International Journal of Modern Physics D

The Thirring–Lense effect is the phenomenon that an observer near a rotating mass, being in a state which is non-rotating with respect to the rest of the universe, experiences extra inertial forces, i.e. becomes dizzy. The first anticipation of the effect goes back to Ernst Mach; its first quantitative prediction on the basis of general relativity was given by Hans Thirring and Joseph Lense. Almost ninety years later, the effect seems to be experimentally verified.

This work has been motivated by the criticisms raised on the error budget contribution — on a recently performed measurement of the Lense–Thirring effect — from the uncertainties of the secular variations of the Earth's even zonal harmonics. The relativistic secular precession has been observed from the analysis of 11 years of LAGEOS and LAGEOS II laser ranging data. In the analysis, the recent EIGEN–GRACE02S gravity field model (derived from GRACE data only) was used during the orbit determination process using the NASA Goddard software package GEODYN II. In particular, the measurement has been derived combining the nodes only of the two LAGEOS satellites in order to cancel the larger error source, due to the uncertainty of the first even zonal harmonic, and solved for the Lense–Thirring effect predicted by Einstein's general relativity. The authors of the relativistic measurement claimed an error of about 1% of the relativistic effect as due to the temporal variation of the even zonal harmonics. The main criticism is that on a much larger error estimate, about 11% of the relativistic effect on the analyzed time span of the two LAGEOS satellites orbital data should be considered. Moreover, the authors of the relativistic measurement emphasized that whatever the value they chose for the secular variations, in particular of the effective value for , they always obtained the same discrepancy of about 1% between the observed and predicted effect, without however providing a detailed explanation. In the present work we address all the cited aspects. In particular, we explain the physical reason for the results obtained by the authors of the relativistic measurement in all their simulations. As we will see, two additional errors (linear in time) must be considered in the satellites orbit analysis if we want to correctly explain the experimental results. The first is a time-dependent error related with the mismodeling of the secular variations of the even zonal harmonics. The inclusion of this error in the error analysis explains why the same discrepancy between the observed and predicted effect has been always obtained independently of the assumed value for , i.e. for the errors in the time variations of the even zonal harmonics. The second is a time-independent error related to the non-coincidence between the reference epoch of the gravity field, i.e. the middle epoch of the time span during which the gravity field has been determined by the GRACE mission, and the reference epoch fixed in the orbit analysis program. The inclusion of this error in the error analysis explains the 1% value for the discrepancy between the prediction and the observations. In order to validate our results we fitted for an effective from the combined nodes of the LAGEOS satellites with the EIGEN2S gravity field model obtained from the CHAMP mission. From our fit, we consistently confirmed our previous statements. In particular, we prove a very interesting and new approach in order to compute the effective values of the time variations of the even zonal harmonics from the estimate of the time-independent error previously cited.

A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity is due to the existence of a critical speed. The dynamics of particles moving faster than the critical speed could then be contrary to Newtonian expectations. Working within the framework of gravitoelectromagnetism, the implications of the existence of a critical speed are explored. The results are expected to be significant for high energy astrophysics.

We investigate the possibility of measuring the post-Newtonian general relativistic gravitomagnetic Lense–Thirring effect in the Jovian system of its Galilean satellites Io, Europa, Ganymede and Callisto in view of recent developments in processing and modeling their optical observations spanning a large time interval (125 years). The present day best observations have an accuracy between several kilometers to few tens of kilometers, which is just the order of magnitude of the Lense–Thirring shifts of the orbits of the Galilean satellites over almost a century. From a comparison between analytical development and numerical integration it turns out that, unfortunately, most of the secular component of the gravitomagnetic signature is removed in the process of fitting the initial conditions. Indeed, an estimation of the magnitude of the Lense–Thirring effect in the ephemerides residuals is given; the resulting residuals have a maximum magnitude of 20 meters only (over 125 years).

In this article I present a simple Newtonian heuristic for motivating a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames (the Einstein equivalence principle), plus the use of Galilean coordinate transformations to connect the freely falling local inertial frames back to the "fixed stars." Because of the heuristic and quasi-Newtonian manner in which the specific choice of spacetime geometry is motivated, we are at best justified in expecting it to be a weak-field approximation to the true spacetime geometry. However, in the case of a spherically symmetric point mass the result is coincidentally an exact solution of the full vacuum Einstein field equations — it is the Schwarzschild geometry in Painlevé–Gullstrand coordinates.

This result is much stronger than the well-known result of Michell and Laplace whereby a Newtonian argument correctly estimates the value of the Schwarzschild radius — using the heuristic presented in this article one obtains the entire Schwarzschild geometry. The heuristic also gives sensible results — a Riemann flat geometry — when applied to a constant gravitational field. Furthermore, a subtle extension of the heuristic correctly reproduces the Reissner–Nordström geometry and even the de Sitter geometry. Unfortunately the heuristic construction is not truly generic. For instance, it is incapable of generating the Kerr geometry or anti-de Sitter space.

Despite this limitation, the heuristic does have useful pedagogical value in that it provides a simple and direct plausibility argument (not a derivation) for the Schwarzschild geometry — suitable for classroom use in situations where the full power and technical machinery of general relativity might be inappropriate. The extended heuristic provides more challenging problems — suitable for use at the graduate level.

The idea that quantum gravity manifestations are associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. Other related ideas seem to be drowning in interpretational quagmires. This leads us to consider alternative lines of thought for such a phenomenological search. We discuss the underlying viewpoints and briefly mention their possible connections with other current theoretical ideas.

The names tetrad, tetrads, cotetrads have been used with many different meanings in the physics literature, not all of them equivalent from the mathematical point of view. In this paper, we introduce unambiguous definitions for each of those terms, and show how the old miscellanea made many authors introduce in their formalism an ambiguous statement called the "tetrad postulate," which has been the source of much misunderstanding, as we show explicitly by examining examples found in the literature. Since formulating Einstein's field equations intrinsically in terms of cotetrad fields θ^a, a = 0, 1, 2, 3 is a worthy enterprise, we derive the equation of motion of each θ^a using modern mathematical tools (the Clifford bundle formalism and the theory of the square of the Dirac operator). Indeed, we identify (giving all details and theorems) from the square of the Dirac operator some noticeable mathematical objects, namely, the Ricci, Einstein, covariant D'Alembertian and the Hodge Laplacian operators, which permit us to show that each θ^a satisfies a well-defined wave equation. Also, we present for completeness a detailed derivation of the cotetrad wave equations from a variational principle. We compare the cotetrad wave equation satisfied by each θ^a with some others appearing in the literature, and which are unfortunately in error.

Chryssomalakos and Okon, through a uniqueness analysis, have strengthened the Vilela Mendes suggestion that the immunity to infinitesimal perturbations in the structure constants of a physically-relevant Lie algebra should be raised to the status of a physical principle. Since the Poincaré–Heisenberg algebra does not carry the indicated immunity, it is suggested that the Lie algebra for the interface of the gravitational and quantum realms (IGQR) is its stabilized form. It carries three additional parameters: a length scale pertaining to the Planck/unification scale, a second length scale associated with cosmos, and a new dimensionless constant. Here, we show that the adoption of the stabilized Poincaré–Heisenberg algebra (SPHA) for the IGQR has the immediate implication that a "point particle" ceases to be a viable physical notion. It must be replaced by objects which carry a well-defined, representation space-dependent, minimal spatio-temporal extent. The ensuing implications have the potential, without spoiling any of the successes of the Standard Model of particle physics, to resolve the cosmological constant problem while concurrently offering a first-principle hint as to why there exists a coincidence between cosmic vacuum energy density and neutrino masses. The main theses which the essay presents is the following: an extension of the present-day physics to a framework which respects SPHA should be seen as the most natural and systematic path towards gaining a deeper understanding of outstanding questions, if not providing answers to them.

"Doubly-special relativity" (DSR), the idea of a Planck-scale Minkowski limit that is still a relativistic theory, but with both the Planck scale and the speed-of-light scale as nontrivial relativistic invariants, was proposed as a physics intuition for several scenarios which may arise in the study of the quantum-gravity problem, but most DSR studies focused exclusively on the search of formalisms for the description of a specific example of such a Minkowski limit. A novel contribution to the DSR physics intuition came from a recent paper by Smolin suggesting that the emergence of the Planck scale as a second nontrivial relativistic invariant might be inevitable in quantum gravity, relying only on some rather robust expectations concerning the semiclassical approximation of quantum gravity. Here, we attempt to strengthen Smolin's argument by observing that an analysis of some independently-proposed Planck-scale particle-localization limits, such as the "Generalized Uncertainty Principle" often attributed to string theory in the literature, also suggests that the emergence of a DSR Minkowski limit might be inevitable. We discuss a possible link between this observation and recent results on logarithmic corrections to the entropy-area black-hole formula, and observe that both the analysis reported here and Smolin's analysis appear to suggest that the examples of DSR Minkowski limits for which a formalism has been sought in the literature might not be sufficiently general. We also stress that, as we now contemplate the hypothesis of a DSR Minkowski limit, there is an additional challenge for those in the quantum-gravity community attributing to the Planck length the role of "fundamental length scale."

We show that heavy pure states of gravity can appear to be mixed states to almost all probes. Our arguments are made for AdS₅ Schwarzschild black holes using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For certain supersymmetric states of the theory, our account is exact: the microstates are described in gravity by a spacetime "foam", the precise details of which are invisible to almost all probes.

We discuss simple vacuum solutions to the Einstein Equations in five-dimensional space–times compactified in two different ways. In such spaces, one black hole phase and more than one black string phase may exist. Several old metrics are adapted to new background topologies to yield new solutions to the Einstein Equations. We then briefly talk about the angular momentum they may carry, the horizon topology and phase transitions that may occur.

We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument are causality, the uncertainty principle from quantum mechanics and a dynamical criteria for gravitational collapse from classical general relativity called the hoop conjecture. The inability of any gedanken experiment to measure a sub-Planckian distance suggests the existence of a minimal length.

Among the suggested solutions to the cosmological constant problem, we find the idea of a dynamic vacuum, with an energy density decaying with the universe expansion. We investigate the possibility of a variation in the gravitational constant as well, induced, at the cosmological scale, by the vacuum decay. We consider an effective Brans–Dicke theory in the spatially flat FLRW spacetime, finding late time solutions characterized by a constant ratio between the matter and vacuum energy densities. By using the observed limits for the universe age, we fix the only free parameter of our solutions, obtaining a relative matter density in the range 0.25<Ω_m<0.4. In particular, for Ht = 1 we obtain Ω_m = 1/3. This constitutes a possible explanation for another problem related to the cosmological term, the cosmic coincidence problem.

In this essay, we explore the hypothesis that gravity is best viewed as a non-quantized field, at least not in the usual sense of being quantized. It is linked to the energy localization hypothesis that energy, including the contribution from gravity, is localized in the region of the energy–momentum tensor. Evidence is gathered from among other aspects, the peculiar nature of gravitational plane waves and indirectly from the fact that there are no experimental results that point to a necessity for quantization. Should this hypothesis prove to be correct, it would favor the negation of the very existence of gravitons since gravitational waves would be seen as purely classical general relativistic constructs which carry no energy. Most significantly, unquantized gravity would turn the evidently unsolvable cosmological constant problem, viewed by various experts as the major crisis of modern physics, into a non-problem. In spite of this, there are indications to suggest that the study of limiting properties will lead to new insights into both the essence of space–time and the quantum world.

The presence of gravity implies corrections to the Einstein–Planck formula E = hν. This gives hope that the divergent blueshift in frequency, associated to the presence of a black hole horizon, could be smoothed out for the energy. Using simple arguments based on Einstein's equivalence principle, we show that this is only possible if a black hole emits, in a first approximation, not just a single particle, but thermal radiation.

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes, neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: (i) the singularity theorem, (ii) the area theorem, (iii) the uniqueness theorem, (iv) the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.

We argue that in the context of string theory, the usual restriction to globally hyperbolic space–times should be considerably relaxed. We exhibit an example of a space–time which only satisfies the causal condition, and so is arbitrarily close to admitting closed causal curves, but which has a well-behaved dual description, free of paradoxes.

Radiating black holes pose a number of puzzles for semiclassical and quantum gravity. These include the transplanckian problem — the nearly infinite energies of Hawking particles created near the horizon, and the final state of evaporation. A definitive resolution of these questions likely requires robust inputs from quantum gravity. We argue that one such input is a mechanism for a quantum bound on curvature. We show how the same method leads to an upper limit on the redshift of a Hawking emitted particle, to a maximum temperature for a black hole, and to the prediction of a Planck scale remnant.

We show that a suitably chosen position-momentum commutator can elegantly describe many features of gravity, including the IR/UV correspondence and dimensional reduction ("holography"). Using the most simplistic example based on dimensional analysis of black holes, we construct a commutator which qualitatively exhibits these novel properties of gravity. Dimensional reduction occurs because the quanta size grow quickly with momenta, and thus cannot be "packed together" as densely as naively expected. We conjecture that a more precise form of this commutator should be able to quantitatively reproduce all of these features.

We propose that stringy symmetries play a crucial role in the resolution of the cosmological constant problem. In the presence of constant fluxes along compact directions, it is possible to construct potentials for the moduli. For suitable choice of fluxes, they admit minima with non-zero cosmological constant and such solutions break duality symmetry. The corresponding duality symmetric solutions have vanishing cosmological constant. The naturalness hypothesis of 't Hooft may be invoked to argue that the cosmological constant must remain small since symmetry preserving solutions correspond to vanishing cosmological constant.

The information loss paradox for Schwarzschild black holes is examined, using the ADS/CFT correspondence extended to the M₆(4, 2) bulk. It is found that the only option compatible with the preservation of the quantum unitarity is when a regular remnant region of the black hole survives to the black hole evaporation process, where information can be stored and eventually retrieved.

During the black hole radiation, the interior contains all the matter of the initial black hole, together with the negative energy quanta entangled with the exterior Hawking radiation. Neither the initial matter nor the negative energy quanta evaporate from the black hole interior. Therefore, the information is not lost during the radiation. The black hole mass eventually drops to zero in semiclassical gravity, but this semiclassical state has an infinite temperature and still contains all the initial matter together with the negative energy entangled with the exterior radiation.

The Einstein–Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self-contained, perspective on gravity and (ii) a concrete mathematical framework in which the description of space–time dynamics by Einstein's equations is similar to the description of a continuum solid in the thermodynamic limit.

It is well known that an excited atom, placed near a boundary, such as a mirror, undergoes an energy shift due to its interaction with the reflected field. In this paper, we use a generalized Hertz potential to prove that a radiating dipole embedded in a continuously inhomogeneous medium also experiences a position-dependent self-interaction energy shift and a corresponding self-force. Consequently, an excited atom inside a cylindrical cavity embedded in a quasi-homogeneous gravitational field, which acts as an effective "soft" boundary, is shown to experience an effective gravitational acceleration dependent on the atomic quantum state. We predict that excited trapped atom interferometers will thus provide an unexpected tool for ground-based experimentation on radiation backscattering in a Schwarzschild background.

Motivated by stringy considerations, Randall and Sundrum have proposed a model where all the fields and particles of physics, save gravity, are confined on a four-dimensional brane embedded in five-dimensional anti-de Sitter space. Their scenario features a stable bound state of bulk gravity waves and the brane that reproduces standard general relativity. We demonstrate that in addition to this zero-mode, there is also a discrete set of metastable bound states that behave like massive four-dimensional gravitons which decay by tunneling into the bulk. These are resonances of the bulk-brane system akin to black hole quasinormal modes — as such, they give rise to the dominant corrections to four-dimensional gravity. The phenomenology of braneworld perturbations is greatly simplified when these resonant modes are taken into account, which is illustrated by considering gravitational radiation emitted from nearby sources and early universe physics.

The process of gravitationally-induced particle creation (Hawking radiation), if it exists, necessitates, in accordance with general thermodynamic principles, a corresponding process of gravitationally-induced particle resorption into the vacuum. Although the former process occurs in the external vicinity of the Schwarzschild surface where matter density is relatively low, the latter process would be expected to occur inside the Schwarzschild surface where the stellar material is enormously compressed and fermions fill all quantum states up to the Fermi level. I show that the occurrence of particle resorption provides a general mechanism, irrespective of the interactions of the constituent particles, which halts the collapse of a black hole to a singular point and leads to an equilibrium state of macroscopic extent.

It has been claimed recently that the black hole information-loss paradox has been resolved: the evolution of quantum states in the presence of a black hole is unitary and information preserving. We point out that, contrary to some claims in literature, information-preserving black holes still violate the baryon number and any other quantum number which follows from an effective (and thus approximate) or anomalous symmetry.

Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. We argue that this follows naturally from loop quantum gravity and a result of Kolmogorov and Bardzin' on the the realizability of networks in three dimensions. This represents an alternative to other approaches in which some sort of correlation between field configurations helps limit the degrees of freedom within a region. It also provides an approach to thinking about black hole entropy in terms of states inside rather than on its surface. Intuitively, a spin network complicated enough to imbue a region with volume only lets that volume grow as quickly as the area bounding it.

Entropy plays a crucial role in the characterization of information and entanglement, but it is not a scalar quantity and for many systems it is different for different relativistic observers. We discuss two examples: entropy of a single qubit and renormalized entropy as given by a uniformly accelerated observer. Loop quantum gravity predicts the Bekenstein–Hawking term for black hole entropy and the logarithmic correction to it. The latter originates in the entanglement between the pieces of spin networks that describe black hole horizon. Entanglement between gravity and matter may restore the unitarity in the black hole evaporation process. If the collapsing matter is assumed to be initially in a pure state, then entropy of the Hawking radiation is exactly the created entanglement between matter and gravity.

Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical symmetry which can be broken, perhaps at a level detectable by new tests in space.

Interactions within the cosmic medium modify its equation of state. We discuss implications of interacting dark energy models both for the spatially homogenous background and for the perturbation dynamics.

Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter q₀ is given by the square of the string coupling, , up to a negative sign. Hence, the expansion of the universe must accelerate eventually, and the observed value of q₀ corresponds to . In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small.

If our universe underwent inflation, its entropy during the inflationary phase would have been substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomly-chosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty space–time. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time.

In general relativity, gravitational waves propagate at the speed of light, and so gravitons are massless. The masslessness can be traced to symmetry under diffeomorphisms. However, another elegant possibility exists: masslessness can instead arise from spontaneous violation of local Lorentz invariance. We construct the corresponding theory of gravity. It reproduces the Einstein–Hilbert action of general relativity at low energies and temperatures. Detectable signals occur for sensitive experiments, and potentially profound implications emerge for our theoretical understanding of gravity.

If string theory is correct, then our observable universe may be a three-dimensional "brane" embedded in a higher-dimensional spacetime. This theoretical scenario should be tested via the state-of-the-art in gravitational experiments — the current and upcoming gravity-wave detectors. Indeed, the existence of extra dimensions leads to oscillations that leave a spectroscopic signature in the gravity-wave signal from black holes. The detectors that have been designed to confirm Einstein's prediction of gravity waves, can in principle also provide tests and constraints on string theory.

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.