Orbital motion of test particles in regular Hayward black hole
**space**-time

**space**-time. Our results show that the

**time**-like orbits are divided into four types: unstable circular orbits, separates stable orbits, stable hyperbolic orbits and elliptical orbits in regular Hayward black hole

**space**-time. We find that the orbital properties vary with the change of $\ell$ (a convenient encoding of the central energy density $3/8\pi\ell^{2}$). If $\ell =\frac{1}{3}$ and $b < 3.45321$, the test particles which moving toward the black hole will definitely be plunging into the black hole. In addition, it is obtained that the innermost stable circular orbit happens at $r_{min}$ = 5.93055 for $b$ = 3.45321.

10/10 relevant

arXiv

Hadamard renormalization for a charged scalar field

**space**-time, and hence in addressing issues such as the quantum stability of the inner horizon. Expand abstract.

**space**-

**time**is a powerful tool for computations of renormalized expectation values. We study the Hadamard form of the Feynman Green's function for a massive charged complex scalar field in an arbitrary number of

**space**-

**time**dimensions. Explicit expressions for the coefficients in the Hadamard parametrix are given for two, three and four

**space**-

**time**dimensions. We then develop the formalism for the Hadamard renormalization of the expectation values of the scalar field condensate, current and stress-energy tensor. These results will have applications in the computation of renormalized expectation values for a charged quantum scalar field on a charged black hole

**space**-time, and hence in addressing issues such as the quantum stability of the inner horizon.

7/10 relevant

arXiv

The Scattering Map on Oppenheimer--Snyder **Space**time

**space**-time, and look at the implications of our boundedness results on this scattering map. Specifically, it is shown that the energy of $\phi$ remains uniformly bounded going forward in

**time**and going backwards in

**time**for both the reflective and the permeating cases, and it is then shown that the scattering map is bounded going forwards, but not backwards, and is therefore not surjective onto the

**space**of finite energy on $\mathcal{I}^+\cup\mathcal{H}^+$. Thus there does not exist a backwards scattering map from finite energy radiation fields on $\mathcal{I}^+\cup\mathcal{H}^+$ to finite energy radiation fields on $\mathcal{I}^-$. We will then contrast this with the situation for scattering in pure Schwarzschild.

4/10 relevant

arXiv

Joint H\"older continuity of local **time** for a class of interacting
branching measure valued diffusions

**time**for a class of superprocesses with dependent spatial motion, as well as sharp estimates from the theory of uniformly parabolic partial differential equations, the joint H\"older continuity in time and

**space**of said local

**times**is obtained in two and... Expand abstract.

**time**for a class of superprocesses with dependent spatial motion, as well as sharp estimates from the theory of uniformly parabolic partial differential equations, the joint H\"older continuity in

**time**and

**space**of said local

**times**is obtained in two and three dimensional Euclidean

**space**.

4/10 relevant

arXiv

Dark matter scattering cross section in Yang-Mills theory

**time**the scattering cross section between lightest glueballs in SU(2) pure Yang-Mills theory, which are good candidates of dark matter. In the first step, we evaluate the interglueball potential on lattice using the

**time**-dependent formalism of the HAL QCD method, with one lattice spacing. The statistical accuracy is improved by employing the cluster-decomposition error reduction technique and by using all

**space**-

**time**symmetries. We then derive the scattering phase shift and the scattering cross section at low energy, which is compared with the observational constraint on the dark matter self-scattering. We determine the lower bound on the scale parameter of the SU(2) Yang-Mills theory, as $\Lambda$ > 60 MeV.

4/10 relevant

arXiv

Nonexistence results for a higher-order evolution equation with an
inhomogeneous term depending on **time** and **space**

**time**and

**space**. Expand abstract.

**time**and

**space**. We first derive a general criterion for the nonexistence of weak solutions. Next, we study the particular case when the inhomogeneity depends only on

**space**. In that case, we obtain the first critical exponent in the sense of Fujita, as well as the second critical exponent in the sense of Lee and Ni.

6/10 relevant

arXiv

Parameter estimation for SPDEs based on discrete observations in **time**
and **space**

**time**and

**space**. Expand abstract.

**space**dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in both coordinates, we prove central limit theorems for realized quadratic variations based on temporal and spatial increments as well as on double increments in

**time**and

**space**. Resulting method of moments estimators for the diffusivity and the volatility parameter inherit the asymptotic normality and can be constructed robustly with respect to the sampling frequencies in

**time**and

**space**. Upper and lower bounds reveal that in general the optimal convergence rate for joint estimation of the parameters is slower than the usual parametric rate. The theoretical results are illustrated in a numerical example.

5/10 relevant

arXiv

Higher-spin kinematics & no ghosts on quantum **space**-**time** in Yang-Mills
matrix models

**space**-

**time**solution of the IIB matrix model is given, which leads to a higher-spin gauge theory. In particular, the no-ghost-theorem is established. The physical on-shell modes consist of 2 towers of higher-spin modes, which are effectively massless but include would-be massive degrees of freedom. The off-shell modes consist of 4 towers of higher-spin modes, one of which was missing previously. The noncommutativity leads to a cutoff in spin, which disappears in the semi-classical limit. An explicit basis allows to obtain the full propagator, which is governed by a universal effective metric. The physical metric fluctuations arise from would-be massive spin 2 modes, which were previously shown to include the linearized Schwarzschild solution. Due to the relation with ${\cal N}=4$ super-Yang-Mills, this is expected to define a consistent quantum theory in 3+1 dimensions, which includes gravity.

10/10 relevant

arXiv

Locally contorted **space**-**time** invokes inflation, dark energy, and a
non-singular Big Bang

**space**-time. In the Friedman model this leads to a scalar field built from contortion and the metric with the property of dark energy, which transforms the cosmological constant to a

**time**-dependent function. Moreover, the quadratic Rieman-Cartan term in the CCGG field equations adds a geometrical curvature correction to the Friedman equations. Applying the standard $\Lambda$CDM parameter set, those equations give a unique solution for the cosmological field. With a relatively small "deformation" parameter of the theory that determines the strength of the quadratic term and thus the deviation from the Einstein-Hilbert theory, the resulting evolution of the universe starts from a finite extension, undergoes a violent, Big Bang-like, or a smooth and slow bounce process followed by an inflation phase, and exits gracefully to the current dark energy era. The calculations of the SNeIa Hubble diagram and of the most recent transition point from deceleration to acceleration compare well with astronomical observations. The theory also provides a new handle to resolving the cosmological constant problem.

10/10 relevant

arXiv

Kinetic limit for a chain of harmonic oscillators with a point Langevin thermostat

**time**only a finite number of collisions takes place (Boltzmann-Grad limit). We prove that, after the hyperbolic

**space**-

**time**rescaling, the Wigner distribution, describing the energy density of phonons in

**space**-frequency domain, converges to a positive energy density function $W(t, y, k)$ that evolves according to a linear kinetic equation, with the interface condition at $y=0$ that corresponds to reflection, transmission and absorption of phonons. The paper extends the results of [3], where a thermostatted harmonic chain (with no inter-particle scattering) has been considered.

4/10 relevant

arXiv