Search

A novel nonlocal four-photon interaction on the deformed spacetime is derived and studied in the three selected models (I, II, III). The first two models (I, II) are obtained via two distinct second-order θ9-exact Seiberg-Witten maps of the noncommutative U(l) gauge field strength on Moyal space. The third one (III), inspired by the manifestly gauge invariant structures emerging in the first two, due to the model generality has been constructed with a different set of freedom parameters. The physical relevancy of all models is analyzed by evaluating the four-photon-tadpole diagram, which, when combined with the bubble graph, enables us to fully consider all contributions to the one-loop photon polarization tensor. For an arbitrary noncommutative matrix θμν, the full quadratic IR divergence cancellation in the one-loop photon two-point function is obtained with particular combinations of Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II. Finally, our model III enables complete elimination of all pathological terms in the photon polarization tensor at one-loop order if a special value for the θ matrix is chosen. [ABSTRACT FROM AUTHOR]

A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under four-dimensional (4D) frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential A always transforms homogeneously under 4D rotations in spacetime, but if the gauge is changed by the rotation, one can restore the gauge back to the original gauge by adding an inhomogeneous term. It is then not a 4-vector, but two 4-vectors: one for rotation and one for translation. For such a gauge, it is much more important to preserve explicit homogeneous Lorentz covariance by simply skipping the troublesome gauge-restoration step. A gauge-independent separation of A into a dynamical term and a nondynamical term in Abelian gauge theories is redefined more generally as the terms caused by the presence and absence, respectively, of the 4-current term in the inhomogeneous Maxwell equations for A. Such a separation cannot in general be extended to non-Abelian theories where A satisfies nonlinear differential equations. However, in the linearized iterative solution that is perturbation theory, the usual Abelian quantizations in the usual gauges can be used. Some nonlinear complications are briefly reviewed. [ABSTRACT FROM AUTHOR]

The article discusses the self-force on a static scalar and electrostatic field within the five-dimensional (5D) spacetime of a Schwarzschild-Tangherlini black hole, including several mathematical equations depiction this subject. An overview of the electric charges in the static scalar and electrostatic fields in the 5D black hole spacetime is provided.

We study a static, spherically symmetric and asymptotic flat spacetime, assuming the hypersurface orthogonal Einstein-aether theory with an ultraviolet modification motivated by the Hořava-Lifshitz theory, which is composed of the z = 2 Lifshitz scaling terms such as scalar combinations of a three-Ricci curvature and the acceleration of the aether field. For the case with the quartic term of the acceleration of the aether field, we obtain a two-parameter family of black hole solutions, which possess a regular universal horizon. Whereas, if a three-Ricci curvature squared term is joined in ultraviolet modification, we find a solution with a thunderbolt singularity such that the universal horizon turns out to be a spacelike singularity. [ABSTRACT FROM AUTHOR]

Stationary and axially symmetric spacetimes play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum subclass of these spacetimes is known as Weyl's class, and contains the Schwarzschild spacetime as its most prominent example. This paper is going to study the space of Killing tensor fields of valence 3 for spacetimes of Weyl's class. Killing tensor fields play a crucial role in physics since they are in correspondence to invariants of the geodesic motion (i.e. constants of the motion). It will be proven that in static and axially symmetric vacuum spacetimes the space of Killing tensor fields of valence 3 is generated by Killing vector fields and quadratic Killing tensor fields. Using this result, it will be proven that for the family of Zipoy-Voorhees metrics, valence-3 Killing tensor fields are always generated by Killing vector fields and the metric. [ABSTRACT FROM AUTHOR]

We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general-relativistic initial data sets with asymptotically Kerr-de Sitter ends. The corresponding Hamiltonians are calculated. Some implications for black-hole thermodynamics are pointed out. [ABSTRACT FROM AUTHOR]

We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-anti-de Sitter (AdS) black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion, we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable circular orbits (ISCOs) for these asymptotically AdS spacetimes, as well as the location of null circular orbits. We find that the ISCO dives below the ergosurface for black holes rotating close to extremality and merges with the event horizon exactly at extremality, in analogy with the four-dimensional Kerr case. For sufficiently massive black holes in AdS, there exists a spin parameter range in which the background spacetime is stable against super-radiance and the ISCO lies inside the ergoregion. Our results for massless geodesics show that there are no stable circular null orbits outside the horizon, but there exist such orbits inside the horizon, as well as around overextremal spacetimes, i.e., naked singularities. We also discuss how these orbits deform from the static to the rotating case. [ABSTRACT FROM AUTHOR]

We study the geodesic motion of massive and massless test particles in the background of a particular class of multiple charge black holes in gauged supergravity theories in D = 4. We have analyzed the horizon structure along with the nature of the effective potentials for the case of four equal charges. In view of the corresponding effective potentials, we have discussed all the possible orbits in detail for different values of energy and angular momentum of the incoming test particles. The periods for one complete revolution of circular orbits and the advance of perihelion of the planetary orbit have also been investigated in greater detail for massive test particles. We have also discussed the time period of unstable circular motion and cone of avoidance of massless test particles in detail. All the corresponding results obtained for massive and massless test particles are then compared accordingly. [ABSTRACT FROM AUTHOR]

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension; it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point, while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without a big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no spacetime inside and with "Schwarzschild-like" horizons with a lower spectral dimension. [ABSTRACT FROM AUTHOR]

We compute the one-loop photon contribution to the graviton self-energy on a de Sitter background and use it to solve the linearized Einstein equation for a point mass. Our results show that a comoving observer sees a logarithmic spatial running Newton's constant. Equivalently, a static observer reports a secular suppression of the Newtonian potential. [ABSTRACT FROM AUTHOR]

Quantum graphity (QG) is a model of emergent geometry in which space is represented by a dynamical graph. The graph evolves under the action of a Hamiltonian from a high-energy pregeometric state to a low- energy state in which geometry emerges as a coarse-grained effective property of space. Here we show the results of numerical modeling of the evolution of the QG Hamiltonian, a process we term "ripening" by analogy with crystallographic growth. We find that the model as originally presented favors a graph composed of small disjoint subgraphs. Such a disconnected space is a poor representation of our Universe. A new term is introduced to the original QG Hamiltonian, which we call the hypervalence term. It is shown that the inclusion of a hypervalence term causes a connected latticelike graph to be favored over small isolated subgraphs. [ABSTRACT FROM AUTHOR]

We investigate spherically symmetric, static spacetimes in Eddington-inspired Born-Infeld gravity coupled to Born-Infeld electrodynamics. The two constants, b² and κ which parametrize the Born-Infeld structures in the electrodynamics (matter) and gravity sectors, characterize the features of our analytical solutions. Black holes or naked singularities are found to arise, depending on the values of b² and κ, as well as charge and mass. Several such solutions are classified and understood through the analysis of the associated metric functions for fixed κ, varying b² and vice versa. Further, we also compare the new metric functions with those for the known b² → ∞ (Maxwell) and the κ → 0 (geonic black hole) cases. Interestingly, for a particular relation between these two parameters, b² = 1/4κ, κ > 0, we obtain a solution resembling the well-known Reissner-Nordström line element, albeit some modifications. Using this particular solution as the background spacetime, we study null geodesics for Born-Infeld photons and also gravitational lensing. Among the interesting features we note (i) an increase in the radius of the photon sphere with increasing κ and (ii) a net positive contribution in the leading order correction term involving κ, in the weak lensing formula for the deflection angle. We also investigate the effective potential and light propagation for various other solutions through numerics and plots. In summary, our paper is the first attempt towards figuring out how Born-Infeld structures in both the matter and gravity sectors can influence the nature and character of resulting gravitational fields. [ABSTRACT FROM AUTHOR]

The global structure of the family of Kerr-de Sitter spacetimes is reexamined. Taking advantage of the natural length scale set by the cosmological constant Λ > 0, conditions on the parameters (Λ, M, a) have been found, so that a Kerr-de Sitter spacetime either describes a black hole with well-separated horizons, or describes degenerate configurations where two or more horizons coincide. As long as the rotation parameter a² is subject to the constraint a²Λ ≪ 1, and the mass parameter M is subject to a² [1 + O(a²Λ)²)] < M² < 1/9Λ [1 + 2a²Λ + O(a²Λ)²)], then a Kerr-de Sitter spacetime with parameters in these ranges describes a black hole possessing an inner horizon separated from an outer horizon and the hole is embedded within a pair of cosmological horizons. Still for a²Λ ≪ 1, but assuming that either M² > 1/9Λ[1 + 2a²Λ + O(a²Λ)²)] or M² < a² [1 + O(a²Λ)²)], the Kerr-de Sitter spacetime describes a ringlike singularity enclosed by two cosmological horizons. A Kerr-de Sitter spacetime may also describe configurations where the inner, the outer and one of the cosmological horizons coincide. However, we found that this coalescence occurs provided M²Λ ~ 1 and due to the observed smallness of Λ, these configurations are probably irrelevant in astrophysical settings. Extreme black holes, i.e. black holes where the inner horizon coincides with the outer black hole horizon, are also admitted. We have found that in the limit M²Λ ≪ 1 and a²Λ ≪ 1, extreme black holes occur, provided a² = Ma² (1 + O(ΛM²)). Finally a coalescence between the outer and the cosmological horizon, although in principle possible, is likely to be unimportant at the astrophysical level, since this requires M²Λ ~ 1. Our analysis shows that as far as the structure of the horizons is concerned, the family of Kerr-de Sitter spacetimes exhibits similar structure to the Reissner-Nordstrom-de Sitter family of spacetimes. [ABSTRACT FROM AUTHOR]

We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of locally causal dynamical triangulations. Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we find numerical evidence that the continuum limit of the model lies in a new universality class of two-dimensional quantum gravity theories, inequivalent to both Euclidean and causal dynamical triangulations. The presence of significant fmite-size effects, which are present even at the largest volumes investigated, prevents us from reaching a more definite conclusion. [ABSTRACT FROM AUTHOR]

We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. Further, we work within the context of the "two time framework" (TTF) approximation, which describes the leading nonlinear effects for small amplitude perturbations, and is therefore suitable for studying the weakly turbulent instability of AdS-including both collapsing and noncollapsing solutions. We have previously identified a class of quasiperiodic (QP) solutions to the TTF equations, and in this paper we analyze their stability. We show that there exist several families of QP solutions that are stable to linear order, and we argue that these solutions represent islands of stability in TTF. We extract the eigenmodes of small oscillations about QP solutions, and we use them to predict approximate recurrence times for generic noncollapsing initial data in the full (non-TTF) system. Alternatively, when sufficient energy is driven to high-frequency modes, as occurs for initial data far from a QP solution, the TTF description breaks down as an approximation to the full system. Depending on the higher order dynamics of the full system, this often signals an imminent collapse to a black hole. [ABSTRACT FROM AUTHOR]

We formulate a generic Newtonian-like analogous potential for static spherically symmetric general relativistic (GR) spacetime and subsequently derived proper Newtonian-like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials were found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behaviors with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian-like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in active galactic nuclei (AGNs) or in x-ray binaries (XRBs) in the presence of naked singularities and thereby to explore any noticeable differences in their observational features from those in the presence of black holes (BHs) to ascertain outstanding debatable issues relating to gravity--whether the end state of gravitational collapse in our physical Universe renders BH or naked singularity. [ABSTRACT FROM AUTHOR]

We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2 + 1)- dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Banados-Teitelbom-Zanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational radii. When the shell is pushed to its own gravitational radius and its temperature is taken to be the Hawking temperature of the corresponding black hole, the entropy of the shell coincides with the Bekenstein-Hawking entropy. In addition, we consider simple ansätze for the equations of state, as well as a power-law equation of state where the entropy and the thermodynamic stability conditions can be examined analytically. [ABSTRACT FROM AUTHOR]

We discuss the effective field theory for spacetime symmetry breaking from the local symmetry point of view. By gauging spacetime symmetries, the identification of Nambu-Goldstone (NG) fields and the construction of the effective action are performed based on the breaking pattern of diifeomorphism, local Lorentz, and (an)isotropic Weyl symmetries as well as the internal symmetries including possible central extensions in nonrelativistic systems. Such a local picture distinguishes, e.g., whether the symmetry breaking condensations have spins and provides a correct identification of the physical NG fields, while the standard coset construction based on global symmetry breaking does not. We illustrate that the local picture becomes important in particular when we take into account massive modes associated with symmetry breaking, the masses of which are not necessarily high. We also revisit the coset construction for spacetime symmetry breaking. Based on the relation between the Maurer-Cartan one form and connections for spacetime symmetries, we classify the physical meanings of the inverse-Higgs constraints by the coordinate dimension of broken symmetries. Inverse Higgs constraints for spacetime symmetries with a higher dimension remove the redundant NG fields, whereas those for dimensionless symmetries can be further classified by the local symmetry breaking pattern. [ABSTRACT FROM AUTHOR]

The extended Skyrme-Faddeev model possesses vortex solutions in a (3 + 1)-dimensional Minkowski space-time with target space CPN. They have finite energy per unit of length and contain waves propagating along the vortices with the speed of light. We introduce various types of the potentials which correspond with holomorphic solutions of the integrable sector and also with several numerical solutions outside of this sector. The presented solutions constitute a strong indication that the current model contains a large class of solutions with a wide range of coupling constants, and the exact solution is just a particular case. [ABSTRACT FROM AUTHOR]

We study the stability of a spherically symmetric perturbation around the flat Friedmann-Lemaître-Robertson-Walker spacetime in the ghost-free bigravity theory, retaining nonlinearities of the helicity-0 mode of the massive graviton. It has been known that, when the graviton mass is smaller than the Hubble parameter, homogeneous and isotropic spacetimes suffer from the Higuchi-type ghost or the gradient instability against the linear perturbation in the bigravity. Hence, the bigravity theory has no healthy massless limit for cosmological solutions at linear level. In this paper we show that the instabilities can be resolved by taking into account nonlinear effects of the scalar graviton mode for an appropriate parameter space of coupling constants. The growth history in the bigravity can be restored to the result in general relativity in the early stage of the Universe, in which the Stückelberg fields are nonlinear and there is neither ghost nor gradient instability. Therefore, the bigravity theory has the healthy massless limit, and cosmology based on it is viable even when the graviton mass is smaller than the Hubble parameter. [ABSTRACT FROM AUTHOR]

In this paper, we explore asymptotically flat charged thin-shell wormholes of third order Lovelock gravity in higher dimensions, taking into account the cut-and-paste technique. Using the generalized junction conditions, we determine the energy-momentum tensor of these solutions on the shell, and explore the issue of the energy conditions and the amount of normal matter that supports these thin-shell wormholes. Our analysis shows that for negative second-order and positive third-order Lovelock coefficients, there are thin-shell wormhole solutions that respect the weak energy condition. In this case, the amount of normal matter increases as the third-order Lovelock coefficient decreases. We also find novel solutions which possess specific regions where the energy conditions are satisfied for the case of a positive second-order and negative third-order Lovelock coefficients. Finally, a linear stability analysis in higher dimensions around the static solutions is carried out. Considering a specific cold equation of state, we find a wide range of stability regions. [ABSTRACT FROM AUTHOR]

The geometry of thermodynamic state space is studied for asymptotically anti-de Sitter black holes in D-dimensional space-times. Convexity of thermodynamic potentials and the analytic structure of the response functions is analyzed. The thermodynamic potentials can be used to define a metric on the space of thermodynamic variables, and two commonly used such metrics are the Weinhold metric, derived from the internal energy, and the Ruppeiner metric, derived from the entropy. The intrinsic curvature of these metrics is calculated for charged and for rotating black holes, and it is shown that the curvature diverges when heat capacities diverge but, contrary to general expectations, the singularities in the Ricci scalars do not reflect the critical behavior. When a cosmological constant is included as a state space variable, it can be interpreted as a pressure and the thermodynamically conjugate variable as a thermodynamic volume. The geometry of the resulting extended thermodynamic state space is also studied, in the context of rotating black holes, and there are curvature singularities when the heat capacity at constant angular velocity diverges and when the black hole is incompressible. Again the critical behavior is not visible in the singularities of the thermodynamic Ricci scalar. [ABSTRACT FROM AUTHOR]

Linearized gravitational waves in de Sitter spacetime are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically, (i) In the exact theory, the intrinsic geometry of I is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from Diff(X) to the de Sitter group. Our results show explicitly that this condition is physically unreasonable, (ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at I+. (iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy. Finally, (iv) we demonstrate that the flux formulas reduce to the familiar ones in Minkowski spacetime in spite of the fact that the limit Λ ≤ 0 is discontinuous (since, in particular, I changes its spacelike character to null in the limit). [ABSTRACT FROM AUTHOR]

We discuss how the assumption of variable equation of state (EoS) allows the elimination of the instability at equilibrium throat radius a0 - 3M featured by previous Schwarzschild thin-shell wormhole models. Unobstructed stability regions are found for three choices of variable EoS. Two of these EoS entail linear stability at every equilibrium radius. Particularly, the thin shell remains stable as ao approaches the Schwarzschild radius 2M. A perturbative analysis of the wormhole equation of motion is carried out in the case of variable Chaplygin EoS. The squared proper angular frequency tug of small throat oscillations is linked with the second derivative of the thin-shell potential. In various situations ω02 remains positive and bounded in the limit a0 → 2M. [ABSTRACT FROM AUTHOR]

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding nonperturbative phenomena in quantum electrodynamics. However, for the limited set of known solutions, the field often depends on one coordinate only, which could be the time t, a spatial coordinate such as x or r, or a light-cone coordinate such as ct-x. By swapping the roles of known and unknown quantities in the Dirac equation, we are able to generate families of solutions of the Dirac equation in the presence of genuinely space-time dependent electromagnetic fields in 1+1 and 2+1 dimensions. [ABSTRACT FROM AUTHOR]

We study the cylinder-plate and the cylinder-cylinder Casimir interaction in the (D + 1)-dimensional Minkowski spacetime due to the vacuum fluctuations of massless scalar fields. Different combinations of Dirichlet (D) and Neumann (N) boundary conditions are imposed on the two interacting objects. For the cylinder-cylinder interaction, we consider the case where one cylinder is inside the other and the case where the two cylinders are outside each other. By computing the transition matrices of the objects and the translation matrices that relate different coordinate systems, the explicit formulas for the Casimir interaction energies are derived. From these formulas, we compute the large separation and small separation asymptotic behaviors of the Casimir interaction. For the cylinder-plate interaction with R ≪ L, where R is the radius of the cylinder and L is the distance from the center of the cylinder to the plate, the order of decay of the Casimir interaction only depends on the boundary conditions imposed on the cylinder. The orders are L"D+1/ln(L) and L-D-l/lnL, respectively, for the Dirichlet and Neumann boundary conditions on the cylinder. For two cylinders with radii R1 and R2 lying parallelly outside each other, the orders of decay of the Casimir interaction energies when R1 + R2 ≪ L are L-D+l/(lnL)², L-D-1/ln L, and L-d-3, respectively, for DD, DN/ND, and NN boundary conditions, where L is the distance between the centers of the cylinders. The more interesting and important characteristic of Casimir interaction appears at small separation. Using the perturbation technique, we compute the small separation asymptotic expansions of the Casimir interaction energies up to the next-to-leading-order terms. The leading terms coincide with the respective results obtained using the proximity force approximation, which is of order d-D+1/2, where d is the distance between the two objects. The results on the next-to-leading-order terms are more interesting and important. We find some universal behaviors. It is also noticed that for the case of Dirichlet-Dirichlet cylinder-plate interaction the next-to-leading-order term agrees with that obtained using the derivative expansion. Hence, based on our results on other boundary conditions and on the cylindercylinder interaction, we postulate a formula for the derivative expansion to expand the Casimir interaction energy up to the next-to-leading-order terms for DD, DN, ND, and NN boundary conditions, for the interaction between two curved surfaces in (D + l)-dimensional Minkowski spacetime. It is found that the postulate agrees with our previous results on the sphere-sphere interactions except when D = 4. [ABSTRACT FROM AUTHOR]

Recently, a family of exact force-free electrodynamic (FFE) solutions was given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Michel, Menon and Dermer, and other authors. These solutions have been proposed as useful models for describing the outer magnetosphere of conducting stars. As with any exact analytical solution that aspires to describe actual physical systems, it is vitally important that the solution possess the necessary stability. In this paper, we show via fully nonlinear numerical simulations that the aforementioned FFE solutions, despite being highly special in their properties, are nonetheless stable under small perturbations. Through this study, we also introduce a three-dimensional pseudospectral relativistic FFE code that achieves exponential convergence for smooth test cases, as well as two additional well-posed FFE evolution systems in the appendix that have desirable mathematical properties. Furthermore, we provide an explicit analysis that demonstrates how propagation along degenerate principal null directions of the spacetime curvature tensor simplifies scattering, thereby providing an intuitive understanding of why these exact solutions are tractable, i.e. why they are not backscattered by spacetime curvature. [ABSTRACT FROM AUTHOR]

It has recently been argued that if spacetime M possesses nontrivial structure at small scales, an appropriate semiclassical description of it should be based on nonlocal bitensors instead of local tensors such as the metric gab(p). Two most relevant bitensors in this context are Synge's world function O(p,p0) and the van Vleck determinant (VVD) (p,p0), as they encode the metric properties of spacetime and (de)focusing behavior of geodesics. They also characterize the leading short distance behavior of two point functions of the d'Alembartian p0p. We begin by discussing the intrinsic and extrinsic geometry of equigeodesic surfaces SG,p0={p M|O(p,p0)=constant} in a geodesically convex neighborhood of an event p0 and highlight some elementary identities relating the VVD with geometry of SG,p0. As an aside, we also comment on the contribution of SG,p0 to the surface term in the Einstein-Hilbert (EH) action and show that it can be written as a volume integral of ln. We then proceed to study the small scale structure of spacetime in presence of a Lorentz invariant short distance cutoff l0 using O(p,p0) and (p,p0), based on some recently developed ideas. We derive a second rank bitensor qab(p,p0;l0)=qab[gab,O] which naturally yields geodesic intervals bounded from below and reduces to gab for O»l20/2. We present a general and mathematically rigorous analysis of short distance structure of spacetime based on (a) geometry of equigeodesic surfaces SG,p0 of gab, (b) structure of the nonlocal d'Alembartian p0passociated with qab, and (c) properties of VVD. In particular, we prove the following: (i) The Ricci biscalar Ric(p,p0) of qab is completely determined by SG,p0, the tidal tensor and first two derivatives of (p,p0), and has a nontrivial classical limit (see text for details): liml00limO0±Ric(p,p0)=±DRabqaqb (ii) The GHY term in EH action evaluated on equigeodesic surfaces straddling the causal boundaries of an event p0 acquires a nontrivial structure. These results strongly suggest that the mere existence of a Lorentz invariant minimal length l0 can leave unsuppressed residues independent of l0 and (surprisingly) independent of many precise details of quantum gravity. For example, the coincidence limit of Ric(p,p0) is finite as long as the modification of distances Sl0:2O2O satisfies (i) Sl0(0)=l20 (the condition of minimal length), (ii) S0(x)=x, and (iii) [|Sl0|/S'2l0](0)<8. In particular, the function Sl0(x), which should eventually come from a complete framework of quantum gravity, need not admit a perturbative expansion in l0. Finally, we elaborate on certain technical and conceptual aspects of our results in the context of entropy of spacetime and classical description of gravitational dynamics based on Noether charge of diffeomorphism invariance instead of the EH lagrangian. [ABSTRACT FROM AUTHOR]

It has been established in Schwarzschild spacetime (and more generally in Kerr spacetime) that pairs of geometrically different timelike geodesies with the same radial and azimuthal frequencies exist in the strong-field regime. The occurrence of this so-called isofrequency pairing is of relevance in view of gravitational-wave observations. In this paper we generalize the results on isofrequency pairing in two directions. Firstly, we allow for a (positive) cosmological constant, i.e., we replace the Schwarzschild spacetime with the Schwarzschild-de Sitter spacetime. Secondly, we consider not only spinless test particles (i.e., timelike geodesies) but also test particles with spin. In the latter case we restrict to the case that the motion is in the equatorial plane with the spin perpendicular to this plane. We find that the cosmological constant as well as the spin have distinct impacts on the description of bound motion in the frequency domain. [ABSTRACT FROM AUTHOR]

In this paper we establish a formalism for the computation of observables due to acceleration-induced particle physics processes. General expressions for the transition rate, multiplicity, power, spectra, and displacement law of particles undergoing time-dependent acceleration and transitioning into a final state of arbitrary particle number are obtained. The transition rate, power, and spectra are characterized by unique polynomials of multiplicity and thermal distributions of both bosonic and fermionic statistics. The acceleration-dependent multiplicities are computed in terms of the branching fractions of the associated inertial processes. The displacement law of the spectra predicts that the energy of the emitted particles is directly proportional to the accelerated temperature. [ABSTRACT FROM AUTHOR]

Misner spacetime is among the simplest solutions of Einstein's equation that exhibits a Cauchy horizon with a smooth extension beyond it. Besides violating strong cosmic censorship, this extension contains closed timelike curves. We analyze the stability of the Cauchy horizon and prove that neighboring spacetimes in one parameter families of solutions through Misner's in pure gravity, gravity coupled to a scalar field, or Einstein-Maxwell theory end at the Cauchy horizon developing a curvature singularity. [ABSTRACT FROM AUTHOR]

The existence of stable bound orbits of test particles is one of the most characteristic properties in black hole spacetimes. In higher-dimensional black holes, due to the dependence of gravity on the spacetime dimensions, there is no stable bound orbit balanced by Newtonian gravitational monopole force and centrifugal force, although this balance occurs in the four-dimensional Kerr black hole. In this paper, however, the existence of stable bound orbits of massive and massless particles is shown in six-dimensional singly spinning Myers-Perry black holes with a value of the spin parameter larger than a critical value. The innermost stable bound orbits and the outermost stable bound orbits are found on the rotational axis. [ABSTRACT FROM AUTHOR]

The critical behavior of a relativistic Z2-symmetric Yukawa model at zero temperature and density is discussed for a continuous number of fermion degrees of freedom and of spacetime dimensions, with emphasis on the role played by multimeson exchange in the Yukawa sector. We argue that this should be generically taken into account in studies based on the functional renormalization group, either in fourdimensional high-energy models or in lower-dimensional condensed-matter systems. By means of the latter method, we describe the generation of multicritical models in less than three dimensions, both at infinite and finite numbers of flavors. We also provide different estimates of the critical exponents of the chiral Ising universality class in three dimensions for various field contents, from a couple of massless Dirac fermions down to the supersymmetric theory with a single Majorana spinor. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the thermodynamics of hyperscaling-violating Lifshitz black branes in the presence of a nonlinear massless electromagnetic field. We, first, obtain analytic nonlinear charged black brane solutions with a hyperscaling-violating factor in dilaton gravity and give the condition on the parameters of the metric for having black brane solutions. Second, we introduce the appropriate finite action in the grand canonical and canonical ensembles for a nonlinear electromagnetic field. Next, by generalizing the counterterm method for the asymptotic Lifshitz spacetimes with a hyperscaling-violating factor, we calculate the energy density of our solutions. Furthermore, we present a relation between the energy density and the thermodynamic quantities, electric potential, charge density, temperature and entropy density. This relation is the generalization of the Smarr formula for anti-de Sitter black branes and charged Lifshitz solutions. Finally, we perform a stability analysis in both the canonical and grand canonical ensembles. We show that the nonlinearity of the electromagnetic field can make the solutions unstable in the grand canonical ensemble. [ABSTRACT FROM AUTHOR]

Certain local thermal observables are considered in well-known examples of spatially open FRW spaces: Milne, open de Sitter and anti-de Sitter as well as Einstein static universes. Another value for fixing the ambiguity in defining the Wick square and, hence, the local temperature is motivated in the last example. Physical consequences of that choice are discussed for static and conformai vacua in those spaces. [ABSTRACT FROM AUTHOR]

We use effective field theory tools to study nonconservative effects in the gravitational two-body problem in general spacetime dimension. Using the classical version of the Closed Time Path formalism, we treat both the radiative gravitational field and its dynamical sources within a single action principle. New results include the radiation-reaction effective action in arbitrary dimensions to leading and +1PN orders, as well as the generalized quadrupole formula to order 4-1 PN. [ABSTRACT FROM AUTHOR]

The phenomenon discovered in 2009 by Bañados, Silk and West where particle collisions can achieve arbitrary high center-of-mass (c.m.) energies close to the event horizon of an extreme Kerr black hole, has generated a lot of interest. Although rotation seemed to be an essential requirement, it was later shown that arbitrary high energies can also be achieved for collisions between radially moving particles near the horizon of the electrically charged extreme Reissner-Nordström black hole. Recently Patil and Joshi claimed that instead of spinning up the black hole one can also crank up the c.m. energy of particle collisions by "charging up" a static black hole with a massless scalar field. In this regard they showed that infinite energies can be attained in the vicinity of the naked singularity of the Janis-Newman-Wincour (JNW) spacetime, which contains a massless scalar field that also becomes infinite at the position of the curvature singularity. In this study we show that Patil and Joshi's claim does not apply for other static black hole systems endowed with a massless scalar field. In particular we consider the well-known Bekenstein black hole and the recently discovered Martinez-Troncoso-Zanelli black hole, and show that the expression of the c.m. energy for particle collisions near the event horizons of these black holes is no different than the corresponding case with vanishing scalar field represented by the Schwarzschild solution. Moreover by studying the motion of scalar test charges that interact with the background scalar field in these black hole spacetimes we show that the resulting c.m. energies are even smaller than in the case of free particles. This shows that the infinite energies obtained by Patil and Joshi may not be due to the fact that the black hole contains a massless scalar field, but may be instead related to the geometry of the naked singularity in the JNW spacetime. An analogous case of infinite c.m. energy in the vicinity of a naked singularity is also presented. [ABSTRACT FROM AUTHOR]

The statistical response of a Kerr black hole to incoming quantum radiation has heretofore been studied by the methods of maximum entropy or quantum field theory in curved spacetime. Neither approach pretends to take into account the quantum structure of the black hole itself. To address this last issue we calculate here the conditional probability distribution associated with the hole's response by assuming that the horizon area has a discrete quantum spectrum, and that its quantum evolution corresponds to jumps between adjacent area eigenvalues, possibly occurring in series, with consequent emission or absorption of quanta, possibly in the same mode. This "atomic model" of the black hole is implemented in two different ways and recovers the previously calculated radiation statistics in both cases. The corresponding conditional probability distribution is here expressed in closed form in terms of a hypergeometric function. [ABSTRACT FROM AUTHOR]

The choice of the area operator in loop quantum gravity is by no means unique. In addition to the area operator commonly used in loop quantum gravity there is also an area operator introduced by Krasnov in 1998, which gives uniformly spaced area spectra for the horizons of spacetime. Using Krasnov's area operator we consider the thermodynamics of spherically symmetric spacetimes equipped with horizons in loop quantum gravity. Among other things, our approach implies, in a pretty simple manner, that every horizon of spacetime emits thermal radiation and possesses entropy which, in the natural units, is onequarter of its area. When applied to the de Sitter spacetime loop quantum gravity provides an explanation both to the presence and the smallness of the cosmological constant. [ABSTRACT FROM AUTHOR]

We investigate properties of higher-dimensional generally rotating black-hole spacetimes, so-called Kerr-NUT-(anti)-de Sitter spacetimes, as well as a family of related spaces which share the same explicit and hidden symmetries. In these spaces, we study a particle motion in the presence of a weak electromagnetic field and compare it with its operator analogies. First, we find general commutativity conditions for classical observables and for their operator counterparts, then we investigate a fulfillment of these conditions in the Kerr-NUT-(anti)-de Sitter and related spaces. We find the most general form of the weak electromagnetic field compatible with the complete integrability of the particle motion and the comutativity of the field operators. For such a field we solve the charged Hamilton-Jacobi and Klein-Gordon equations by separation of variables. [ABSTRACT FROM AUTHOR]

In this paper, we study classical general relativistic static wormhole configurations with pseudospherical symmetry. We show that, in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in [Phys. Rev. D 82, 044034 (2010)], there exists another wormhole class, which is a truly pseudospherical counterpart of spherical Morris-Thome wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thome for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes, the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris-Thome wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that a hyperbolic wormhole cannot be sustained at the throat by phantom energy and that there are pseudospherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess). [ABSTRACT FROM AUTHOR]

We consider the motion of classical spinning test particles in Schwarzschild and Kerr metrics and investigate innermost stable circular orbits (ISCO). The main goal of this work is to find analytically the small-spin corrections for the parameters of ISCO (radius, total angular momentum, energy, orbital angular frequency) of spinning test particles in the case of vectors of black hole spin, particle spin and orbital angular momentum being collinear to each other. We analytically derive the small-spin linear corrections for arbitrary Kerr parameter a. The cases of Schwarzschild, slowly rotating and extreme Kerr black hole are considered in detail. For a slowly rotating black hole, the ISCO parameters are obtained up to quadratic in a and particle's spin s terms. From the formulas obtained it is seen that the spin-orbital coupling has attractive character when spin and angular momentum are parallel and repulsive when they are antiparallel. For the case of the extreme Kerr black hole with co-rotating particle we succeed to find the exact analytical solution for the limiting ISCO parameters for arbitrary spin. It has been shown that the limiting values of ISCO radius and frequency do not depend on the particle's spin while values of energy and total angular momentum depend on it. We have also considered circular orbits of arbitrary radius and have found smallspin linear corrections for the total angular momentum, energy and frequency at given radius. System of equations for numerical calculation of ISCO parameters for arbitrary a and y is also explicitly written. [ABSTRACT FROM AUTHOR]

We show that a hypothesis that spacetime is quantum with coordinate algebra [xi,t] = λPxi, and spherical symmetry under rotations of the xi, essentially requires in the classical limit that the spacetime metric is the Bertotti-Robinson metric, i.e., a solution of Einstein's equations with a cosmological constant and a non-null electromagnetic field. Our arguments do not give the value of the cosmological constant or the Maxwell field strength, but they cannot both be zero. We also describe the quantum geometry and the full moduli space of metrics that can emerge as classical limits from this algebra. [ABSTRACT FROM AUTHOR]

We study the stability and the scattering properties of a spacetime with a topological defect along a spherical bubble. This bubble connects two flat spacetimes which are asymptotically Minkowski, so that the resulting universe may be regarded as containing a wormhole. Its distinguished feature is the absence of exotic matter, i.e., its matter content respects all the energy conditions. Although this wormhole is nontraversable, waves and quantum particles can tunnel between both universes. Interestingly enough, the wave equation alone does not uniquely determine the evolution of scalar waves on this background, and the theory of self-adjoint extensions of symmetric operators is required to find the relevant boundary conditions in this context. Here we show that, for a particular boundary condition, this spacetime is stable and gives rise to a scattering pattern which is identical to the more usual thin-shell wormhole composed of exotic matter. Other boundary conditions of interest are also analyzed, including an unstable configuration with sharp resonances at well-defined frequencies. [ABSTRACT FROM AUTHOR]

Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain the post- Newtonian expansions of the linear-in-mass-ratio corrections to the spin-precession angle and tidal invariants for a particle in circular orbit around a Schwarzschild black hole. We extract coefficients up to 20 post-Newtonian order from numerical results that are calculated with an accuracy greater than 1 part in 10500. These results can be used to calibrate parameters in effective-one-body models of compact binaries, specifically the spin-orbit part of the effective Hamiltonian and the dynamically significant tidal part of the main radial potential of the effective metric. Our calculations are performed in a radiation gauge, which is known to be singular away from the particle. To overcome this irregularity, we define suitable Detweiler-Whiting singular and regular fields in this gauge, and we compute the invariants using mode-sum regularization in combination with averaging from two sides of the particle. The detailed justification of this regularization procedure will be presented in a forthcoming companion paper. [ABSTRACT FROM AUTHOR]

We propose a new method of detecting Ellis wormholes by use of the images of wormholes surrounded by optically thin dust. First, we derive steady solutions of dust and a more general medium surrounding the wormhole by solving relativistic Euler equations. We find two types of dust solutions: one is a static solution with arbitrary density profile, and the other is a solution of dust which passes into the wormhole and escapes into the other side with constant velocity. Next, solving null geodesic equations and radiation transfer equations, we investigate the images of the wormhole surrounded by dust for the above steady solutions. Because the wormhole spacetime possesses unstable circular orbits of photons, a bright ring appears in the image, just as in Schwarzschild spacetime. This indicates that the appearance of a bright ring solely confirms neither a black hole nor a wormhole. However, we find that the intensity contrast between the inside and the outside of the ring are quite different. Therefore, we could tell the difference between an Ellis wormhole and a black hole with high-resolution very-long-baseline-interferometry observations in the near future. [ABSTRACT FROM AUTHOR]

In the present paper we prove a uniqueness theorem for the static and asymptotically flat solutions to the Einstein-scalar field equations which possess a photon sphere. We show that such solutions are uniquely specified by their mass M and scalar charge q and that they are isometric to the Janis-Newman-Winicour solution with the same mass and scalar charge subject to the inequality q²/M² < 3. [ABSTRACT FROM AUTHOR]

A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schrödinger picture wave function depends upon space and time coordinates for each particle, as well as an inexorably increasing evolution parameter s which labels a foliation of spacelike hypersurfaces. The model is constructed to be manifestly Lorentz invariant in the interaction picture. Free particle states and interactions are discussed in this framework. Then, the formalism of the continuous spontaneous localization (CSL) theory of dynamical collapse is applied. The collapse-generating operator is chosen to be the particle number space-time density. Unlike previous relativistically invariant models, the vacuum state is not excited. The collapse dynamics depends upon two parameters, a parameter Λ which represents the collapse rate/volume and a scale factor ℓ. A common example of collapse dynamics, involving a clump of matter in a superposition of two locations, is analyzed. The collapse rate is shown to be identical to that of nonrelativistic CSL when the GRW-CSL choice of ℓ = a = 10−5 cm, is made, along with Λ = λ/a³ (GRW-CSL choice λ = 10−16s−1). The collapse rate is also satisfactory with the choice ℓ as the size of the Universe, with Λ = λ/ℓa². Because the collapse narrows wave functions in space and time, it increases a particle's momentum and energy, altering its mass. It is shown that, with ℓ = a, the change of mass of a nucleon is unacceptably large but, when ℓ is the size of the Universe, the change of mass over the age of the Universe is acceptably small. [ABSTRACT FROM AUTHOR]

Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need to be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to ⟨ϕ²⟩ren, namely the renormalized ⟨ϕ²⟩. So far we have formulated two variants of this method: t-splitting (aimed for stationary backgrounds) and angular splitting (for spherically symmetric backgrounds). In this paper we introduce our basic approach, and then focus on the t-splitting variant, which is the simplest of the two (deferring the angular-splitting variant to a forthcoming paper). We then use this variant, as a first stage, to calculate ⟨ϕ²⟩ren in Schwarzschild spacetime, for a massless scalar field in the Boulware state. We compare our results to previous ones, obtained by a different method, and find full agreement. We discuss how this approach can be applied (using the angular-splitting variant) to analyze the dynamical self-consistent evaporation of black holes. [ABSTRACT FROM AUTHOR]

A static self-gravitating electrically charged spherical thin shell embedded in a (3+1)-dimensional spacetime is used to study the thermodynamic and entropic properties of the corresponding spacetime. Inside the shell, the spacetime is flat, whereas outside it is a Reissner-Nordström spacetime, and this is enough to establish the energy density, the pressure, and the electric charge in the shell. Imposing that the shell is at a given local temperature and that the first law of thermodynamics holds on the shell one can find the integrability conditions for the temperature and for the thermodynamic electric potential, the thermodynamic equilibrium states, and the thermodynamic stability conditions. Through the integrability conditions and the first law of thermodynamics an expression for the shell's entropy can be calculated. It is found that the shell's entropy is generically a function of the shell's gravitational and Cauchy radii alone. A plethora of sets of temperature and electric potential equations of state can be given. One set of equations of state is related to the Hawking temperature and a precisely given electric potential. Then, as one pushes the shell to its own gravitational radius and the temperature is set precisely equal to the Hawking temperature, so that there is a finite quantum backreaction that does not destroy the shell, one finds that the entropy of the shell equals the Bekenstein-Hawking entropy for a black hole. The other set of equations of state is such that the temperature is essentially a power law in the inverse Arnowitt-Deser-Misner (ADM) mass and the electric potential is a power law in the electric charge and in the inverse ADM mass. In this case, the equations of thermodynamic stability are analyzed, resulting in certain allowed regions for the parameters entering the problem. Other sets of equations of state can be proposed. Whatever the initial equation of state for the temperature, as the shell radius approaches its own gravitational radius, the quantum backreaction imposes the Hawking temperature for the shell in this limit. Thus, when the shell's radius is sent to the shell's own gravitational radius the formalism developed allows one to find the precise form of the Bekenstein-Hawking entropy of the correlated black hole. [ABSTRACT FROM AUTHOR]