Showing papers on "Scalar curvature published in 2018"
Dissertation•
28 Sep 2018
TL;DR: In this paper, the authors studied several modified Teleparallel theories of gravity with emphasis on late-time cosmology, and classified them according to their ability to describe the current cosmological observations.
Abstract: Teleparallel gravity is an alternative formulation of gravity which has the same field equations as General Relativity (GR), therefore, it is also known as the Teleparallel equivalent of General Relativity (TEGR). This theory is a gauge theory of the translations with the torsion tensor being non-zero but with a vanishing curvature tensor, hence, the manifold is globally flat. An interesting approach for understanding the late-time accelerating behaviour of the Universe is called modified gravity where GR is extended or modified. In the same spirit, since TEGR is equivalent to GR, one can consider its modifications and study if they can describe the current cosmological observations. This thesis is devoted to studying several modified Teleparallel theories of gravity with emphasis on late-time cosmology. Those Teleparallel theories are in general different to the modified theories based on GR, but one can relate and classify them accordingly. Various Teleparallel theories are presented and studied such as Teleparallel scalar-tensor theories, quintom models, Teleparallel non-local gravity, and f(T,B) gravity and its extensions (coupled with matter, extensions of new GR and Gauss-Bonnet) where T is the scalar torsion and B is the boundary term which is related with the Ricci scalar via R=-T+B.
148 citations
TL;DR: In this article, the Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations for quantum gravity with curvature invariants beyond Ricci scalars.
Abstract: We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from fðRÞ-type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.
133 citations
TL;DR: In this article, a two-field inflationary model consisting of the Ricci scalar squared (R2) term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein R term is analyzed.
Abstract: We analyze a two-field inflationary model consisting of the Ricci scalar squared (R2) term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein R term. Detailed analysis of the power spectrum of this model with mass hierarchy is presented, and we find that one can describe this model as an effective single-field model in the slow-roll regime with a modified sound speed. The scalar spectral index predicted by this model coincides with those given by the R2 inflation and the Higgs inflation implying that there is a close relation between this model and the R2 inflation already in the original (Jordan) frame. For a typical value of the self-coupling of the standard Higgs field at the high energy scale of inflation, the role of the Higgs field in parameter space involved is to modify the scalaron mass, so that the original mass parameter in the R2 inflation can deviate from its standard value when non-minimal coupling between the Ricci scalar and the Higgs field is large enough.
110 citations
TL;DR: In this article, the authors established several inequalities for manifolds with positive scalar curvature and, more generally, for the scalars curvature bounded from below, based on the Schoen-Yau descent method via minimal hypersurfaces.
Abstract: We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on the distances between conjugates points in surfaces with positive sectional curvatures. The techniques of our proofs is based on the Schoen–Yau descent method via minimal hypersurfaces, while the overall logic of our arguments is inspired by and closely related to the torus splitting argument in Novikov’s proof of the topological invariance of the rational Pontryagin classes.
105 citations
TL;DR: In this article, all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit were shown to be regularized at short distances such that they are singularity-free.
Abstract: In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a Ricci flat vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with the Weyl tensor. Secondly, these curvatures are regularized at short distances such that they are singularity-free, in particular the same happens for the Kretschmann invariant. Unlike the others, the Weyl tensor vanishes at short distances, implying that the spacetime metric approaches conformal-flatness in the region of non-locality, in the ultraviolet. We briefly discuss the solution in the non-linear regime, and argue that 1/r metric potential cannot be the solution in the short-distance regime, where non-locality becomes important.
90 citations
TL;DR: In this paper, a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables.
Abstract: We consider the Palatini formulation of f(R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f(R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type $$f=R-\alpha ^2/R+g(T)$$
and $$f=R+\alpha ^2R^2+g(T)$$
are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.
85 citations
TL;DR: In this article, the number densities of black hole micromolecules and the thermodynamic scalar curvature for the small and large black holes on the coexistence curve based on the so-called Ruppeiner thermodynamic geometry were derived.
Abstract: Considering the unexpected similarity between the thermodynamic features of charged AdS black holes and that of the van der Waals fluid system, we calculate the number densities of black hole micromolecules and derive the thermodynamic scalar curvature for the small and large black holes on the coexistence curve based on the so-called Ruppeiner thermodynamic geometry. We reveal that the microscopic feature of the small black hole perfectly matches that of the ideal anyon gas and that the microscopic feature of the large black hole matches that of the ideal Bose gas. More importantly, we investigate the issue of molecular potential among micromolecules of charged AdS black holes and point out explicitly that the well-known experiential Lennard-Jones potential is a feasible candidate to describe interactions among black hole micromolecules completely from a thermodynamic point of view. The behavior of the interaction force induced by the Lennard-Jones potential coincides with that of the thermodynamic scalar curvature. Both the Lennard-Jones potential and the thermodynamic scalar curvature offer a clear and reliable picture of microscopic structures for the small and large black holes on the coexistence curve for charged AdS black holes.
78 citations
TL;DR: In this article, a generalized hybrid metric-Palatini matter theory, given by a gravitational Lagrangian $f(R,\mathcal{R}), where $R$ is the metric Ricci scalar, and $R} is a Palatini scalar curvature defined in terms of an independent connection, and a matter Lagrangians, is found.
Abstract: Wormhole solutions in a generalized hybrid metric-Palatini matter theory, given by a gravitational Lagrangian $f(R,\mathcal{R})$, where $R$ is the metric Ricci scalar, and $\mathcal{R}$ is a Palatini scalar curvature defined in terms of an independent connection, and a matter Lagrangian, are found. The solutions are worked in the scalar-tensor representation of the theory, where the Palatini field is traded for two scalars, $\ensuremath{\varphi}$ and $\ensuremath{\psi}$, and the gravitational term $R$ is maintained. The main interest in the solutions found is that the matter field obeys the null energy condition (NEC) everywhere, including the throat and up to infinity, so that there is no need for exotic matter. The wormhole geometry with its flaring out at the throat is supported by the higher-order curvature terms, or equivalently, by the two fundamental scalar fields, which either way can be interpreted as a gravitational fluid. Thus, in this theory, in building a wormhole, it is possible to exchange the exoticity of matter by the exoticity of the gravitational sector. The specific wormhole displayed, built to obey the matter NEC from the throat to infinity, has three regions, namely, an interior region containing the throat, a thin shell of matter, and a vacuum Schwarzschild anti-de Sitter (AdS) exterior. For hybrid metric-Palatini matter theories this wormhole solution is the first where the NEC for the matter is verified for the entire spacetime keeping the solution under asymptotic control. The existence of this type of solutions is in line with the idea that traversable wormholes bore by additional fundamental gravitational fields, here disguised as scalar fields, can be found without exotic matter. Concomitantly, the somewhat concocted architecture needed to assemble a complete wormhole solution for the whole spacetime may imply that in this class of theories such solutions are scarce.
74 citations
TL;DR: In this article, the functional renormalization group equation is used to study the non-Gaussian group fixed points (NGFPs) arising within the framework of f (R ) -gravity minimally coupled to an arbitrary number of scalar, Dirac, and vector fields.
73 citations
Posted Content•
TL;DR: In this article, the authors study metrics with positive scalar curvatures in domains with corners and suggest possible extensions of the concept of positive scalars curvature to singular spaces, where corners are assumed to have corners.
Abstract: We study metrics with positive scalar curvatures in domains with corners and suggest possible extensions of the concept of positive scalar curvature to singular spaces.
67 citations
TL;DR: In this article, the authors introduced the notion of K-semistability for Sasakian manifolds and extended it to the irregular case of the orbifold k-seministability of Ross-Thomas.
Abstract: We introduce a notion of K-semistability for Sasakian manifolds. This extends to the irregular case of the orbifold K-semistability of Ross–Thomas. Our main result is that a Sasakian manifold with constant scalar curvature is necessarily K-semistable. As an application, we show how one can recover the volume minimization results of Martelli–Sparks–Yau, and the Lichnerowicz obstruction of Gauntlett–Martelli–Sparks–Yau from this point of view.
Posted Content•
TL;DR: For scalar curvature type equations with more singular right hand side, the authors proved Donaldson's conjecture on the equivalence between geodesic stability and existence of cscK.
Abstract: In this paper, we derive estimates for scalar curvature type equations with more singular right hand side. As an application, we prove Donaldson's conjecture on the equivalence between geodesic stability and existence of cscK when $Aut_0(M,J)
eq0$. Moreover, we also show that when $Aut_0(M,J)
eq0$, the properness of $K$-energy with respect to a suitably defined distance implies the existence of cscK.
TL;DR: In this article, a cosmological model with a specific form of the Hubble parameter is constructed in a flat homogeneous, and isotropic background in the framework of $f(R,T)$ gravity, where R$ is the scalar curvature and T$ is a trace of the stress energymomentum tensor.
Abstract: A cosmological model with a specific form of the Hubble parameter is constructed in a flat homogeneous, and isotropic background in the framework of $f(R,T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of the stress-energy-momentum tensor. The proposed functional form of the Hubble parameter is taken in such a way that it fulfills the successful bouncing criteria to find the solution of the gravitational field equations provided the Universe is free from initial singularity. The various constraints on the parameters are involved in the functional form of the Hubble parameter which are analyzed in detail. In addition, we explore physical and geometrical consequences of the model based on the imposed constraints. Furthermore, we demonstrate the bouncing scenario which is realized in our model with some particular values of the model parameters. As a result, we find that all of the necessary conditions are satisfied for a successful bouncing model.
TL;DR: This review article reports on the utilization of IG methods to define measures of complexity in both classical and quantum physical settings, and investigates complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information.
Abstract: Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.
TL;DR: In this paper, the Ricci tensor scalar and Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant were derived.
Abstract: It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R2, or shortly R2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index (ns), a tensor-to-scalar ratio (r) and a tensor tilt (nt). It appears that ns remains the same as in the local R2 inflation in the leading slow-roll approximation, while r and nt get modified due to modification of the tensor power spectrum. This class of models allows for any value of r < 0.07 with a modified consistency relation which can be fixed by future observations of primordial B-modes of the CMB polarization. This makes the UV complete R2 gravity a natural target for future CMB probes.
TL;DR: In this article, it was shown that Ricci flows with bounded scalar curvature and entropy converge smoothly away from a singular set of codimension in the Riemannian case.
Abstract: In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature converge smoothly away from a singular set of codimension $\geq 4$. We also establish a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case.
These results are based on a compactness theorem for Ricci flows with bounded scalar curvature, which states that any sequence of such Ricci flows converges, after passing to a subsequence, to a metric space that is smooth away from a set of codimension $\geq 4$. In the course of the proof, we will also establish $L^{p < 2}$-curvature bounds on time-slices of such flows.
TL;DR: In this article, a nonminimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables.
Abstract: We consider the Palatini formulation of $f(R,T)$ gravity theory, in which a nonminimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the $f(R,T)$ gravity in the Palatini formulation. Cosmological models with Lagrangians of the type $f=R-\alpha ^2/R+g(T)$ and $f=R+\alpha ^2R^2+g(T)$ are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.
TL;DR: In this article, a two-field inflationary model consisting of the Ricci scalar squared ($R^2$) term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein $R$ term is analyzed.
Abstract: We analyze a two-field inflationary model consisting of the Ricci scalar squared ($R^2$) term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein $R$ term. Detailed analysis of the power spectrum of this model with mass hierarchy is presented, and we find that one can describe this model as an effective single-field model in the slow-roll regime with a modified sound speed. The scalar spectral index predicted by this model coincides with those given by the $R^2$ inflation and the Higgs inflation implying that there is a close relation between this model and the $R^2$ inflation already in the original (Jordan) frame. For a typical value of the self-coupling of the standard Higgs field at the high energy scale of inflation, the role of the Higgs field in parameter space involved is to modify the scalaron mass, so that the original mass parameter in the $R^2$ inflation can deviate from its standard value when non-minimal coupling between the Ricci scalar and the Higgs field is large enough.
Posted Content•
TL;DR: In this article, the authors generalize their apriori estimates on cscK to more general scalar curvature type equations (e.g., twisted csck metric equation).
Abstract: In this paper, we generalize our apriori estimates on cscK(constant scalar curvature Kahler) metric equation to more general scalar curvature type equations (e.g., twisted cscK metric equation). As applications, under the assumption that the automorphism group is discrete, we prove the celebrated Donaldson's conjecture that the non-existence of cscK metric is equivalent to the existence of a destabilized geodesic ray where the $K$-energy is non-increasing. Moreover, we prove that the properness of $K$-energy in terms of $L^1$ geodesic distance $d_1$ in the space of Kahler potentials implies the existence of cscK metric. Finally, we prove that weak minimizers of the $K$-energy in $(\mathcal{E}^1, d_1)$ are smooth.
TL;DR: In this article, the authors generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory, and limit their scope to the five-dimensional braneworld scenario.
Abstract: The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory. Then, we limit our scope to the five-dimensional braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields nonminimally coupled to gravity.
TL;DR: In this paper, the spherically symmetric wormhole models in f(R, T) gravity were investigated, where T and R are trace of stress energy tensor and the Ricci scalar, respectively.
Abstract: This paper is devoted to investigate the spherically symmetric wormhole models in f(R, T) gravity, where T and R are trace of stress energy tensor and the Ricci scalar, respectively. In this context, we discuss three distinct cases of fluid distributions viz, anisotropic, barotropic and isotropic matter contents. After considering the exponential f(R, T) model, the behavior of energy conditions are analyzed that will help us to explore the general conditions for wormhole geometries in this gravity. It is inferred that the usual matter in the throat could obey the energy conditions but the gravitational field emerging from higher order terms of modified gravity favor the existence of the non-standard geometries of wormholes. The stability as well as the existence of wormholes are also analyzed in this theory.
TL;DR: In this article, the potential vector field of an η-Einstein soliton is derived from the soliton equation and a nonlinear second-order PDE is derived.
Abstract: If the potential vector field of an η-Einstein soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. Under certain conditions, the existence of an η-Einstein soliton forces the manifold to be of constant scalar curvature.
TL;DR: In this article, the authors investigated the past evolution of an anisotropic Bianchi I universe in the setting of f(R) gravity and showed that there exists a new two-parameter set of solutions that includes both an isotropic "false radiation" solution and a stable generalized Kasner solution.
Abstract: In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $$R+R^2$$
gravity. Using the dynamical system approach we show that there exists a new two-parameter set of solutions that includes both an isotropic “false radiation” solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behavior of the shear from a specific property of f(R) gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally, we numerically check our results.
TL;DR: In this article, a class of exact rotating black hole solutions of gravity nonminimally coupled to a self-interacting scalar field in arbitrary dimensions is presented, and the thermodynamic analysis is carried out in the grand canonical ensemble.
Abstract: A class of exact rotating black hole solutions of gravity nonminimally coupled to a self-interacting scalar field in arbitrary dimensions is presented. These spacetimes are asymptotically locally anti-de Sitter manifolds and have a Ricci-flat event horizon hiding a curvature singularity at the origin. The scalar field is real and regular everywhere, and its effective mass, coming from the nonminimal coupling with the scalar curvature, saturates the Breitenlohner-Freedman bound for the corresponding spacetime dimension. The rotating black hole is obtained by applying an improper coordinate transformation to the static one. Although both spacetimes are locally equivalent, they are globally different, as it is confirmed by the nonvanishing angular momentum of the rotating black hole. It is found that the mass is bounded from below by the angular momentum, in agreement with the existence of an event horizon. The thermodynamical analysis is carried out in the grand canonical ensemble. The first law is satisfied, and a Smarr formula is exhibited. The thermodynamical local stability of the rotating hairy black holes is established from their Gibbs free energy. However, the global stability analysis establishes that the vacuum spacetime is always preferred over the hairy black hole. Thus, the hairy black hole is likely to decay into the vacuum one for any temperature.
TL;DR: In this article, it was shown that if an asymptotically Euclidean manifold with nonnegative scalar curvature has long-time existence of Ricci flow, the ADM mass is nonnegative.
Abstract: In this paper, we prove that if an asymptotically Euclidean manifold with nonnegative scalar curvature has long-time existence of Ricci flow, the ADM mass is nonnegative. We also give an independent proof of the positive mass theorem in dimension three.
TL;DR: In this article, all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit were shown to be singularity-free in the ultraviolet regime.
Abstract: In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with the Weyl tensor. Secondly, these curvatures are regularized at short distances such that they are singularity-free, in particular the same happens for the Kretschmann invariant. Unlike the others, the Weyl tensor vanishes at short distances, implying that the spacetime metric becomes conformally flat in the region of non-locality, in the ultraviolet. As a consequence, the non-local region can be approximated by a conformally flat manifold with non-negative constant curvatures. We briefly discuss the solution in the non-linear regime, and argue that $1/r$ metric potential cannot be the solution where non-locality is important in the ultraviolet regime.
TL;DR: Geometric horizons as mentioned in this paper are a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character, and they are used for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial invariants that vanish on this surface.
Abstract: We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.
TL;DR: In this article, the projective invariance of the Einstein-Hilbert action has been studied for scalar-tensor theories in the metric-affine formalism.
Abstract: We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class $^{2}\mathrm{N}\text{\ensuremath{-}}\mathrm{I}/\mathrm{Ia}$ of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, nonminimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.
TL;DR: In this article, the axial current at finite rotation and temperature in curved space is calculated and the chiral vortical effect is shown to satisfy a relation of the chari gap effect, that is, a fermion mass shift by a scalar curvature.
Abstract: We perform an explicit calculation of the axial current at finite rotation and temperature in curved space. We find that finite curvature and mass corrections to the chiral vortical effect satisfy a relation of the chiral gap effect, that is, a fermion mass shift by a scalar curvature. We also point out that a product term of the angular velocity and the scalar curvature shares the same coefficient as the mixed gravitational chiral anomaly. We discuss possible applications of the curvature-induced chiral vortical effect to rotating astrophysical compact objects described by the Kerr metric. Instead of direct calculation, we assume that the Chern-Simons current can approximate the physical axial current. We make a proposal that the chiral vortical current from rotating compact objects could provide a novel microscopic mechanism behind the generation of collimated jets.
TL;DR: A new explicit class of black holes in general quadratic gravity with a cosmological constant is presented, and it is demonstrated that for a certain range of positive cosmology constant there are both black-hole and cosMological horizons, with a static region between them.
Abstract: We present a new explicit class of black holes in general quadratic gravity with a cosmological constant. These spherically symmetric Schwarzschild-Bach-(anti-)de Sitter geometries, derived under the assumption of constant scalar curvature, form a three-parameter family determined by the black-hole horizon position, the value of the Bach invariant on the horizon, and the cosmological constant. Using a conformal to Kundt metric ansatz, the fourth-order field equations simplify to a compact autonomous system. Its solutions are found as power series, enabling us to directly set the Bach parameter and/or cosmological constant equal to zero. To interpret these spacetimes, we analyze the metric functions. In particular, we demonstrate that for a certain range of positive cosmological constant there are both black-hole and cosmological horizons, with a static region between them. The tidal effects on free test particles and basic thermodynamic quantities are also determined.