Resolution of Curvature Singularities in Higher Derivative Gravity

Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity

In this work we explore general leading singularities of one-loop amplitudes in higher-derivative Yang-Mills and quadratic gravity. These theories are known to possess propagators which contain quadratic and quartic momentum dependence, which leads to the presence of an unstable ghostlike resonance. However, unitarity cuts are not to be taken through unstable particles and therefore unitarity is still satisfied. On the other hand, this could engender issues when calculating leading singularities which are generalizations of unitarity cuts. Nevertheless, we will show with explicit examples how …

Construct $α^{\prime}$ corrected or loop corrected solutions without curvature singularities

For the bosonic gravi-dilaton system, we provide systematical approaches to construct non-perturbative string cosmological solutions without curvature singularities, which can match the perturbative solution to any order in $α^{\prime}$ expansion. When higher order $α^{\prime}$ corrections are calculated, they can be straightforwardly plugged in to generate compatible non-perturbative evolutions without curvature singularities. We also give a (phenomenological) map between $α^{\prime}$ corrected EOM and loop corrected EOM. This map enables us to easily generate a loop corrected solution from a…

On Newtonian singularities in higher derivative gravity models

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higher-derivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancellation of contributions from scalar and tensor massive modes.

Singularities in Spherically Symmetric Solutions with Limited Curvature Invariants

We investigate static, spherically symmetric solutions in gravitational theories which have limited curvature invariants, aiming to remove the singularity in the Schwarzschild space-time. We find that if we only limit the Gauss-Bonnet term and the Ricci scalar, then the singularity at the origin persists. Moreover we find that the event horizon can develop a curvature singularity. We also investigate a new class of theories in which all components of the Riemann tensor are bounded. We find that the divergence of the quadratic curvature invariants at the event horizon is avoidable in this theor…

Static dilaton solutions and singularities in six dimensional warped compactification with higher derivatives

Static solutions with a bulk dilaton are derived in the context of six dimensional warped compactification. In the string frame, exponentially decreasing warp factors are identified with critical points of the low energy $β$-functions truncated at a given order in the string tension corrections. The stability of the critical points is discussed in the case of the first string tension correction. The singularity properties of the obtained solutions are analyzed and illustrative numerical examples are provided.

Complete classification of Friedmann-Lemaître-Robertson-Walker solutions with linear equation of state: parallelly propagated curvature singularities for general geodesics

We completely classify the Friedmann-Lemaître-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ for perfect fluids with linear equation of state $p=wρ$, where $ρ$ and $p$ are the energy density and pressure, without assuming any energy conditions. We extend our previous work to include all geodesics and parallelly propagated curvature singularities, showing that no non-null geodesic emanates from or terminates at the null portion of conformal infinity and that the initial singularity for $K=0,-1$ and $-5/3<w<-1$ is a null non-scalar polynomial curvature singularity. We thus obtain …

Curvature Singularities: the Good, the Bad, and the Naked

Necessary conditions are proposed for the admissibility of singular classical solutions with 3+1-dimensional Poincare invariance to five-dimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain bounded above for a solution to be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem.

The NSVZ $β$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

The contributions of the matter superfields and of the Faddeev--Popov ghosts to the $β$-function of ${\cal N}=1$ supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the $β$-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the $β$-function beyond the one-loop approximation is …

Jackiw-Teitelboim引力中的量子涨落和曲率奇性

Quantum Fluctuations and Curvature Singularities in Jackiw-Teitelboim Gravity

考虑了具有物质自由度的Jackiw-Teitelboim引力。经典模型是精确可解的，其解描述了物质波包的非平凡引力散射。对于大量的解，散射时空不存在曲率奇点。然而，对场方程的量子修正不可避免地导致（霹雳）曲率奇点的形成，只在极限$\hbar\to 0$中消失。该模型的灵感来自于四维纯爱因斯坦引力的降维，仅限于具有两个可交换类空Killing向量的时空。物质自由度也源于四维空间。连续积分的措施是明智地选择和一个循环的贡献（包括引力子和引力子）进行评估。对于数量的物质领域$N=24$，我们甚至获得确切的有效行动，应用DDK程序。有效作用量是非定域的，但半经典方程可以用Hankel变换的某些理论来求解。

Resolving Gravitational Singularities

We review recent progress on the resolution of gravitational singularities in string theory. The main example is the fundamental string in five dimensions which is singular in the standard supergravity description but regular after taking into account higher derivative corrections determined by anomalies and supersymmetry. The application of the AdS/CFT correspondence to geometries that require higher derivatives for regularity poses interesting challenges.