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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]