black hole. In this method, the Hawking radiation restores general covariance in an effective theory of near-horizon physics which otherwise exhibits a gravitational anomaly at the quantum level. The method has been shown to work for broad classes of black holes in arbitrary space–time dimensions. These include static black holes, accreting or evaporating black holes, charged black holes, rotating black holes, and even black rings. In the cases of charged and rotating black holes, the expected superradiant current is also reproduced.

We show that gravitational wave emission, both in the linear approximation and in the full nonlinear regime of general relativity, gives a hint of black hole thermodynamic processes by which a black hole evolves emitting part of its perturbation in the form of gravitational waves and absorbing the remnant, reaching a final configuration with a larger entropy. The partition of energy in this process is constrained by the maximum entropy principle, and the final entropy obtained numerically is given as a distribution function of the efficiency of the process. The distribution function is in the realm of nonextensive thermostatistics with entropic index q ≃ 1/2, a result that is validated analytically by the linear approximation.

We show that holography follows directly from the basic structure of spherically symmetric loop quantum gravity. The result is not dependent on detailed assumptions about the dynamics of the theory being considered. It ties strongly the amount of information contained in a region of space to the tight mathematical underpinnings of loop quantum geometry.

It is argued that high energy density excitations, responsible for UV divergences in quantum field theories, including quantum gravity, are likely to be the source of child universes which carry them out of the original space–time. This decoupling prevents the high UV excitations from having any influence on physical amplitudes. Child universe production could therefore be responsible for UV regularization in quantum field theories which take into account gravitational effects. Finally, we discuss child universe production in the last stages of black hole evaporation, the prediction of the absence of trans-Planckian primordial perturbations, the connection with the minimum length hypothesis, and in particular the connection with the maximal curvature hypothesis.

We explore the possible physical consequences derived from the fact that the only static and asymptotically flat vacuum space–time possessing a regular horizon is the Schwarzschild solution (Israel theorem). If small deviations from the Schwarzschild metric are described by means of exact solutions to Einstein equations (as should be the case), then for very compact configurations, at the time scale at which radiatable multipole moments are radiated away, important physical phenomena should occur, as illustrated by some results on different solutions belonging to the Weyl class of static, axially symmetric solutions to the Einstein equations.

It is well known that black holes are the most extreme objects in nature: they have the maximal energy and entropy capacities allowed by the laws of physics. In this essay we reveal another extreme property of these fascinating objects: black holes have the fastest relaxation dynamics allowed by a quantum theory of gravity. From information theory and thermodynamic considerations a universal bound on the relaxation time τ of a perturbed physical system is inferred, τ ≥ ħ/πT, where T is the system's temperature. We then show that black holes may actually attain this fundamental bound, which makes them the fastest-relaxing objects in the universe.

We suggest that the (small but nonvanishing) cosmological constant, and the holographic properties of gravitational entropy, may both reflect unconventional quantum spin statistics at a fundamental level. This conjecture is motivated by the nonlocality of quantum gravity and the fact that spin is an inherent property of space–time. As an illustration we consider the "quon" model, which interpolates between Fermi and Bose statistics, and show that this can naturally lead to an arbitrarily small cosmological constant. In addition to laboratory tests, we briefly discuss the possible observable imprint on cosmological fluctuations from inflation.

It has long been a primary objective of cosmology to understand the apparent isotropy in our universe and to provide a mathematical formulation for its evolution. A promising school of thought for its explanation is quiescent cosmology, which already possesses a mathematical framework, namely the definition of an isotropic singularity, but only for the initial state of the universe. A complementary framework is necessary in order to also describe possible final states of the universe. Our new definitions of an anisotropic future endless universe and an anisotropic future singularity, whose structure and properties differ significantly from those of the isotropic singularity, offer a promising realization for this framework. The combination of the three definitions together may then provides the first complete formalization of the quiescent cosmology concept.

It is shown that non-local, higher-derivative operators, which arise generically in string field theory, can act as additional sources of friction on the inflaton field as it rolls away from a maximum in its potential. Moreover, the cosmic dynamics can be quantified in terms of a local field theory, where the curvature of an effective potential has been suppressed. A prolonged phase of quasi-exponential expansion can therefore be realised with steep potentials that typically arise in particle physics models. We illustrate this effect within the context of p-adic string theory.

String theory tells us that quantum gravity has a dual description as a field theory (without gravity). We use the field theory dual to ask what happens to an object as it falls into the simplest black hole: the two-charge extremal hole. In the field theory description the wave function of a particle is spread over a large number of "loops," and the particle has a well-defined position in space only if it has the same "position" on each loop. For the infalling particle we find one definition of "same position" on each loop, but there is a different definition for outgoing particles and no canonical definition in general in the horizon region. Thus the meaning of "position" becomes ill-defined inside the horizon.

There are strong reasons to believe that the gravitational interaction — described in terms of a metric on a smooth space–time — is an emergent, long wavelength phenomenon, like elasticity. I describe a concrete framework for realizing this paradigm against the backdrop of several recent results. In this perspective, quantum fluctuations of the microscopic degrees of freedom of the space–time lead to residual random displacements of any null surface. The latter can be described in terms of an effective theory using an action associated with the normal displacements of the null surfaces. Extremizing this action leads to an equation determining the background geometry. The resulting theory is Einstein gravity at the lowest order with the Lanczos–Lovelock type quantum corrections. The metric is not a dynamical variable in this approach and gravity arises as a coarse-grained statistical feature of an underlying microscopic theory.

A consistent approach to cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such corrections. This approach has been criticized, however, on the grounds that its effects may be gauge artifacts. We apply the fully covariant formalism of Zalaletdinov's macroscopic gravity and show that, after making some essential gauge choices, the cosmological equations receive space–time scalar corrections which are therefore observable in principle, and further, that the broad structure of these corrections is identical to those derived by Buchert.

Stable end-point stars currently fall into two distinct classes — white dwarfs and neutron stars — differing enormously in central density and radial size. No stable cold dead stars are thought to span the intervening densities or have masses beyond ~2–3 solar masses. I show, however, that the general-relativistic condition of hydrostatic equilibrium augmented by the equation of state of a neutron condensate at 0 K generates stable sequences of cold stars that span the density gap and can have masses well beyond prevailing limits. The radial sizes and mass limit of each sequence are determined by the mass and scattering length of the composite bosons. Solutions for hypothetical bosons of ultrasmall mass and large scattering length yield huge self-gravitating systems of low density, resembling galactic dark matter halos.

There are fundamental reasons why there should exist a reformulation of quantum mechanics which does not refer to a classical space–time manifold. It follows that quantum mechanics as we know it is a limiting case of a more general nonlinear quantum theory, with the nonlinearity becoming significant at the Planck mass/energy scale. This nonlinearity is responsible for a dynamically induced collapse of the wave function, during a quantum measurement, and it hence falsifies the many-worlds interpretation of quantum mechanics. We illustrate this conclusion using a mathematical model based on a generalized Doebner–Goldin equation. The non-Hermitian part of the Hamiltonian in this norm-preserving, nonlinear, Schrödinger equation dominates during a quantum measurement, and leads to a breakdown of linear superposition.

The tremendous progress in the science and technology of timing devices and laser sources has reached a stage where their stability and coherence are sufficient for implementing unbalanced interferometers over a length scale exceeding the Earth–Moon distance. This opens up the possibility of optical homodyne interferometry over such distances, either to the Moon or to artificial satellites that are at large distances from the Earth. The precision of the measurement of changes in the orbital distance would increase by a factor of 10⁴ or more, enabling new ultrahigh precision tests of the equivalence principle, study of gravitomagnetism, and of subtle gravitational phenomena, including the constancy of the gravitational constant and possible gravitational expansion of space. It would enable geodesy and tide studies with unprecedented precision. Such interferometers would also be useful for the detection and study of low frequency gravitational waves.

We present the current status of the new approach to quantum general relativity based on the exact resummation of its perturbative series as this series was formulated by Feynman. We show that the resummed theory is UV-finite and we present some phenomenological applications as well.

We give a mathematically exact and physically faithful embedding of curved 4D cosmology in a flat 5D space, thereby enabling visualization of the big bang in a new and informative way. In fact, in unified theories of fields and particles with real extra dimensions, it is possible to dispense with the initial singularity.

Cosmic acceleration is explained quantitatively, as an apparent effect due to gravitational energy differences that arise in the decoupling of bound systems from the global expansion of the universe. "Dark energy" is a misidentification of those aspects of gravitational energy which by virtue of the equivalence principle cannot be localized, namely gradients in the energy due to the expansion of space and spatial curvature variations in an inhomogeneous universe. A new scheme for cosmological averaging is proposed which solves the Sandage – de Vaucouleurs paradox. Concordance parameters fit supernova luminosity distances, the angular scale of the sound horizon in the CMB anisotropies, and the effective comoving baryon acoustic oscillation scale seen in galaxy clustering statistics. Key observational anomalies are potentially resolved, and unique predictions made, including a quantifiable variance in the Hubble flow below the scale of apparent homogeneity.

Different models of the cosmic substratum which pretend to describe the present stage of accelerated expansion of the Universe, like the ΛCDM model or the Chaplygin gas, can be seen as special realizations of a holographic dark energy cosmology if the option of an interaction between pressureless dark matter and dark energy is taken seriously. The corresponding interaction strength parameter plays the role of a cosmological constant. Differences occur at the perturbative level. In particular, the pressure perturbations are intrinsically nonadiabatic.

Black holes behave as thermodynamic systems, and a central task of any quantum theory of gravity is to explain these thermal properties. A statistical-mechanical description of black hole entropy once seemed remote, but today we suffer an embarrassment of riches: despite counting very different states, many inequivalent approaches to quantum gravity obtain identical results. Such "universality" may reflect an underlying two-dimensional conformal symmetry near the horizon, which can be powerful enough to control the thermal characteristics independent of other details of the theory. This picture suggests an elegant description of the relevant degrees of freedom as Goldstone-boson-like excitations arising from symmetry breaking by the conformal anomaly.

We elucidate how black holes form in trans-Planckian collisions. In the rest frame of one of the incident particles, the gravitational field of the other, which is rapidly moving, looks like a gravitational shock wave. The shock wave focuses the target particle down to a much smaller impact parameter. In turn, the gravitational field of the target particle captures the projectile when the resultant impact parameter is smaller than its own Schwarzschild radius, forming a black hole. One can deduce this by referring to the original argument of escape velocities exceeding the speed of light, which Michell and Laplace used to discover the existence of black holes.

Relativistic heavy ion collisions create a strongly coupled quark–gluon plasma. Some of the plasma's properties can be approximately understood in terms of a dual black hole. These properties include shear viscosity, thermalization time, and drag force on heavy quarks. They are hard to calculate from first principles in QCD.

Extracting predictions about quark–gluon plasmas from dual black holes mostly involves solving Einstein's equations and classical string equations of motion. AdS/CFT provides a translation from gravitational calculations to gauge theory predictions. The gauge theory to which the predictions apply is super-Yang–Mills theory. QCD is different in many respects from super-Yang–Mills, but it seems that its high temperature properties are similar enough for us to make some meaningful comparisons.

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole "molecules" of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations.

We demonstrate that as we extrapolate the current ΛCDM universe forward in time, all evidence of the Hubble expansion will disappear, so that observers in our "island universe" will be fundamentally incapable of determining the true nature of the universe, including the existence of the highly dominant vacuum energy, the existence of the CMB, and the primordial origin of light elements. With these pillars of the modern Big Bang gone, this epoch will mark the end of cosmology and the return of a static universe. In this sense, the coordinate system appropriate for future observers will perhaps fittingly resemble the static coordinate system in which the de Sitter universe was first presented.