Infinite Derivative Theory Of Gravity Research Articles

Charged black holes in the infinite derivative theory of gravity

The infinite derivative theory of gravity is a generalization of Einstein gravity with many interesting properties, but the black hole solutions in this theory are still not fully understood. In the paper, we concentrate on studying the charged black holes in such a theory. Adding the electromagnetic field part to the effective action, we show how the black hole solutions around the Reissner–Nordström metric can be solved perturbatively and iteratively. We further calculate the corresponding temperature, entropy and electrostatic potential of the black holes and verify the first law of thermodynamics.

An anisotropic bouncing universe in non-local gravity

We show that it is possible to realize a cosmological bouncing solution in an anisotropic but homogeneous Bianchi-I background in a class of non-local, infinite derivative theories of gravity. We show that the anisotropic shear grows slower than in general relativity during the contraction phase, peaks to a finite value at the bounce point, and then decreases as the universe asymptotes towards isotropy and homogeneity, and ultimately to de Sitter. Along with a cosmological constant, the matter sector required to drive such a bounce is found to consist of three components — radiation, stiff matter and k-matter (whose energy density decays like the inverse square of the average scale factor). Generically, k-matter exerts anisotropic pressures. We will test the bouncing solution in local and non-local gravity and show that in the latter case it is possible to simultaneously satisfy positivity of energy density and, at least in the late time de Sitter phase, avoid the introduction of propagating ghost/tachyonic modes.

Ghost-free higher-order theories of gravity with torsion

In this manuscript we will present the theoretical framework of the recently proposed infinite derivative theory of gravity with a non-symmetric connection. We will explicitly derive the field equations at the linear level and obtain new solutions with a non-trivial form of the torsion tensor in the presence of a fermionic source, and show that these solutions are both ghost and singularity-free.

Black hole solutions and thermodynamics in the infinite derivative theory of gravity

In this paper we derive black hole solutions and thermodynamics in the infinite derivative theory of gravity that is quadratic in curvature. The higher-derivative terms in the action bring about corrections to both the original Schwarzschild black hole metric and the corresponding black hole temperature and entropy, while the topology of the black hole remains the same.

Linearized metric solutions in ghost-free nonlocal gravity

In this manuscript we review some aspects of linearized metric solutions in ghost-free nonlocal gravity, in which the action is made up of non-polynomial differential operators containing covariant derivatives of infinite order. By working with the simplest model of such a wide class of infinite derivative theories of gravity, we will first compute the spacetime metric generated by a static point-like source and show that all curvature invariants are nonsingular at the origin. Secondly, a similar computation is performed for an electrically charged source and also in this case the regularizing feature of nonlocality plays a crucial role. As a third case, we consider the spacetime metric generated by a Dirac delta distribution on a ring and show that, at least in the linear regime, Kerr-like singularities can be avoided in ghost-free non-local gravity.

Transmutation of nonlocal scale in infinite derivative field theories

In this paper we will show an ultraviolet -infrared connection for ghost-free infinite derivative field theories where the Lagrangians are made up of exponentials of entire functions. In particular, for $N$-point amplitudes a new scale emerges in the infrared from the ultraviolet, i.e. $M_{\rm eff}\sim M_s/N^\alpha,$ where $M_s$ is the fundamental scale beyond the Standard Model, and $\alpha>0$ depends on the specific choice of an entire function and on whether we consider zero or nonzero external momenta. We will illustrate this by first considering a scalar toy model with a cubic interaction, and subsequently a scalar toy-model inspired by ghost-free infinite derivative theories of gravity. We will briefly discuss some phenomenological implications, such as making the nonlocal region macroscopic in the infrared.

Towards conformally flat, non-Kasner vacuum solution in infinite derivative gravity

In this paper, we will show that the equations of motion of the quadratic in curvature, ghost free, infinite derivative theory of gravity will not permit an anisotropic collapse of a homogeneous Universe such as Kasner-type vacuum solution. However, such a solution is shown to be admissible in the local quadratic curvature gravity. Therefore pointing towards the crucial role played by the non-local infinite derivatives. We will show that it is possible to obtain conformally flat and singularity-free spacetime metrics.

Nonsingular metric for an electrically charged point-source in ghost-free infinite derivative gravity

In this paper we will construct a linearized metric solution for an electrically charged system in a {\it ghost-free} infinite derivative theory of gravity which is valid in the entire region of spacetime. We will show that the gravitational potential for a point-charge with mass $m$ is non-singular, the Kretschmann scalar is finite, and the metric approaches conformal-flatness in the ultraviolet regime where the non-local gravitational interaction becomes important. We will show that the metric potentials are bounded below one as long as two conditions involving the mass and the electric charge are satisfied. Furthermore, we will argue that the cosmic censorship conjecture is not required in this case. Unlike in the case of Reissner-Nordstr\"om in general relativity, where $|Q|\leq m/M_p$ has to be always satisfied, in {\it ghost-free} infinite derivative gravity $|Q|>m/M_p$ is also allowed, such as for an electron.

Conformally-flat, non-singular static metric in infinite derivative gravity

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

Rotating metric in nonsingular infinite derivative theories of gravity

In this paper we will provide a non-singular rotating space time metric for a ghost free infinite derivative theory of gravity. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that from general relativity.

Light bending in infinite derivative theories of gravity

Light bending is one of the significant predictions of general relativity (GR) and it has been confirmed with great accuracy during the last one hundred years. In this paper, we semiclassically calculate the deflection angle for the photons that just grazing the Sun in the infinite derivative theories of gravity (IDG) which is a ghost and singularity free theory of gravity. From our calculations, we find that the deflection angle $\theta$ only depends on $\Lambda/E$. $\theta \rightarrow \theta_E$ when $\Lambda/E \rightarrow \infty$ and decrease to zero when $\Lambda/E \rightarrow 0$. The transition interval occurs at $10^{4}< E/\Lambda < 10^{7}$. It should be pointed out that this model can be tested by the Chandra X-ray Observatory if $0.01 eV < \Lambda < 0.1 eV$.

Defocusing of null rays in infinite derivative gravity

Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any ansatz to solve the full equations of motion.

Generalised boundary terms for higher derivative theories of gravity

In this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.

Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity

In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory—a toy model depiction of a covariant infinite-derivative, non-local extension of Einstein’s general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it asymptotically free, thus providing strong prospects of resolving various classical and quantum divergences. In particular, we will find that at one loop, the two-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet behavior of all other one-loop diagrams as well as the two-loop, two-point function remains well under control. We will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.

Wald Entropy for Ghost-Free, Infinite Derivative Theories of Gravity.

In this Letter, we demonstrate that the Wald entropy for any spherically symmetric black hole within an infinite derivative theory of gravity that is quadratic in curvature is determined solely by the area law. Thus, the infrared behavior of gravity is captured by the Einstein-Hilbert term, provided that the massless graviton remains the only propagating degree of freedom in the spacetime.

String-inspired infinite-derivative theories of gravity: A brief overview

In String Theory, there often appears a rather interesting class of higher derivative theories containing an infinite set of derivatives in the form of an exponential. These theories may provide a way to tame ultraviolet (UV) divergences without introducing ghost-like states. Here we provide a brief overview on the progress that has been made over the last decade to construct such infinite-derivative theories of gravity (IDG) which may be able to address the singularity problems in gravity. In the process, we will present some general results that applies to covariant torsion-free metric theories of gravity.

Generalized ghost-free quadratic curvature gravity

In this paper we study the most general covariant action of gravity up to terms that are quadratic in curvature. In particular this includes non-local, infinite derivative theories of gravity which are ghost-free and exhibit asymptotic freedom in the ultraviolet. We provide a detailed algorithm for deriving the equations of motion for such actions containing an arbitrary number of the covariant D’Alembertian operators, and this is our main result. We also perform a number of tests on the field equations we derive, including checking the Bianchi identities and the weak-field limit. Lastly, we consider the special subclass of ghost and asymptotically free theories of gravity by way of an example.